McGraw Hill Math

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 20.2 Triangles: Congruent and Similar to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 20.2 Triangles: Congruent and Similar

Exercises

IDENTIFY

Identify each set of triangles as similar, congruent, or neither. Explain your answer.

Question 1.

Answer:
Congruent Triangles,

Explanation:
Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.  Given triangles have equal sides and equal angles
therefore they are congruent.

Question 2.

Answer:
Neither,

Explanation:
Given triangles have one common angle and lengths but they have different angles so they are neither congruent nor all similar angles.

Question 3.

Answer:
Congruent Triangles,

Explanation:
Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.  Given triangles have equal sides and equal angles
therefore they are congruent.

Question 4.

Answer:
Similar Triangles,

Explanation:
Similar triangles are triangles with same shape but with different sizes and also with same
angles. So given triangles are similar.

Question 5.

Answer:
Similar Triangles,

Explanation:
Similar triangles are triangles with same shape but with different sizes and also with same
angles. So given triangles are similar.

Question 6.

Answer:
Congruent Triangles,

Explanation:
Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.  Given triangles have equal sides and equal angles
therefore they are congruent.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 20.1 Triangles: Acute, Right, Obtuse, Equilateral, Isosceles, and Scalene to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 20.1 Triangles: Acute, Right, Obtuse, Equilateral, Isosceles, and Scalene

Exercises

IDENTIFY

Identity as acute, right, or obtuse.

Question 1.

Answer:
Acute Triangle,

Explanation:
An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles or an acute angle is an angle that is less than 90°.
Given triangle has all interior angles, so it is acute triangle.

Question 2.

Answer:
Obtuse Triangle,

Explanation:
An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° degrees. Given triangle one of interior angle measures
more than 90° degrees, so it is obtuse triangle.

Question 3.

Answer:
Right Triangle,

Explanation:
A right angled triangle is a triangle with one of the angles as 90 degrees.
As given triangle has one angle 90 degress so it is right triangle.

Question 4.

Answer:
Acute Triangle,

Explanation:
An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles or an acute angle is an angle that is less than 90°.
Given triangle has interior angles less than 90 degress so it is acute triangle.

Question 5.

Answer:
Right Triangle,

Explanation:
A right angled triangle is a triangle with one of the angles as 90 degrees.
As given triangle has one angle 90 degress, so it is right triangle.

Question 6.

Answer:
Acute Triangle,

Explanation:
An acute angle triangle (or acute-angled triangle) is a triangle in which all the interior angles are acute angles or an acute angle is an angle that is less than 90°.
Given triangle has all interior angles are acute.

Identify as isosceles, scalene, or equilateral.

Question 7.

Answer:
Equilateral Triangle,

Explanation:
All the given sides are 4 and equal so given triangle is equilateral triangle.

Question 8.

Answer:
Isosceles Triangle,

Explanation:
As given triangle has 2 sides with 8 and one side with 4 lengths so it is an isosceles triangle. As an isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.

Question 9.

Answer:
Scalene Triangle,

Explanation:
Given triangle is a scalene triangle as it has different side lengths so it is
scalene triangle, A scalene triangle is a triangle in which all three sides are in different lengths, and all three angles are of different measures. However, the sum of all the interior angles is always equal to 180 degrees.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 2.2 Problem Solving to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 2.2 Problem Solving

Exercises Solve

Question 1.
Don volunteers 18 hours a week at the local hospital. If he volunteered 45 weeks last year, how many hours did he spend volunteering?
Answer:
810 hours,

Explanation:
As Don volunteers 18 hours a week at the local hospital. If he volunteered 45 weeks last year, Number of many hours did he spend volunteering are 18 hours X 45 = 810 hours.

Question 2.
Milos can ride his bicycle an average of 81 miles a day. If he wants to visit his cousin 324 miles away, how many days will it take for him to ride there?
Answer:
4 days,

Explanation:
As Milos can ride his bicycle an average of 81 miles a day. If he wants to visit his cousin 324 miles away, Number of days will it take for him to ride there are 324 divided by 81 is
81)324(4
    324
0     , Therefore 4 days.

Question 3.
Lorraine’s cell phone plan allows for 1,200 minutes of free usage every month. During the month of March (March has 31 days), how many minutes a day can Lorraine talk without exceeding her monthly limit?
Answer:
38 minutes 22 seconds,

Explanation:
Given Lorraine’s cell phone plan allows for 1,200 minutes of free usage every month. During the month of March (March has 31 days), Number of minutes a day can Lorraine talk without exceeding her monthly limit 1,200 minutes divided by 31 is
31)1,200(38
     114
     060
      38
22
therefore 38 minutes 22 seconds.

Question 4.
Basil launched his website this year. During the first three months of operation, his site recorded 835,884 hits. If he maintains that same monthly average, how many hits should he expect by the end of the fifteenth month?
Answer:
4,179,420 hits,

Explanation:
As Basil launched his website this year. During the first three months of operation, his site recorded 835,884 hits. If he maintains that same monthly average, Number of hits should he expect by the end of the fifteenth month is 15 divided by 3 is 5 So hits are
1,2,4,4,2
835,884
       X 5
4,179,420.

Question 5.
Camille is counting the number of bricks she needs to build a retaining wall for her herb garden. She calculates that she will need 485 bricks to complete the project. If the bricks come in stacks of 24, how many stacks will she need to complete the project?
Answer:
20 stacks and 5 bricks,

Explanation:
As Camille is counting the number of bricks she needs to build a retaining wall for her herb garden. She calculates that she will need 485 bricks to complete the project. If the bricks come in stacks of 24, Number of many stacks will she need to complete the project is
24)485(20
      480
          5
So 20 stacks and 5 bricks.

Question 6.
Iris volunteered to register voters for an upcoming election. She was able to sign up 374 new voters in just 1 voting precinct. If there are 11 precincts in the town, and Iris expects to have the same amount of success in each precinct, how many new voters will she sign up before the election?
Answer:
38 voters,

Explanation:
Given Iris volunteered to register voters for an upcoming election.
She was able to sign up 374 new voters in just 1 voting precinct.
If there are 11 precincts in the town, and Iris expects to have the same amount of
success in each precinct, Number of many new voters will she sign up before the election
11)374(38
     374
0
38 voters.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 2.1 Multiplying and Dividing Whole Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 2.1 Multiplying and Dividing Whole Numbers

Exercises Multiply

Question 1.

Answer:
2,820,

Explanation:
1
235
X 12
0470
2350
2,820

Question 2.

Answer:
3,652,

Explanation:
332
X 11
0332
3320
3,652

Question 3.

Answer:
3,363,

Explanation:
6,6
177
X 19
1,593
1,770
3,363

Question 4.

Answer:
5,720,

Explanation:
1
44
X 130
0000
1320
4400
5,720

Question 5.

Answer:
84,210,

Explanation:
401
X 210
00000
04010
80200
84,210

Question 6.

Answer:
31,049

Explanation:
5
509
X 61
00509
30540
31,049

Question 7.

Answer:
11,343,

Explanation:
597
X 19
05373
05970
11,343

Question 8.

Answer:
17,922,

Explanation:
618
X 29
05,562
12,360
17,922

Question 9.
Ariel earns money by mowing lawns in his neighborhood. If he can mow 3 lawns in an hour, how many lawns can he mow working 30 hours a week?
Answer:
90 lawns in a week,

Explanation:
Given Ariel earns money by mowing lawns in his neighborhood.
If he can mow 3 lawns in an hour, Number how many lawns can he mow working 30 hours a week is 30 X 3 lawns = 90 lawns in a week.

Question 10.
Winona is tracking the amount of water that the people of her town use during the summer months. She calculates that 47,005 gallons of water are used every day. If Wmona tracks the water usage for 112 days, how much water will be used during that time?
Answer:
52,64,560 gallons of water,

Explanation:
As Winona is tracking the amount of water that the people of her town use during the summer months. She calculates that 47,005 gallons of water are used every day. If Wmona tracks the water usage for 112 days, how much water will be used during that time is 47,005 X 112 = 52,64,560 gallons of water.

Exercises Divide

Question 1.

Answer:
156 R7,

Explanation:
Given to divide 1255 by 8 we get
8)1255(156
   08
    45
    40
      55
      48
        7
so it is 156R7.

Question 2.

Answer:
1,274R1,

Explanation:
Given to divide 15,289 by 12 we get
12) 15,289(1,274
      12
        32
        24
        088
          84
             49
             48
                1
So it is 1,274R1.

Question 3.

Answer:
83R43,

Explanation:
Given to divide 4,027 by 48 we get
48) 4027(83
      384
       187
        144
          43
So it is 83R43.

Question 4.

Answer:
144R5,

Explanation:
Given to divide 1,301 by 9 we get
9)1,301(144
      09
       40
       36
          41
          36  
So it is 144R5.

Question 5.

Answer:
47R10,

Explanation:
Given to divide 715 by 15 we get
15)715(47
      60
       115
        105
          10
So it is 47R10.

Question 6.

Answer:
33R7,

Explanation:
Given to divide 403 by 12 we get
12) 403(33
      36
       43
       36
         7
So it is 33R7.

Question 7.

Answer:
107,

Explanation:
Given to divide 321 by 3 we get
3)321(107
    30
     21
     21
      0
So it is 107.

Question 8.

Answer:
85,

Explanation:
Given to divide 425 by 5 we get
5)425(85
    40
     25
     25
      0
So it is 85.

Question 9.
Aubrey wants to divide his penny collection equally among his 14 cousins. ¡f he has 1,722 pennies in his collection, how many pennies will each one of his cousinš receive?
Answer:
Each one of his cousinš receive 123 pennies,

Explanation:
As Aubrey wants to divide his penny collection equally among his 14 cousins.
If he has 1,722 pennies in his collection, Number of pennies will each one of
his cousinš receive are 14 divides 1,722 are
14)1,722(123
      14
         32
         28
         42
42
0
123 pennies.

Question 10.
Emily wants to bring candy to share with her class at school. If she has 210 pieces of candy, and there are 30 students in her class, how many pieces of candy will each student receive?
Answer:
7 pieces of candy will each student receive,

Explanation:
As Emily wants to bring candy to share with her class at school. If she has 210 pieces of candy, and there are 30 students in her class, Number of pieces of candy will each student receive are 210 divides by 30 we get
30)210(7
     210
0
7 pieces of candy.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 19.3 Finding Missing Angle Measurements to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 19.3 Finding Missing Angle Measurements

Exercises

SOLVE

Question 1.
Fill in the angle measurements for the other seven angles.

∠a = _________
∠b = _________
∠c = _________
∠d = _________
∠e = _________
∠f = _________
∠g = _________
Answer:
∠a = 108⁰, 
∠b = 72⁰,
∠c = 108⁰,
∠d = 72⁰,
∠e = 108⁰, 
∠f =  72⁰, 
∠g = 108⁰,
∠h = 72⁰, 

Explanation:
Given ∠h = 72⁰, As ∠e = 180⁰ – 72⁰ = 108⁰, 
∠h = 72⁰ = ∠f = 72⁰, ∠g = 180⁰ – 72⁰ = 108⁰, ∠e = ∠a = 108⁰,
 ∠b = 180⁰ – 108⁰ = 72⁰,  ∠c = ∠g = 108⁰, ∠d = 180⁰ – 108⁰ = 72⁰.
Therefore ∠a = 108⁰,  ∠b = 72⁰, ∠c = 108⁰, ∠d = 72⁰,
∠e = 108⁰,  ∠f =  72⁰,  ∠g = 108⁰, ∠h = 72⁰..

Question 2:
Angle 3 is 48 degrees. List the measurements of the other seven angles.

∠1 = _________
∠2 = _________
∠3 = _________
∠4 = _________
∠5 = _________
∠6 = _________
∠7 = _________
Answer:
∠1 = 48⁰, 
∠2 = 132⁰,
∠3 = 48⁰,
∠4 = 132⁰,
∠5 = 48⁰, 
∠6 =  132⁰, 
∠7 = 48⁰,
∠8 = 132⁰, 

Explanation:
Given ∠3 = 48⁰, As ∠4 = 180⁰ – 48⁰ = 132⁰, 
∠1 = ∠3 = 48⁰, ∠2 = 180⁰ – 48⁰ = 132⁰,
∠5 = ∠1 = 48⁰,  ∠6 = 180⁰ – 48⁰ = 132⁰,
 ∠7 = ∠3 = 48⁰, ∠8 = 180⁰ – 108⁰ = 132⁰.
Therefore ∠1 = 48⁰,  ∠2 = 132⁰, ∠3 = 48⁰, ∠4 = 132⁰,
∠5 = 48⁰,  ∠6 =  132⁰,  ∠7 = 48⁰, ∠8 = 132⁰, 

Question 3.

Fill in the angle measurements for the other seven angles.
∠a = _________
∠b = _________
∠c = _________
∠d = _________
∠e = _________
∠g = _________
∠h = _________
Answer:
∠a = 125⁰, 
∠b = 55⁰,
∠c = 125⁰,
∠d = 55⁰,
∠e = 125⁰, 
∠g = 125⁰,
∠h = 55⁰, 

Explanation:
Given ∠f = 55⁰, So ∠g = 180⁰ – 55⁰ = 125⁰, 
∠g = ∠e = 125⁰, ∠h = 180⁰ – 125⁰ = 55⁰,
∠e = ∠a = 125⁰,  ∠b = 180⁰ – 125⁰ = 55⁰,  ∠c = ∠g = 125⁰,
∠d = 180⁰ – 125⁰ = 55⁰.
Therefore ∠a = 125⁰,  ∠b = 55⁰, ∠c = 125⁰, ∠d = 55⁰,
∠e = 125⁰,  ∠g = 125⁰, ∠h = 55⁰,

Question 4.

What is the measurement of ∠FOE? ______________
What is the measurement of ∠EOC? ______________
What is the measurement of ∠BOC? ______________
Answer:
The measurement of ∠FOE is 46⁰,
The measurement of ∠EOC is 90⁰,
The measurement of ∠BOC is 45⁰,

Explanation:
Given figure the measurement of ∠FOE is 46⁰ as
∠EOG = 90⁰ and given ∠FOG = 44⁰ , so therefore
∠FOE = ∠EOG – ∠FOG = 90⁰ – 44⁰ = 46⁰.
The measurement of ∠EOC is 90⁰ as ∠EOC = ∠EOG = 90⁰.
Now the measurement of ∠BOC is 45⁰ as ∠COA = 90⁰ = ∠AOB  + ∠BOC,
So ∠BOC = 90⁰ – ∠AOB  = 90⁰ – 45⁰ = 45⁰.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 19.2 Types of Angles: Supplementary, Complementary, Interior, and Exterior to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 19.2 Types of Angles: Supplementary, Complementary, Interior, and Exterior

Exercises

IDENTIFY

Question 1.
From the figure below, give examples of two complementary, two supplementary and two vertical angles.
Complementary ________________
Supplementary ________________
Vertical ________________

Answer:
Complementary angles are CD, FG,
Supplementary angles are AD, CF,
Vertical angles are BE, AD,

Explanation:
Complementary: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees. Vertical angles are angles opposite each other where two lines cross.
Vertical angles are angles that are opposite each other when two lines intersect
each other. The two pairs of opposite angles are equal to each other.
The two pairs of neighboring angles are supplementary, meaning they
add up to 180 degrees. Therefore given Complementary angles are CD,
FG, Supplementary angles are AD, CF, Vertical angles are BE, AD.

Question 2.
For the figure below, list all complementary and supplementary angles.

Complementary ________________
Supplementary ________________
Answer:
Complementary angles : Angle AC, Angle CE,
Supplementary: Angle AE or Angle EA,

Explanation:
Complementary: Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Question 3.

Are angle DOB and angle DOC complementary? Explain.
Answer:
Yes, Complementary,

Explanation:
Yes angle DOB and angle DOC are complementary as there sum of angles of
DOB and DOC  is 90 degrees.

Question 4.
In the figure below, a line is intersecting two parallel lines. Fill in the missing information:

∠a = ∠_________ = ∠_________ = ∠___________
Answer:
∠a = ∠e = ∠d = ∠h,

Explanation:
The missing information a line is intersecting two parallel lines are
∠a = ∠e = ∠d = ∠h.

Question 5.
In the figure below, a line is intersecting two parallel lines. Fill in the missing angle measurements:

∠a = _________;
∠b = _________;
∠c = _________;
∠d = _________;
∠e = _________;
∠f = _________;
∠h = _________;
Answer:
∠a = 125 degrees;
∠b = 55 degrees;
∠c = 125 degrees;
∠d = 55 degrees;
∠e = 125 degrees;
∠f = 55 degrees;
∠g= 125 degrees,
∠h = 55 degrees,

Explanation:
Given line is intersecting two parallel lines. The missing angle measurements are
∠a = 125 degrees;
∠b = 55 degrees;
∠c = 125 degrees;
∠d = 55 degrees;
∠e = 125 degrees;
∠f = 125 degrees;
∠h = 55 degrees as ∠a  + ∠b = 180 degrees,
∠c + ∠d = 180 degrees and ∠d = 55 degrees so ∠c = 180 – 55 = 125 degrees,
as ∠a = ∠c = 125 degrees, ∠b = 180 – 125 = 55 degrees,
∠e + ∠f = 180 degrees,
∠g + ∠h = 180 degrees and ∠g = 125 degrees so ∠h = 180 – 125 = 55 degrees,
as ∠e = ∠g = 125 degrees, ∠f = 180 – 125 = 55 degrees,

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 19.1 Measuring and Naming Angles to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 19.1 Measuring and Naming Angles

Exercises

IDENTIFY

Identify the angle as acute, right, or obtuse.

Question 1.

Answer:
Acute angle,

Explanation:
An angle which is measuring less than 90 degrees is called an acute angle. The given ∠46^o angle is smaller than the right angle (which is equal to 90 degrees).

Question 2.

Answer:
Right angle,

Explanation:
An angle that is measuring equal to 90 degrees is called a right angle. The given ∠90^o angle is the right angle (which is equal to 90 degrees).

Question 3.

Answer:
Acute angle,

Explanation:
An angle which is measuring less than 50 degrees is called an acute angle. The given ∠50^o angle is smaller than the right angle (which is equal to 90 degrees).

Question 4.

Answer:
Obtuse angle,

Explanation:
An obtuse angle is an angle that is greater than 90° and less than 180°.
In other words, an obtuse angle is between a right angle and a straight angle.
So the given ∠131^o angle is an obtuse angle.

Question 5.

Answer:
Acute angle,

Explanation:
An angle which is measuring less than 30 degrees is called an acute angle. The given ∠30^o angle is smaller than the right angle (which is equal to 90 degrees).

Question 6.

Answer:
Obtuse angle,

Explanation:
An obtuse angle is an angle that is greater than 90° and less than 180°.
In other words, an obtuse angle is between a right angle and a straight angle.
So the given ∠120^o angle is an obtuse angle.

Question 7.

Answer:
Right angle,

Explanation:
Explanation:
An angle which is measuring equal to 90 degrees is called a right angle. The given ∠90^o angle is the right angle (which is equal to 90 degrees).

Question 8.

Answer:
Obtuse angle,

Explanation:
An obtuse angle is an angle which is greater than 90° and less than 180°.
In other words, an obtuse angle is between a right angle and a straight angle.
So the given ∠175^o angle is obtuse angle.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Unit Test Lessons 1–6 to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Unit Test Lessons 1–6 Answer Key

Solve.

Question 1.
Edie’s local newspaper has 4,476 pages of advertising each year. If the magazine is published once a week, about how many pages of advertising are in each issue? (Calculate using 52 weeks in a year.) How many pages exactly?
Answer:
90,86
Explanation:
4,476 pages of advertising each year
the magazine is published once a week and there are 52 weeks in a year
\(\frac{4476}{52}\)
= 86.0769
86 to 90 pages for each issue

Add or subtract.

Question 2.

Answer:
41606
Explanation:
Start by lining up the number, to add by place value.
Add up each place value, starting in the ones place.
If the total of a place value has 2 digits,
write the second digit and carry the first digit to the next column.

Question 3.

Answer:
236137
Explanation:
Start by lining up the number, to add by place value.
Add up each place value, starting in the ones place.
If the total of a place value has 2 digits,
write the second digit and carry the first digit to the next column.

Question 4.

Answer:
1511691
Explanation:
Start by lining up the number, to add by place value.
Add up each place value, starting in the ones place.
If the total of a place value has 2 digits,
write the second digit and carry the first digit to the next column.

Question 5.

Answer:
193
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 6.

Answer:
1389
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 7.

Answer:
120109
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 8.

Answer:
91785
Explanation:
Line up the numbers according to their place values.
Subtract each value, starting from ones place.
Regroup the numbers and borrow one ten from the next place value.

Question 9.
\(\frac{31}{4}\) + \(\frac{3}{4}\)
Answer:
8\(\frac{1}{2}\)
Explanation:
\(\frac{31}{4}\) + \(\frac{3}{4}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{31 + 3}{4}\)
= \(\frac{34}{4}\)
= 8\(\frac{1}{2}\)

Question 10.
\(\frac{19}{43}\) – \(\frac{13}{43}\)
Answer:
\(\frac{6}{43}\)
Explanation:
\(\frac{19}{43}\) – \(\frac{13}{43}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{19 – 13}{4}\)
= \(\frac{6}{43}\)

Question 11.
4\(\frac{5}{11}\) + 5\(\frac{6}{11}\)
Answer:
10
Explanation:
4\(\frac{5}{11}\) + 5\(\frac{6}{11}\)
Convert the mixed fraction in to improper fraction.
\(\frac{49}{11}\) + \(\frac{61}{11}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{49 + 61}{11}\)
= \(\frac{110}{11}\)
= 10

Question 12.
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
Answer:
3\(\frac{8}{39}\)
Explanation:
2\(\frac{23}{39}\) + \(\frac{24}{39}\)
Convert the mixed fraction in to improper fraction.
\(\frac{101}{39}\) + \(\frac{24}{39}\)
As both the denominators are same,
numerators can be added directly.
\(\frac{101 + 24}{39}\)
= \(\frac{125}{39}\)
= 3\(\frac{8}{39}\)

Question 13.
\(\frac{12}{61}\) – \(\frac{3}{61}\)
Answer:
\(\frac{9}{61}\)
Explanation:
\(\frac{12}{61}\) – \(\frac{3}{61}\)
As both the denominators are same,
numerators can be subtracted directly.
\(\frac{12 – 3{61}\)
= \(\frac{9}{61}\)

Change each to a mixed number.

Question 14.
\(\frac{45}{7}\)
Answer:
6\(\frac{3}{7}\)
Explanation:

6\(\frac{3}{7}\)

Question 15.
\(\frac{66}{8}\)
Answer:
8\(\frac{1}{4}\)
Explanation:

= 8\(\frac{1}{4}\)

Question 16.
\(\frac{1}{2}\) × 44
Answer:
22
Explanation:
\(\frac{1}{2}\) × 44
\(\frac{44}{2}\)

Question 17.
\(\frac{1}{4}\) × 22
Answer:
5\(\frac{1}{2}\)
Explanation:
\(\frac{1}{4}\) × 22
\(\frac{22}{4}\)

= 5\(\frac{1}{2}\)

Question 18.
\(\frac{11}{18}\) × \(\frac{11}{22}\)
Answer:
\(\frac{11}{36}\)
Explanation:
\(\frac{11}{18}\) × \(\frac{11}{22}\)
= \(\frac{11 x 11}{18 x 22}\)
= \(\frac{11}{18 x 2}\)
= \(\frac{11}{36}\)

Question 19.
\(\frac{2}{3}\) × 4\(\frac{3}{5}\)
Answer:
3\(\frac{1}{15}\)
Explanation:
\(\frac{2}{3}\) × 4\(\frac{3}{5}\)
Convert the mixed fraction in to improper fraction.
= \(\frac{2}{3}\) × \(\frac{23}{5}\)
= \(\frac{2 x 23}{3 x 5}\)
= \(\frac{46}{15}\)
= 3\(\frac{1}{15}\)

Question 20.
18 × \(\frac{7}{9}\)
Answer:
14
Explanation:
18 × \(\frac{7}{9}\)
= \(\frac{18 x 7}{9}\)
= \(\frac{2 x 7}{1}\)
= 14

Question 21.
\(\frac{15}{29}\) ÷ 45
Answer:
\(\frac{1}{87}\)
Explanation:
\(\frac{15}{29}\) ÷ 45
= \(\frac{15}{45 x 29}\)
= \(\frac{1}{3 x 29}\)
= \(\frac{1}{87}\)

Question 22.
\(\frac{54}{47}\) ÷ 18
Answer:
\(\frac{3}{47}\)
Explanation:
= \(\frac{54}{47}\) ÷ 18
= \(\frac{54}{18 x 47}\)
= \(\frac{3}{47}\)

Question 23.
42 ÷ \(\frac{7}{3}\)
Answer:
18
Explanation:
42 ÷ \(\frac{7}{3}\)
= \(\frac{42 x 3}{7}\)
= 18

Question 24.
\(\frac{4}{27}\) ÷ 3
Answer:
\(\frac{4}{81}\)
Explanation:
\(\frac{4}{27}\) ÷ 3
= \(\frac{4}{3 x 27}\)
= \(\frac{4}{81}\)

Question 25.
\(\frac{75}{83}\) ÷ 15
Answer:
\(\frac{5}{83}\)
Explanation:
\(\frac{75}{83}\) ÷ 15
= \(\frac{75}{15 x 83}\)
= \(\frac{5}{83}\)

Determine if the following proportions are equal. (Write Yes or No.)

Question 26.
\(\frac{5}{4}\) = \(\frac{24}{26}\)
Answer:
No
Explanation:
\(\frac{5}{4}\) = \(\frac{24}{26}\)

Question 27.
\(\frac{21}{12}\) = \(\frac{7}{36}\)
Answer:
No
Explanation:
\(\frac{21 x 3}{12 x 3}\) = \(\frac{21}{36}\)
\(\frac{21}{12}\) is not equal to \(\frac{7}{36}\)

Question 28.
\(\frac{12}{19}\) = \(\frac{38}{48}\)
Answer:
No
Explanation:
\(\frac{12 x 3}{19 x 3} \) = \(\frac{36}{57}\)
\(\frac{12}{19}\) is not equal to \(\frac{38}{48}\)

Question 29.
\(\frac{1}{4}\) = \(\frac{6}{24}\)
Answer:
Yes
Explanation:
\(\frac{1}{4}\) = \(\frac{6}{24}\)
\(\frac{1 x 6}{4 x 6}\) = \(\frac{6}{24}\)
\(\frac{1}{4}\) = \(\frac{6}{24}\)
So, both the proportions equal.

Solve for x.

Question 30.
\(\frac{x}{10}\) = \(\frac{30}{20}\)
Answer:
x = 15
Explanation:
\(\frac{x}{10}\) = \(\frac{30}{20}\)
x = \(\frac{30 x 10}{20}\)
x = 15

Question 31.
\(\frac{20}{x}\) = \(\frac{40}{100}\)
Answer:
x = 50
Explanation:
\(\frac{20}{x}\) = \(\frac{40}{100}\)
x = \(\frac{20 x 100}{40}\)
x = 50

Question 32.
\(\frac{36}{90}\) = \(\frac{12}{x}\)
Answer:
x = 30
Explanation:
\(\frac{36}{90}\) = \(\frac{12}{x}\)
x = \(\frac{12 x 90}{36}\)
x = 30

Solve.

Question 33.
Walter looked at the list of nutrients in the fruit juice he bought. He noticed that there were a total of 4 grams of carbohydrates and 3 grams of sugar in every bottle of juice. Compare the amount of sugar to carbohydrates in the fruit juice.
Answer:
\(\frac{3}{4}\) grams
Explanation:
Walter noticed that there were a total of 4 grams of carbohydrates and 3 grams of sugar in every bottle of juice. Compare the amount of sugar to carbohydrates in the fruit juice,
= \(\frac{3}{4}\) grams.

Question 34.
Will rides his unicycle at an average speed of 8 miles per hour. How far will he travel in 2\(\frac{1}{2}\) hours?
Answer:
20 miles.
Explanation:
Will rides his unicycle at an average speed of 8 miles per hour.
Total distance he travel in 2\(\frac{1}{2}\) hours,
= 2\(\frac{1}{2}\) x 8
= \(\frac{5}{2}\) x 8
= 2 x 8 + \(\frac{8}{2}\)
= 16 + 4
= 20 miles

Question 35.
Jack makes 22 muffins for every 3 batches he bakes. How many batches of muffins will he need to bake in order to sell 242 muffins?
Answer:
33 batches.
Explanation:
22 muffins for 3 batches
242 muffins  —- x batches
x X 22 = 3 x 242
x = \(\frac{3 x 242}{22}\)
x = 3 x 11
x = 33 batches

Question 36.
Priscilla drinks an average of \(\frac{2}{3}\) quart of water for each mile she walks. How many quarts of water will she drink if she walks \(\frac{2}{3}\) miles?
Answer:
\(\frac{4}{9}\) qts.
Explanation:
Priscilla drinks an average of \(\frac{2}{3}\) quart of water for each mile she walks.
Total quarts of water she drink if she walks \(\frac{2}{3}\) miles,
= \(\frac{2}{3}\) x \(\frac{2}{3}\)
= \(\frac{2 x 2}{3 x 3}\)
= \(\frac{4}{9}\) qts

Question 37.
Jenny changes the oil in her car every 2,250 miles. How many times will she need to change the oil in her car if she takes a trip that is 9,000 miles in length?
Answer:
4 times.
Explanation:
Jenny changes the oil in her car every 2,250 miles.
Number of times she need to change the oil in her car if she takes a trip that is 9,000 miles in length,
= \(\frac{9000}{2250}\)
= 2250 x 4 = 9000
= \(\frac{9000}{2250}\) = 4

Question 38.
30% of 1\(\frac{2}{5}\)
Answer:
\(\frac{21}{50}\)
Explanation:
30% of 1\(\frac{2}{5}\)
= \(\frac{30}{100}\) x \(\frac{7}{5}\)
= \(\frac{3}{10}\) x \(\frac{7}{5}\)
= \(\frac{3 x 7}{10 x 5}\)
= \(\frac{21}{50}\)

Question 39.
40% of 440
Answer:
176
Explanation:
40% of 440
= \(\frac{40}{100}\) x 440
= \(\frac{4}{10}\) x \(\frac{440}{1}\)
= \(\frac{4 x 440}{10}\)
= 4 x 44
= 176

Question 40.
\(\frac{1}{4}\) of 48%
Answer:
12%
Explanation:
\(\frac{1}{4}\) of 48%
= \(\frac{1}{4}\) x \(\frac{48}{100}\)
= \(\frac{1 x 48}{4 x 100}\)
= \(\frac{12}{100}\)
= 12%

Question 41.
\(\frac{2}{5}\) of 70%
Answer:
28%
Explanation:
\(\frac{2}{5}\) of 70%
= \(\frac{2}{5}\) x \(\frac{70}{100}\)
= \(\frac{2 x 70}{100}\)
= \(\frac{2 x 14 }{100}\)
= 28%

Question 42.
\(\frac{3}{8}\) of 340%
Answer:
127.5%
Explanation:
\(\frac{3}{8}\) of 340%
= \(\frac{3}{8}\) x \(\frac{340}{100}\)
= \(\frac{3 x 340}{8 x 100}\)
= \(\frac{127.5 }{4 x 100}\)
= 127.5%

Question 43.
43% of .705
Answer:
0.3032
Explanation:
43% of .705
\(\frac{43}{100}\) x 0.705
= 0.43 x 0.705
= 0.3032

Question 44.
84% of 1.906
Answer:
1.601
Explanation:
84% of 1.906
\(\frac{84}{100}\)
= 0.84 x 1.906
= 1.601

Question 45.
\(\frac{3}{4}\) of 160%
Answer:
120%
Explanation:
\(\frac{3}{4}\) of 160%
= \(\frac{3}{4}\) x \(\frac{160}{100}\)
= \(\frac{3 x 160}{4 x 100}\)
= \(\frac{3 x 40}{100}\)
= 120%

Question 46.
Pete’s Pet Emporium is having a sale on birdcages. Pete is selling his $50 cages at a 20% discount, his $75 cages at \(\frac{1}{3}\) off, and his $100 cages at 60% off the original price. What are the new sale prices for the 3 cages?
$50 cage ________ $75 cage _________ $100 cage
Answer:
$40, $50, $40
Explanation:
Pete is selling his $50 cages at a 20% discount,
$50 cages at a 20% discount,
50 x 20 / 100 = 10
$50 – $10 = $40
his $75 cages at \(\frac{1}{3}\) off,
his $75 cages at \(\frac{1}{3}\) off,
$75 x \(\frac{1}{3}\) = $25
$75 – $25 = $50
and his $100 cages at 60% off the original price,
$100 x 60/100 = 60
$100 – $60 = $40
the new sale prices for the 3 cages,
$50 cage __$40
$75 cage __$50
$100 cage __$40

Question 47.
Tom is selling wristbands for $4.50. He has to charge sales tax of 6% on each wristband. What is the cost to the customer, including sales tax, for one wristband?
Answer:
$4.77
Explanation:
Tom is selling wristbands for $4.50.
He has to charge sales tax of 6% on each wristband.
$4.50x 6%
4.50 x 0.06 = 0.27
the cost to the customer, including sales tax, for one wristband,
4.50 + 0.27 = $4.77

Question 48.
Ursula put $200 into a money market account that pays 3% simple interest. How much will she have in her account at the end of 1 year if she does not deposit any more money in the account? How much will she have at the end of 2 years?
Answer:
$206.00, $212.00

Question 49.
Pam put $400 into a savings account that pays 2.5% in compound interest. How much will she have in the account at the end of 2 years, if she does not deposit any more money in the account? How much will she have at the end of 5 years?
Answer:
$420.25; $452.56

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Pretest to secure good marks & knowledge in the exams.

Complete the following test items.

Question 1.
Kathy runs 16 miles a week. If she continues to run at this rate, how many miles will she run in a year?
Answer:
832 miles.
Explanation:
Kathy runs 16 miles a week.
If she continues to run at this rate,
There are 52 weeks in a year,
16 x 52 = 832 miles

Question 2.
The women’s clothing department at Ms. Smith’s store had a sale on jeans. There were 945 jeans in stock at the beginning of the sale and another 254 jeans were ordered. At the end of the sale the store still had 245 jeans in stock. How many jeans were sold during the sale?
Answer:
954 jeans.
Explanation:
945 jeans in stock at the beginning of the sale and another 254 jeans were ordered.
At the end of the sale the store still had 245 jeans in stock.
Total 945 + 254 = 1199 jeans
1199 – 245 = 954
954 jeans sold during the sale

Question 3.
Jack has 16 lengths of rope. Each is 6\(\frac{3}{4}\) meters long. How much rope does Jack have to divide among 20 people?
___________________
How much rope will each person receive?
___________________
Answer:
108m;
Each person will receive 5\(\frac{2}{5}\) meters.
Explanation:
Jack has 16 lengths of rope.
Each is 6\(\frac{3}{4}\) meters long.
= 16 x 6\(\frac{3}{4}\)
= 16 x \(\frac{4 x 6 + 3}{4}\)
= 16 x \(\frac{27}{4}\)
= \(\frac{16 x 27}{4}\)
= 4 x 27
= 108 m
Total length of the rope / number of people
\(\frac{108}{20}\)
5\(\frac{2}{5}\)
Each person will receive 5\(\frac{2}{5}\) meters.

Question 4.
David has 176 ounces of hot sauce to divide among the 32 contestants in a chicken-wing eating contest.
How many cups is that per contestant?
Answer:
5.5 oz or 6\(\frac{11}{16}\) cups.
Explanation:
David has 176 ounces of hot sauce to divide among the 32 contestants in a chicken-wing eating contest.
Number of cups for each contestants,

Question 5.
4\(\frac{3}{10}\) + 3\(\frac{2}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\) =
Answer:
8\(\frac{8}{15}\)
Explanation:
4\(\frac{3}{10}\) + 3\(\frac{2}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
converting mixed fractions into improper fraction
= \(\frac{40 +3}{10}\) + 3\(\frac{15 + 2}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
= \(\frac{43}{10}\) + \(\frac{17}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
As denominator are different, take LCM,
LCM of 10, 5, 3, 2 to be found as below shown.

= \(\frac{43}{10}\) + \(\frac{17}{5}\) + \(\frac{1}{3}\) + \(\frac{1}{2}\)
= \(\frac{43 X 3}{30}\) + \(\frac{17 X 6}{30}\) + \(\frac{1 X 10}{30}\) + \(\frac{1 X 15}{30}\)
=\(\frac{129}{30}\) + \(\frac{102}{30}\) + \(\frac{10}{30}\) + \(\frac{15}{30}\)
= \(\frac{129 + 102 + 10 + 15}{30}\)
= \(\frac{256}{30}\)
= 8\(\frac{16}{30}\)
= 8\(\frac{8}{15}\)

Question 6.
-8 + 11 – (-9) + 4(-3) + \(\frac{12}{-4}\) =
Answer:
-3
Explanation:
Given, -8 + 11 – (-9) + 4(-3) + \(\frac{12}{-4}\)
= -8 + 11 + 9 -12 -3
= -8 + 20 -15
= -3

Question 7.
Solve for x: x — 7 = 14
Answer:
x = 21
Explanation:
x — 7 = 14
x — 7 = 14 + 7
x = 21

Question 8.
Solve for x: 2x + 6 = 18
Answer:
x = 6
Explanation:
2x + 6 = 18
2x  = 18 – 6
2x = 12
x = 12/2
x = 6

Question 9.
Solve: 10 + (8 — 6)² — (12 ÷ 4) + 5(6 × 2) + 3(7 — 4) = _______
Answer:
80
Explanation:
10 + (8 — 6)² — (12 ÷ 4) + 5(6 × 2) + 3(7 — 4)
= 10 + (2)² — (3) + 5(12) + 3(3)
= 10 + 4 — 3 + 60 + 9
= 80

Question 10.
Restate in exponent form, then solve: 5 × 5 + 2 × 2 × 2 + 3 × 3 =
___________________
Answer:
5² + 2³+ 3² = 42
Explanation:
5 × 5 + 2 × 2 × 2 + 3 × 3
a x a = a² 
a x a x a = a³ 
5² + 2³+ 3²
= 42

Question 11.
5 meters _________ inches
(Use 2.54 cm = 1 inch)
Answer:
196.85 inches.
Explanation:
5 meters = 500 cms
(by Using 2.54 cm = 1 inch)
1 meter = 39.5
\(\frac{500}{2.54}\)
196.85 inches

Question 12.
10 yards = _________ centimeters
Answer:
914.4 cm
Explanation:
1 yard = 91.44 cm
10 yards = 91.44 x 10
= 914.4 centimeters

Question 13.
What is the area of the rectangle? _______

What is the perimeter?
________________
What is the perimeter, in inches, using the conversion factor of 2.54 cm to the inch?
Answer:
Area = 96 sq cm;
Perimeter = 40 cm or 15.748 in.
Explanation:
Area of a rectangle = Length x width
A = 8 x 12
A = 96 sq cm
Perimeter of a Rectangle = 2(Length + Width)
P = 2( 8 + 12)
P = 2 x 20
P = 40 cm
P = 40/2.54
= 15.748 in

Question 14.

What is the area of the circle? (Use 3.14 for π.)
What is the circumference of the circle?
________________
Answer:
Area = 78.5 sq in;
Circumference = 31.4 inches.
Explanation:
The area of the circle (Use 3.14 for π)
A = π r²
r = 5 cm
A = 3.14 x 5 x 5
A = 78.5 sq in.
The circumference of the circle,
C = 2πr
C = 2 x 3.14 x 5
C = 31.4 inches.

Question 15.
Identify each angle as obtuse, acute, or right.

Answer:

Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as acute.
If the angle formed between two rays is exactly 90° then it is called a right angle.

Question 16.
Identify each triangle as scalene, isosceles, or equilateral.

Answer:

Explanation:
All angles of a scalene triangle are unequal, all are of different size.
An equilateral triangle is a triangle with all three sides of equal length.
An isosceles triangle is a triangle with two equal sides.

Calculate and reduce the fractions.

Question 17.
4\(\frac{3}{5}\) × 5\(\frac{1}{5}\) =
Answer:
23\(\frac{23}{25}\)
Explanation:
4\(\frac{3}{5}\) × 5\(\frac{1}{5}\)
= \(\frac{23}{5}\) × \(\frac{26}{5}\)
= \(\frac{23 X 26}{5 X 5}\)
= \(\frac{598}{25}\)
= 23\(\frac{23}{25}\)

Question 18.
(\(\frac{3}{4}\) × \(\frac{4}{11}\)) × \(\frac{11}{3}\) = _______
Answer:
1
Explanation:
(\(\frac{3}{4}\) × \(\frac{4}{11}\)) × \(\frac{11}{3}\)
= (\(\frac{3 X 4}{4 X 11}\)) × \(\frac{11}{3}\)
= \(\frac{12}{44}\) × \(\frac{11}{3}\)
= \(\frac{12 X 11}{44 X 3}\)
= \(\frac{132}{132}\) = 1

Question 19.
\(\frac{12}{25}\) ÷ \(\frac{4}{5}\) = _____
Answer:
\(\frac{3}{5}\)
Explanation:
\(\frac{12}{25}\) ÷ \(\frac{4}{5}\)
In division the fraction of one is reciprocal to the other.
= \(\frac{12}{25}\) x \(\frac{5}{4}\)
= \(\frac{12 X 5}{25 X 4}\)
= \(\frac{60}{100}\)
= \(\frac{3}{5}\)

Question 20.
Give the coordinates for points on the grid.
A ___ B __
C ___ D ___

What is the slope of a line drawn between points A and B?
Answer:
A(1,3); B(-3,6); C(2, -5); D(-2, -2)
The slope of a line drawn between points A and B –\(\frac{3}{4}\)

Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
So, co-ordinates on grid are A(1,3); B(-3,6); C(2, -5); D(-2, -2).
Slope:
The slope formula is m=(y2-y1)/(x2-x1),
or the change in the y values over the change in the x values.
The coordinates of the first point represent x1 and y1.
The coordinates of the second points are x2, y2
The slope of a line drawn between points A and B –\(\frac{3}{4}\).
A(1,3); B(-3,6)
m = \(\frac{y2 – y1}{x2 – x1}\)
m = \(\frac{6 – 3}{-3 – 1}\)
m = \(\frac{3}{-4}\)
m = –\(\frac{3}{4}\)

Question 21.
What is the measure of angle DBC?

_______
Answer:
50 degrees

Explanation:
The sum of the two angles in right angle is 90°.
40° + x = 90°
x = 90° – 40°
x = 50°

Question 22.

Answer:
1.566667
Explanation:
0.15 x 1000 = 150
0.235 x 1000 = 235

Question 23.

Answer:
0.1562
Explanation:
0.4686 x 10000 = 4686
3 x 10000 = 30000

Question 24.
what is 40% of .775? _____
Answer:
0.31
Explanation:
40% of .775
\(\frac{40}{100}\) x 0.775
= \(\frac{40 X 0.775}{100}\)
= \(\frac{31}{100}\)
= 0.31

Question 25.
What is \(\frac{5}{8}\) of 72% ?_____
Answer:
45%
Explanation:
\(\frac{5}{8}\) of 72%
= \(\frac{5}{8}\) x \(\frac{72}{100}\)
= \(\frac{5 X 72}{8 X 100}\)
= \(\frac{360}{800}\)
= 0.45
Convert 0.45 to %
= 0.45 x 100 = 45%

Question 26.
Restate 4.25 as an improper fraction and a mixed number.
Improper Fraction _____ Mixed Number ______
Answer:
Improper fraction: \(\frac{17}{4}\)
Mixed fraction: 4\(\frac{1}{4}\)
Explanation:
Restate 4.25 as an improper fraction and a mixed number.
Convert decimal to fraction.
4.25 x \(\frac{100}{100}\)
= \(\frac{425}{100}\)
= \(\frac{85}{20}\)
= \(\frac{17}{4}\)
Convert improper fraction to mixed fraction.
\(\frac{17}{4}\) = 4\(\frac{1}{4}\)

Question 27.
Put the following numbers in order from least to greatest.
1.162, 1.161, 2.16302, 2.163, 2.8022, 1.90688, 1.9122, 1.099
___________________
Answer:
1.099, 1.161, 1.162, 1.90688, 1.9122, 2.163, 2.16302, 2.8022
Explanation:
Arrange all the given numbers in ascending order by placing whole numbers first,
then decimals number with the least digit according to their place values.

Question 28.
Solve for x. \(\frac{15}{32}\) = \(\frac{x}{160}\)
Answer:
75
Explanation:
\(\frac{15}{32}\) = \(\frac{x}{160}\)
x = \(\frac{15 X 160}{32}\)
x = \(\frac{2400}{32}\)
x = 75

Question 29.
Restate 2\(\frac{7}{16}\) as a decimal. _____
Answer:
2.4375
Explanation:
Convert the given mixed fraction to improper fraction,
2\(\frac{7}{16}\)
= \(\frac{39}{16}\)
Convert improper fraction into decimal,
= 2.4375

Question 30.
Sarah manufactured surfboards at a cost of $45.00 each. She wants to sell the surfboards at a 50% markup. What will be the selling price for each?
Answer:
$67.50
Explanation:
Sarah manufactured surfboards at a cost of $45.00 each.
She wants to sell the surfboards at a 50% markup.
50% of $45.00
\(\frac{50}{100}\) x 45
= \(\frac{50 X 45}{100}\)
= \(\frac{2250}{100}\)
= 22.5
The selling price for each, 22.5 + 45 = $67.50

Question 31.
Dexter deposits $200 in a bank account that earns 3% simple interest. How much money will he have
in the account after 1 year? _______
After 2 years? _________
Answer:
After 1 year = $206.00;
After 2 years = $212.18.
Explanation:
Simple Interest SI = PTR/100
Principal = $200
Time T = 1 year
Rate of interest R = 3%
SI = (200 x 1 x 3)/100
SI = 6
Amount after one year = $200 + $6
= $206
now
Principal = $206
Time T = 1 year
Rate of interest R = 3%
SI = (206 x 1 x 3)/100
SI = $6.16
Amount after one year = $206 + $6.18
= $212.18

Question 32.
Identify each quadrilateral.

Answer:

Explanation:
A square is closed, two-dimensional shape with 4 equal sides.
Rhombus is a quadrilateral with all equal sides.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.

Question 33.
Restate 5\(\frac{6}{13}\) as an improper fraction.
Answer:
\(\frac{71}{13}\)
Explanation:
Convert the given fraction to improper fraction,
5\(\frac{6}{13}\)
= \(\frac{71}{13}\)

Question 34.
Restate \(\frac{43}{16}\) as a mixed number. _____
Answer:
2\(\frac{11}{6}\)
Explanation:
Convert improper fraction to mixed fraction, \(\frac{43}{16}\)
write the quotient as whole number and remainder as numerator..
quotient = 2
Remainder = 11
2\(\frac{11}{6}\)

Question 35.
\(\frac{4}{7}\) – \(\frac{5}{7}\) + \(\frac{3}{7}\) + \(\frac{4}{7}\) – \(\frac{3}{7}\) = _____
Answer:
\(\frac{3}{7}\)
Explanation:
\(\frac{4}{7}\) – \(\frac{5}{7}\) + \(\frac{3}{7}\) + \(\frac{4}{7}\) – \(\frac{3}{7}\)
As, there is a common denominator in all the fractions add the numerators,
= \(\frac{4 – 5 + 3 + 4 – 3}{7}\)
= \(\frac{3}{7}\)

Question 36.
\(\frac{5}{8}\) × 3\(\frac{13}{25}\) = _____
Answer:
2\(\frac{1}{5}\)
Explanation:
\(\frac{5}{8}\) × 3\(\frac{13}{25}\)
convert mixed fraction improper fraction
= \(\frac{5}{8}\) × \(\frac{75 + 13}{25}\)
= \(\frac{5}{8}\) × \(\frac{88}{25}\)
= \(\frac{5 X 88}{8 X 25}\)
= \(\frac{440}{200}\)
= \(\frac{11}{5}\)
= 2\(\frac{1}{5}\)

Question 37.
10⁴ × 10⁵ = ____
Answer:
10⁹
Explanation:
a^m x aⁿ = a^{m + n}
10⁴ x 10⁵ = 10⁴⁺⁵
= 10⁹

Question 38.
9⁸ ÷ 9⁴ = ____
Answer:
9⁴ or 6561
Explanation:
a^m ÷ aⁿ = a^{m – n}
9⁸ ÷ 9⁴ = 9^{9 – 4} = 9⁴
a⁴ = a x a x a x a
9⁴ = 9 x 9 x 9 x 9
= 81 x 81
= 6561

Question 39.
What is 12²? ________
Answer:
144
Explanation:
a² = a x a =
12² = 12 x 12 = 144

Question 40.
What is the square root of 225? ____
Answer:
15
Explanation:
The square root of 225 is expressed as √225 in the radical form,
and as (225)^½ or (225)^0.5 in the exponent form.
The square root of 225 is 15.
It is the positive solution of the equation x² = 225.
The number 225 is a perfect square.

Question 41.

What is the mode of the data distribution?
____________
What is the median?
_____________
Answer:
Mode = 47
Median = 50
Explanation:
Mode : mode is the number that appears most frequently in the collection of data.

The median is the number in the middle,
if the collection of data has an even numbers of addends,
then the median is the average of the two middle numbers.
22, 23, 31, 36, 38, 42, 47, 47, 47, 53, 54, 54, 56, 56, 61, 64, 64, 65

Median is the average of (47 + 53 )/2 = 100/2 = 50

Question 42.
According to this graph, what frozen yogurt is the most preferred? ____________________
The least preferred? ___________

Answer:
The most preferred frozen yogurt is Mango;
The least preferred frozen yogurt is Strawberry.
Explanation:
A pie chart is a pictorial representation of data in circular statistical graphic,
which is divided into slices to illustrate numerical proportion.

In a pie chart, the arc length of each slice is proportional to the quantity it represents.
The most preferred frozen yogurt is Mango,
due to maximum portion of the pie chart shows Mango;
The least preferred frozen yogurt is Strawberry,
due to minimum portion of the pie chart shows Strawberry.

Question 43.
Brandon collected about 20 cans more than what person? ______
Who collected the second fewest cans? ______________

Answer:
Brandon collected about 20 cans more than Molly.
Megan collected the second fewest cans.
Explanation:
Above chart shows the Recycling contest results.
Brandon collected about 20 cans more than Molly,
he collected 70 cans.
Megan collected the second fewest cans.

Question 44.
How many possible combinations are there?
___________________

Answer:
12
Explanation:
If an event can occur in ‘m’ different ways following,
which another event can occur in ‘n’ different ways,
following which a third event can occur in ‘p’ different ways.
The total number of occurrence to the events in the given order is m x n x p.
2 Shirts,
3 Pants,
2 Shoes,
2 x 3 x 2 = 12

Question 45.
What is the range of the data in the box-and-whisker plot?
______________

Answer:
18
Explanation:

The range difference between the upper extreme to lower extreme
Range = 22 – 4 = 18

Question 46.
Use the Pythagorean Theorem to find the value of x.

Answer:
x = 12
Explanation:
In Pythagorean Theorem the square of the length of the hypotenuse of a right triangle,
equals the sum of the squares of the lengths of the other two sides.

AC² = AB² + BC²
13² = AB² + 5²
169 – 25 = AB²
AB² = 144
AB = 12
x = 12

Question 47.

Name two pairs of alternate interior angles.
________ and ________ ________ and _________

Name two pairs of alternate exterior angles.
________ and ________ ________ and _________
Name a pair of vertical angles.
_______ and _______
Name two pairs of supplementary angles.
_____ and _____ _____ and _____
Answer:
Alternate interior angles:
\(\angle{4}\) and \(\angle{5}\);
\(\angle{3}\) and \(\angle{6}\).
Alternate exterior angles:
\(\angle{2}\) and \(\angle{7}\);
\(\angle{1}\) and \(\angle{8}\).
Vertical angles:
\(\angle{2}\) and \(\angle{3}\);
\(\angle{1}\) and \(\angle{4}\);
\(\angle{6}\) and \(\angle{7}\);
\(\angle{5}\) and \(\angle{8}\).
Supplementary angles:
\(\angle{1}\) and \(\angle{3}\);
\(\angle{2}\) and \(\angle{4}\);
\(\angle{5}\) and \(\angle{7}\);
\(\angle{6}\) and \(\angle{8}\).
Explanation:
Alternate interior angles:
The two angles, formed when a line crosses two other lines,
that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.
If the two lines crossed are parallel, the alternate angles are equal
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
The transversal crosses through the two lines which are Coplanar at separate points.
\(\angle{4}\) and \(\angle{5}\);
\(\angle{3}\) and \(\angle{6}\).
Alternate exterior angles:
The term alternate exterior angles is often used when two lines are cut by a third line, a transversal .
The Alternate Exterior Angles Theorem states that if k and l are parallel ,
then the pairs of alternate exterior angles are congruent .
\(\angle{2}\) and \(\angle{7}\);
\(\angle{1}\) and \(\angle{8}\).
Vertical angles:
Vertical angles are angles opposite each other where two lines cross.
\(\angle{2}\) and \(\angle{3}\);
\(\angle{1}\) and \(\angle{4}\);
\(\angle{6}\) and \(\angle{7}\);
\(\angle{5}\) and \(\angle{8}\).
Supplementary angles:
The two angles or arcs whose sum is 180 degrees.
\(\angle{1}\) and \(\angle{3}\);
\(\angle{2}\) and \(\angle{4}\);
\(\angle{5}\) and \(\angle{7}\);
\(\angle{6}\) and \(\angle{8}\).

Question 48.
Name two line segments.
Name four rays. __________
Name a line. ____________________________

Answer:
Line segments:
\(\overline{AB}\), \(\overline{AC}\), \(\overline{AF}\), \(\overline{DB}\),\(\overline{BE}\), \(\overline{HG}\);
Rays:
\(\overline{AF}\), \(\overline{AC}\), \(\overline{BE}\), \(\overline{BD}\),
\(\overline{AB}\), \(\overline{BA}\);
Line:
\(\overline{AB}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Calculate the volume and surface area of the figures shown.

Question 49.

Volume ___
Surface Area ____
Answer:
Volume = 72 cu in;
Surface Area = 108 sq in.
Explanation:
Volume = length x width x height
V = 4 x 3 x 6
V  = 72 cu in;
Surface Area = 2(lxw + wxh + hxl)
SA= 2(4×3 + 3×6 + 6×4)
SA = 2(12 + 18 + 24)
SA = 108 sq in.

Question 50.

Volume ___
Surface Area ____
Answer:
Volume = 128π cu in;
Surface Area = 96π sq in.
Explanation:
Volume V = π r² h
V = πr²h
V = π x 4² x 8
V = 128π cu in;
Surface Area SA = 2π rh + 2π r²
SA = 2π rh + 2π r²
= 2 π 4 x 8 + 2 π 4 x 4
= 64π +32π
= 96π sq in.

Question 51.

Volume ______
Answer:
Volume = 96π cu units;
Explanation:
Volume of cone V= π r²h(1/3)
V = π 3²x 8 (1/3)
V = π 9 x 8 x 1/3
V = 72 π cu units;

Question 52.
Estimate the value of \(\sqrt{30}\) _____________________ Of \(\sqrt{97}\). _________
Answer:
Estimate: 5.5;
9.8
Explanation:
\(\sqrt{25}\) = 5
\(\sqrt{36}\) = 6
\(\sqrt{30}\) lies between 5 and 6
\(\sqrt{30}\) =5.5
\(\sqrt{100}\) = 10
\(\sqrt{97}\) is nearer to 100
\(\sqrt{97}\) = 9.8

Question 53.
Convert \(2 . \overline{14}\) to an improper fraction. _______
Answer:
\(\frac{212}{99}\)
Explanation:
\(2 . \overline{14}\)
2.14141414…….
Let
x = 2.14141414 ………….. Eq(1)
by multiplying 100 on both sides
100 x = 214.141414 ……………….Eq (2)
by subtracting Eq(1) from Eq(2) as shown below

99 x = 212
x = \(\frac{212}{99}\)

Question 54.
Solve 4x² + 14 — 4x² = 7. ____________________
Answer:
No solution.
Explanation:
4x² + 14 — 4x² = 7
4x² — 4x² = 14 – 7
0 = 7
So, No solution.

Question 55.
Solve 4x² + 7 — 4x² = 7. _________________________________
Answer:
Infinite Solutions.
Explanation:
4x² + 7 — 4x² = 7
4x² — 4x² = 7 – 7
0 = 0
So, Infinite Solutions.

Question 56.
Complete and graph the function table for y = 2x – 1.

Answer:
Explanation:
y = 2x – 1.
Given the values of x.
y = 2 x -2 – 1
y = -4 – 1
y = -5
Create function table for each equation as shown above.
Substitute a number of values of x in the equation,
then complete the equation to determine the value of y as shown above.
Slope refers to the amount by which a line rises or falls,
as you read a co ordinate grid from left to right.
Positive Slope or Negative Slope
Slope = rise/run
Slope =  2/1 = 2

Question 57.
Look at the graph. Is this a linear or nonlinear function?
______________

The function is increasing between points
__________________
The function is decreasing between points
__________________
The function is positive between points
__________________
The function is negative between points
__________________
Answer:
The function is increasing between non-linear points A and B.
The function is decreasing between C and D points.
The function is positive between B or B and C points.
The function is negative between C and D points.
Explanation:
A non-linear equation is such which does not form a straight line.
It looks like a curve in a graph and has a variable slope value.
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin

Question 58.
How many times greater is 6 × 10⁷ than 3 × 10⁵?
Answer:
200 times.
Explanation:
\(\frac{6 x 10⁷}{3 x 10⁵}\)
= 2 x 10²
= 2 x 100
= 200

Question 59.
In the graph below, is triangle ABC congruent to triangle ADC?
__________________
What type of transformation created triangle ADC? __________

Answer:
Yes; Reflection.
Explanation:
Reflection occurs when we create a mirror image of the original.
To do this, pretend you are flipping the figure over an imaginary line called a line of reflection.
Each point of the new image is the same distance from the line as the original image was,
just on the opposite side of the line.

Question 60.
What type of transformation is shown below? _____

Answer:
Dilation.
Explanation:
Dilation occurs when you change the size of the original figure by enlarging or shrinking it.
The process produce an image that is the exact same shape as the original figure,
but is larger or smaller then the original.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Posttest to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Posttest Answer Key

Complete the following test items.

Question 1.
Robin runs 24 kilometers a week. If she continues to run at this rate, how many kilometers will she run in a year?
Answer:
1248 km
Explanation:
Robin runs 24 kilometers a week.
If she continues to run at this rate,
Number of kilometers she run in a year,
1 year = 52 weeks
= 52 x 24
= 1,248 km.

Question 2.
The fashion department at an outlet store had a sale on t-shirts. There were 1,124 t-shirts in stock at the beginning of the sale and another 426 more were ordered. At the end of the sale the store still had 335 t-shirts in stock. How many t-shirts were sold during the sale?
Answer:
1215 T-shirts.
Explanation:
There were 1,124 t-shirts in stock at the beginning of the sale,
another 426 more were ordered.
1124 + 426 = 1550
At the end of the sale the store still had 335 t-shirts in stock.
Total t-shirts sold during the sale,
1550 – 335 = 1215 T- shirts.

Question 3.
Ronnie has 12 lengths of garden hose. Each is 6\(\frac{3}{4}\) meters long. How many meters of garden hose does Ronnie have to divide among 6 people working in the community garden? _____________
How much hose will each person receive? _____________
Answer:
81 meters;
Each person will receive 13\(\frac{1}{2}\).
Explanation:
Ronnie has 12 lengths of garden hose.
Each is 6\(\frac{3}{4}\) meters long.
Ronnie have to divide among 6 people working in the community garden as,
6\(\frac{3}{4}\) x 12
= \(\frac{27}{4}\) x 12
= \(\frac{27 X 12}{4}\)
= \(\frac{324}{4}\)
= 81 meters
Each person receive \(\frac{81}{6}\)
= 13\(\frac{1}{2}\)

Question 4.
Don has 112 quarts of tomato sauce to divide among the 12 contestants in a pasta cooking contest. How many cups is that per contestant?
Answer:
37\(\frac{1}{3}\) cups
Explanation:
Don has 112 quarts of tomato sauce to divide among the 12 contestants in a pasta cooking contest.
1 quart = 4 cups
112 x 4 = 448 cups
Number of cups per contestant,
= \(\frac{448}{12}\) cups
= 37\(\frac{1}{3}\) cups

Question 5.
6\(\frac{5}{8}\) + 3\(\frac{1}{4}\) + \(\frac{1}{6}\) + 1\(\frac{1}{3}\) = _____________
Answer:
11\(\frac{3}{8}\)
Explanation:
6\(\frac{5}{8}\) + 3\(\frac{1}{4}\) + \(\frac{1}{6}\) + 1\(\frac{1}{3}\)
= \(\frac{53}{8}\) + \(\frac{13}{4}\) + \(\frac{1}{6}\) + \(\frac{4}{3}\)
= \(\frac{(53 X 3) + (13 X 6) + (1 X 4) + (4 X 8)}{24}\)
= \(\frac{159 + 78 + 4 + 32}{24}\)
= \(\frac{273}{24}\)
= \(\frac{91}{8}\)
= 11\(\frac{3}{8}\)

Question 6.
-10 + 15 – (-6) + 5(-4) + \(\frac{16}{-8}\) = ______________
Answer:
-11
Explanation:
-10 + 15 – (-6) + 5(-4) + \(\frac{16}{-8}\)
= 5 + 6 – 20 – 2
= 11 – 22
= – 11

Question 7.
Solve for x: x – 8 = 16
Answer:
x = 24
Explanation:
Given, x – 8 = 16
x = 16 + 8
x = 24

Question 8.
Solve for x: 3x + 6 = 30
Answer:
x = 8
Explanation:
Given, 3x + 6 = 30
3x = 30 – 6
3x = 24
x = \(\frac{24}{3}\)
x = 8

Question 9.
Solve: 12 + (11 – 7)² – (16 ÷ 2) + 4(8 × 2) – 3(8 – 2) = ____________
Answer:
66
Explanation:
12 + (11 – 7)² – (16 ÷ 2) + 4(8 × 2) – 3(8 – 2)
= 12 + (4)² – (8) + 4(16) – 3(6)
= 12 + 16 – 8 + 64 – 18
= 28 – 8 + 64 – 18
= 20 + 64 – 18
= 84 – 18
= 66

Question 10.
Restate in exponent form, then solve: 4 × 4 × 4 × 3 × 3 + 5 × 5 = ______________
Answer:
4³ x 3² + 5² = 601
Explanation:
Given, 4 × 4 × 4 × 3 × 3 + 5 × 5
= 4³ x 3² + 5²
= 64 x 9 + 25
576 + 25
= 601

Question 11.
4.65 meters = _____________ inches (Use 2.54 cm = 1 inch)
Answer:
183.1 inches
Explanation:
Given, 4.65 meters
1m = 100 cm
4.65 x 100 = 465 cm
Given, 2.54 cm = 1 inch
465 ÷ 2.54 = 183.1 inches

Question 12.
16 yards = _____________ centimeters
Answer:
1463 yards
Explanation:
1 yard = 91.44
16 yards = 1463 yards

Question 13.
What is the area of the rectangle?

What is the perimeter of the rectangle?
Answer:
Area of the rectangle = 75 sq cm;
Perimeter of the rectangle = 40 cm.
Explanation:
Area of rectangle = length x breadth
length = 15 cm; breadth = 5 cm
A = 15 x 5 = 75 cm
Perimeter of Rectangle = 2 (l + b)
= 2(15 + 5)
= 40 cm

Question 14.
What is the area of the circle? (Use 3.14 for π)

What is the circumference of the circle?
Answer:
Area = 50.24 sq in;
Circumference = 25.12 in.
Explanation:
Area of the circle = π r²
r = 4 cm
A = 3.14 x 4 x 4
A = 50.24 sq in
The circumference of the circle (Use 3.14 for π)
C = 2πr
r = d/2 = 8/2 = 4
C = 2 x 3.14 x 4
C = 25.12 in.

Question 15.
Identify each angle as obtuse, acute, or right.

Answer:

Explanation:
Any angle that is greater than 90° but less than 180° is known as obtuse angle.
If two rays intersect at a vertex, forming an angle that is less than 90° is known as Acute Angle.
Any angle that is greater than 90° but less than 180° is known as obtuse angle.

Question 16.
Identify each triangle as scalene, isosceles, or equilateral.

Answer:

Explanation:
A scalene triangle is a triangle in which all three sides are in different lengths,
and all three angles are of different measures.
The sum of all the interior angles is always equal to 180 degrees.
An equilateral triangle is a triangle with all three sides of equal length.
An Isosceles triangle is a triangle with two equal sides.

Calculate and reduce the fractions.

Question 17.
\(\frac{5}{12}\) × 168 = _____________
Answer:
70
Explanation:
\(\frac{5}{12}\)
= \(\frac{5 X 168}{12}\)
= \(\frac{840}{12}\)
= 70

Question 18.
(\(\frac{1}{3}\) × \(\frac{9}{14}\)) × \(\frac{14}{3}\) = ____________
Answer:
1
Explanation:
(\(\frac{1}{3}\) × \(\frac{9}{14}\)) × \(\frac{14}{3}\)
= \(\frac{9}{42}\) × \(\frac{14}{3}\)
= \(\frac{9 X 14}{42 X 3}\)
= \(\frac{126}{126}\)
= 1

Question 19.
\(\frac{56}{65}\) ÷ 14 = ______________
Answer:
\(\frac{4}{65}\)
Explanation:
\(\frac{56}{65}\) ÷ 14
= \(\frac{56 ÷ 14}{65}\)
= \(\frac{4}{65}\)

Question 20.
Give the coordinates for points on the grid.
A __________
B __________
C __________
D __________
What is the slope of a line drawn between points D and A?

Answer:
A(1,3); B(-3,6); C(2, -5); D(-2,-2); \(\frac{5}{3}\)

Explanation:
The Cartesian plane, is a plane with a rectangular coordinate system,
that associates each point in the plane with a pair of numbers.
In the cartesian plane is defined as a two-dimensional coordinate plane,
which is formed by the intersection of the x-axis and y-axis.
The x-axis and y-axis intersect perpendicular to each other at the point called the origin.
the co-ordinates are A(1,3); B(-3,6); C(2, -5); D(-2,-2);
Slope:
The slope formula is m=(y2-y1)/(x2-x1),
or the change in the y values over the change in the x values.
The coordinates of the first point represent x1 and y1.
The coordinates of the second points are x2, y2.
The slope of a line drawn between points D and A \(\frac{5}{3}\).
D(-2, -2); A(1, 3)
m = \(\frac{y2 – y1}{x2 – x1}\)
m = \(\frac{3 – (-2)}{1 – (-2)}\)
m = \(\frac{3+2}{1+2}\)
m = \(\frac{5}{3}\)

Question 21.
What is the measure of angle DBC?

Answer:
27 °.

Explanation:
The sum of the two angles in right angle is 90°.
63° + x = 90°
x = 90° – 63°
x = 27°

Question 22.

Answer:
1.7
Explanation:
0.35 x 1000 = 350
0.595 x 1000 = 595

Question 23.

Answer:
0.18653
Explanation:
0.5596 x 10000 = 5596
3 x 10000 = 30000

Question 24.
What is 30% of .802?
Answer:
0.2406
Explanation:
30% of 0.802
\(\frac{30}{100}\) x 0.802
= \(\frac{30 X 0.802}{100}\)
= \(\frac{24.06}{100}\)
= 0.2406

Question 25.
What is \(\frac{3}{8}\) of 96%
Answer:
36%
Explanation:
\(\frac{3}{8}\) of 96%
= \(\frac{3 x 96}{8}\)%
= 3 x 12 %
= 36%

Question 26.
Restate 5.625 as an improper fraction and a mixed number.
Improper Fraction ______________
Mixed Number ______________
Answer:
Improper Fraction = \(\frac{45}{8}\)
Mixed Number = 5\(\frac{5}{8}\)
Explanation:
5.625 by multiplying 1000 and divided by 1000 as shown below to get in to p/q form
\(\frac{5.625 x 1000}{1000}\)
= \(\frac{5625}{1000}\)
= \(\frac{45}{8}\)
convert into mixed fraction,
= 5\(\frac{5}{8}\)

Question 27.
Put the following numbers in order from least to greatest.
2.356, 1.3561, 3.56302, 2.5631, 2.35692, 1.35688, 2.5622, 1.599
Answer:
1.3561, 1.35688, 1.599, 2.356, 2.35692, 2.5622, 2.5631, 3.56302
Explanation:
Arrange all the given numbers in ascending order by placing whole numbers first,
then decimals number with the least digit according to their place values.

Question 28.
Solve for x: \(\frac{45}{64}\) = \(\frac{x}{192}\)
Answer:
135
Explanation:
\(\frac{45}{64}\) = \(\frac{x}{192}\)
x = \(\frac{45 X 192}{64}\)
x = \(\frac{8640}{64}\)
x = 135

Question 29.
Restate 2\(\frac{7}{25}\) as a decimal.
Answer:
2.28
Explanation:
Convert the given mixed fraction to improper fraction,
2\(\frac{7}{25}\)
= \(\frac{57}{25}\)
Convert improper fraction into decimal,
= 2.28

Question 30.
An item costs you $13.50 to produce. What price would you charge if you wanted to mark up the item by 20%?
Answer:
$16.20
Explanation:
An item costs you $13.50 to produce.
if wanted to mark up the item by 20%,
20% of $13.50
\(\frac{20}{100}\) x 13.50
= \(\frac{20 X 13.50}{100}\)
= \(\frac{270}{100}\)
= 2.7
total price he should charge = 13.50 + 2.7
= $16.20

Question 31.
Darma deposits $500 in a bank account that earns 2.5% simple interest. How much money will she have in the account after 1 year? ____________
After 2 years? ____________
Answer:
After 1 year $512.50;
After 2 years $525.00.
Explanation:
Simple Interest SI = PTR/100
Principal = $500
Time T = 1 year
Rate of interest R = 2.5%
SI = (500 x 1 x 2.5)/100
SI = 1250/100
SI = 12.5
Amount after one year = $500 + $12.5
= $512.5
now
Principal = $512.5
Time T = 1 year
Rate of interest R = 2.5%
SI = (512.5 x 1 x 3)/100
SI = $12.8125
Amount after one year = $512.5 + $12.8125
= $525.3125 = $525

Question 32.
Identify each quadrilateral.

Answer:

Explanation:
A Square is a simple polygon with 4 equal sides and 4 right angles.
A Rectangle is a four sided-polygon, having all the internal angles equal to 90 degrees.
The two sides at each corner or vertex meet at the right angles.
The opposite sides of the rectangle are equal in length which makes it different from a square.
Rhombus is a quadrilateral with all equal sides.
Since opposite sides of a parallelogram are equal.
So, Rhombus is a special type of a parallelogram whose all sides are equal.
A kite is a flat shape with 4 straight sides that has two pairs of sides,
which are two adjacent sides that are equal in length.
A trapezoid is a flat closed shape having 4 straight sides,
with one pair of parallel sides.

Question 33.
Restate 4\(\frac{11}{13}\) as an improper fraction.
Answer:
\(\frac{63}{13}\)
Explanation:
To convert mixed fraction to improper fraction,
multiply the denominator with whole number and,
then add the numerator.
4\(\frac{11}{13}\)
= \(\frac{63}{13}\)

Question 34.
Restate \(\frac{73}{13}\) as a mixed number.
Answer:
5\(\frac{8}{13}\)
Explanation:
Convert improper fraction to mixed fraction, \(\frac{73}{13}\)
write the quotient as whole number and remainder as numerator..
quotient = 5
Remainder = 8
5\(\frac{8}{13}\)

Question 35.
\(\frac{6}{7}\) – \(\frac{2}{7}\) + \(\frac{5}{7}\) + \(\frac{3}{7}\) – \(\frac{1}{7}\) = ____________
Answer:
\(\frac{11}{7}\) or 1\(\frac{4}{7}\)
Explanation:
\(\frac{6}{7}\) – \(\frac{2}{7}\) + \(\frac{5}{7}\) + \(\frac{3}{7}\) – \(\frac{1}{7}\)
When all the denominators are same add or subtract the numerators.
\(\frac{(6 – 2 + 5 + 3 – 1)}{7}\)
= \(\frac{11}{7}\) or 1\(\frac{4}{7}\)

Question 36.
\(\frac{15}{16}\) × 3\(\frac{1}{5}\) = _____________
Answer:
3
Explanation:
\(\frac{15}{16}\) × 3\(\frac{1}{5}\)
convert mixed fraction to improper fraction
= \(\frac{15}{16}\) × \(\frac{16}{5}\)
= \(\frac{15 X 5}{16 X 16}\)
= \(\frac{75}{256}\)
= 0.29 = 3

Question 37.
10⁷ × 10² = ______________
Answer:
10⁹
Explanation:
a^m x aⁿ = a^{m + n}
10⁷ x 10² = 10⁷⁺²
= 10⁹

Question 38.
4⁶ ÷ 4² = ______________
Answer:
4⁴
Explanation:
a^m ÷ aⁿ = a^{m – n}
4⁶ ÷ 4² = 4^{6 – 2} = 4⁴
a⁴ = a x a x a x a
4⁴ = 4 x 4 x 4 x 4
= 16 x 16
= 256

Question 39.
What is 15²?
Answer:
225
Explanation:
a² = a x a
15² = 15 x 15
= 225

Question 40.
What is the square root of 169?
Answer:
13
Explanation:
The square root of 169 is expressed as √169 in the radical form
and as (169)^½ or (169)^0.5 in the exponent form.
The square root of 169 is 13.
It is the positive solution of the equation x² = 169.
The number 169 is a perfect square.

Question 41.
What is the mode of the data distribution?

What is the median?
Answer:
Mode = 57
Median = 57
Explanation:
32, 33, 42, 43, 46, 48, 54, 57, 57, 57, 61, 62, 64, 64, 66, 71, 74
Mode : mode is the number that appears most frequently in the collection of data.
In the above stem and leaf data 57 is observer 3 number of times,
mode is 57

Median : the median is the number in the middle. if the collection of data has an even numbers of addends, then the median is the average of the two middle numbers.

Question 42.
What is the range of the data in the box and-whisker plot?

Answer:
Range = 20
Explanation:

The range difference between the upper extreme to lower extreme
Range = 25 – 5 = 15

Question 43.
What fruit is the least preferred by the students? ____________
What is the second most preferred fruit? _______________

Answer:
The least fruit preferred by the students is Pineapple.
The second most preferred fruit by the students is Banana.
Explanation:
A pie chart is a pictorial representation of data in circular statistical graphic, which is divided into slices to illustrate numerical proportion.

In a pie chart, the arc length of each slice is proportional to the quantity it represents
The least fruit preferred by the students is Pineapple.
The second most preferred fruit by the students is Banana.

Question 44.
Clarence collected about 5 more stamps than what person? Who collected the second fewest stamps?

Answer:
Frank;
Barton.
Explanation:
Above Stamp collecting chart,
Clarence collected 55 stamps,
Clarence collected about 5 more stamps than Frank.
Barton collected 45 stamps and stood in the second fewest pace.

Question 45.
How many possible combinations are there?

Answer:
18
Explanation:
If an event can occur in ‘m’ different ways following,
which another event can occur in ‘n’ different ways,
following which a third event can occur in ‘p’ different ways.
The total number of occurrence to the events in the given order is m x n x p.
3 Breads,
3 Cold cuts,
3 Cheese
2 x 3 x 3 = 18
18 different combinations are possible from the choices.

Question 46.

Name two pairs of alternate interior angles.
___________ and ___________
___________ and ___________
Name two pairs of alternate exterior angles.
___________ and ___________
___________ and ___________
Name a pair of vertical angles.
___________ and ___________
Name two pairs of supplementary angles.
___________ and ___________
___________ and ___________
Answer:
Alternate interior angles:
\(\angle{D}\) and \(\angle{F}\);
\(\angle{E}\) and \(\angle{C}\).
Alternate exterior angles:
\(\angle{A}\) and \(\angle{G}\);
\(\angle{B}\) and \(\angle{H}\).
Vertical angles:
\(\angle{A}\) and \(\angle{C}\);
\(\angle{B}\) and \(\angle{D}\);
\(\angle{E}\) and \(\angle{G}\);
\(\angle{F}\) and \(\angle{H}\).
Supplementary angles:
\(\angle{A}\) and \(\angle{B}\);
\(\angle{B}\) and \(\angle{C}\);
\(\angle{A}\) and \(\angle{D}\);
\(\angle{F}\) and \(\angle{G}\);
\(\angle{D}\) and \(\angle{F}\);
\(\angle{G}\) and \(\angle{H}\);
\(\angle{H}\) and \(\angle{E}\);
\(\angle{H}\) and \(\angle{A}\).
\(\angle{G}\) and \(\angle{B}\);
\(\angle{E}\) and \(\angle{B}\).
\(\angle{F}\) and \(\angle{A}\).
Explanation:
Alternate interior angles:
The two angles, formed when a line crosses two other lines,
that lie on opposite sides of the transversal line and on opposite relative sides of the other lines.
If the two lines crossed are parallel, the alternate angles are equal
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines.
They lie on the inner side of the parallel lines but on the opposite sides of the transversal.
The transversal crosses through the two lines which are Coplanar at separate points.
Alternate exterior angles:
The term alternate exterior angles is often used when two lines are cut by a third line, a transversal .
The Alternate Exterior Angles Theorem states that if k and l are parallel ,
then the pairs of alternate exterior angles are congruent .
Vertical angles:
Vertical angles are angles opposite each other where two lines cross.
Supplementary angles:
The two angles or arcs whose sum is 180 degrees.

Question 47.
Use the Pythagorean Theorem to find the value of x.

Answer:
8
Explanation:

AC² = AB² + BC²
10² = x² + 6²
100 – 36 = AB²
AB² = 64
AB = 8
x = 8

Question 48.
Name 2 line segments.

Name 4 rays. ______________
Name a line. ______________
Answer:
Line segments:
\(\overline{AB}\), \(\overline{AF}\), \(\overline{AC}\), \(\overline{DB}\),\(\overline{BE}\), \(\overline{HG}\);
Rays:
\(\overline{AF}\), \(\overline{AC}\), \(\overline{BE}\), \(\overline{BD}\),
\(\overline{AB}\), \(\overline{BA}\);
Line:
\(\overline{AB}\)
Explanation:
A line segment is part of a line that has two endpoints and is finite in length.
A ray is a line segment that extends indefinitely in one direction.
A line has no end points.

Calculate the volume and surface area of the figures

Question 49.

Volume _____________
Surface Area ____________
Answer:
Volume = 24 cu in;
Surface Area = 52 sq in.
Explanation:
Volume = length x width x height
V = 2 x 4 x 3
V  = 24 cu in;
Surface Area = 2(lxw + wxh + hxl)
SA= 2(2×4 + 4×3 + 3×2)
SA = 2(8 + 12 + 6)
SA = 52 sq in.

Question 50.

Volume _____________
Surface Area ____________
Answer:
Volume = 288π cu units;
Surface Area = 168π sq units.
Explanation:
Volume = πr² h cu in
V = π 6² 8
V = π x 36 x 8
V = 288π cu in
Surface Area (SA)= 2πrh + 2πr²  sq in
SA = 2π x 6 x 8 + 2π 6²  sq yd
SA = 168π sq in

Question 51.

Volume ______________
Answer:
Volume = \(\frac{40}{3}\)π cubic units.
Explanation:
Volume of cone V= π r²h(1/3)
V = π 2²x 10 (1/3)
V = π 4 x 10 x 1/3
V = \(\frac{40}{3}\)π cu units;

Question 52.
Estimate the value of \(\sqrt{140}\) __________. Of \(\sqrt{48}\) ____________
Answer:
Estimate: 11.8;
6.9
Explanation:
\(\sqrt{140}\)
11 x 11 = 121
12 x 12 = 144
\(\sqrt{140}\) can estimate as nearer to 12
\(\sqrt{140}\) = 11.8
\(\sqrt{48}\)
6 x 6 = 36
7 x 7 = 49
\(\sqrt{48}\) can estimate as nearer to 7
\(\sqrt{48}\) = 6.9

Question 53.
Convert \(0 . \overline{573}\) to a fraction.
Answer:
\(\frac{573}{999}\) = \(\frac{191}{333}\)
Explanation:
\(0 . \overline{573}\)
Let
x = 0.573573573573 …….  Eq(1)
by multiplying 1000 on both sides
1000 x = 573.573573573…….Eq(2)
by subtracting Eq(1) from Eq(2) as shown below

999 x = 573
= \(\frac{573}{999}\)
Dividing both the numerator and denominator by 3
= \(\frac{573÷3}{999÷3}\)
= \(\frac{191}{333}\)

Question 54.
Solve 3(2x + 4) = 6(x + 2).
Answer:
Infinite solutions.
Explanation:
3(2x + 4) = 6(x + 2).
a(b+c) = a x b + a x c Distributive property
3(2x + 4) = 6(x + 2).
6x + 12 = 6x + 12
6x – 6x = 12 – 12
Infinite solutions.

Question 55.
Solve 26x + 4 = 6 + 26x – 3.
Answer:
No solutions.
Explanation:
26x + 4 = 6 + 26x – 3.
26x – 26x = 6 – 3 – 4
26x – 26x = 6 – 7
0 = – 1   No solutions.

Question 56.
Complete and graph the function table for y = x². Is it a linear or nonlinear function?

Answer:
Non Linear
Explanation:
A non-linear equation is such which does not form a straight line.
It looks like a curve in a graph and has a variable slope value.

Question 57.
Look at the graph below.

The function is increasing between points _______________
The function is decreasing between points _______________
Answer:
The function is increasing between points A and B;
The function is decreasing between points B and C.
Explanation:
The function is increasing between points A and B
y value is  increasing from negative to positive
i.e from third quadrant to second quadrant.
The function is decreasing between points B and C.
y value is  decreasing from positive to negative
i.e from  second quadrant to third quadrant

Question 58.
How many times greater is 12 × 10³ than 4 × 10²?
Answer:
30
Explanation:
\(\frac{12 × 10³}{4 x 10²}\)
= 3 x 10^3-2
= 3 x 10
= 30

Question 59.
Are these polygons similar? _____________ If so, what is the scale factor? _____________

Answer:
Yes,
Explanation:
Larger is 6 times bigger than the smaller.
Explanation:

So, when two polygons are similar,
then the ratio of the lengths of any two corresponding sides is called the scale factor.
This means that the ratio of all parts of a polygon is the same as the ratio of the sides.
using the figure above, the simplified ratios of the lengths of the corresponding sides of the similar trapezoids is the scale factor.
\(\frac{PQ}{AB}\) = \(\frac{90}{15}\) = 6
\(\frac{PR}{AC}\) = \(\frac{42}{7}\) = 6
Larger is 6 times bigger than the smaller.

Question 60.
What type of transformation is shown below?

Answer:
Translation:
Explanation:
A translation occurs when we take a figure and make an identical duplicate figure of it.
We can move the figure from left to right or bottom to top or up down.