Go Math Answer Key

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Unit Test Lessons 15-17 will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Unit Test Lessons 15-17 Answer Key

Restate in exponential form, then calculate.

Question 1.
2 × 2 × 2 × 2 + 3 × 3 × 3 _____________
Answer:
The given expression is 2 × 2 × 2 × 2 + 3 × 3 × 3.
The exponential form of above given expression is 2⁴ + 3³.
= 2⁴ + 3³
= 16 + 27
= 43
So, 2⁴ + 3³ is equal to 43.

Question 2.
4 × 4 × 4 × 4 – 5 × 5 × 5 _____________
Answer:
The given expression is 4 × 4 × 4 × 4 – 5 × 5 × 5.
The exponential form of above given expression is 4⁴ – 5³.
= 4⁴ – 5³
= 256 – 125
= 131
So, 4⁴ – 5³ is equal to 131.

Question 3.
2 × 2 × 2 × 2 × 2 × 2 + 6 × 6 – 5 × 5 _____________
Answer:
The given expression is 2 × 2 × 2 × 2 × 2 × 2 + 6 × 6 – 5 × 5.
The exponential form of above given expression is 2⁶ + 6² – 5².
= 2⁶ + 6² – 5²
= 64 + 36 – 25
= 75
So, 2⁶ + 6² – 5² is equal to 75.

Restate using scientific notation.

Question 4.
3,456,984.01 _____________
Answer:
The given number 3,456,984.01 already has a decimal move. Move the decimal to the left until have a number between 1 and 10. So, the number is 3.45698401.
Now count how many places the decimal moved. In this case, the decimal moved 6 places to the left, which means the power is positive.
The scientific notation for 3,456,984.01 is 3.45698401 x 10⁶.

Question 5.
8,694.1 _____________
Answer:
The given number 8,694.1 already has a decimal move. Move the decimal to the left until have a number between 1 and 10. So, the number is 8.6941.
Now count how many places the decimal moved. In this case, the decimal moved 3 places to the left, which means the power is positive.
The scientific notation for 8,694.1 is 8.6941 x 10³.

Question 6.
.00945 _____________
Answer:
The given number .00945 already has a decimal move. Move the decimal to the right until have a number between 1 and 10. So, the number is 9.45.
Now count how many places the decimal moved. In this case, the decimal moved 3 places to the right, which means the power is negative.
The scientific notation for .00945 is 9.45 x 10^-3.

Question 7.
1,094,659,041 _____________
Answer:
Place a decimal at the far right and move the decimal to the left until have a number between 1 and 10. So, the number is 1.094659041.
Now count how many places the decimal moved. In this case, the decimal moved 9 places to the left, which means the power is positive.
The scientific notation for 1,094,659,041 is 1.094659041 x 10⁹.

Question 8.
63.56 _____________
Answer:
The given number 63.56 already has a decimal move. Move the decimal to the left until have a number between 1 and 10. So, the number is 6.356.
Now count how many places the decimal moved. In this case, the decimal moved 1 places to the left, which means the power is positive.
The scientific notation for 63.56 is 6.356 x 10¹.

Calculate using order of operations (PEMDAS).

Question 9.
3 × (6 – 4)² + (15 – 5) × 5 + (5 – 3) × 4 + 3³ ________________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
3 × (6 – 4)² + (15 – 5) × 5 + (5 – 3) × 4 + 3³ = ?
First solve the parts that are inside parenthesis.
3 × 2² + 10 × 5 + 2 × 4 + 3³ = ?
Second solve the parts that have exponents.
3 × 4 + 10 × 5 + 2 × 4 + 27 = ?
Third perform multiplication operation.
12 + 50 + 8 + 27 = ?
Fourth perform Addition operation.
12 + 50 + 8 + 27 = 97
So, the expression 3 × (6 – 4)² + (15 – 5) × 5 + (5 – 3) × 4 + 3³ is equal to 97.

Question 10.
17 – (9 + 5) + (5 – 3) × 2 + (9 – 4)² ________________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
17 – (9 + 5) + (5 – 3) × 2 + (9 – 4)² = ?
First solve the parts that are inside parenthesis.
17 – 14 + 2 × 2 + 5² = ?
Second solve the parts that have exponents.
17 – 14 + 2 × 2 + 25 = ?
Third perform multiplication operation.
17 – 14 + 4 + 25 = ?
Fourth perform Addition and subtraction operation from left to right.
17 – 14 + 4 + 25 = ?
3 + 4 + 25 = 32
So, the expression 17 – (9 + 5) + (5 – 3) × 2 + (9 – 4)²  is equal to 32.

Question 11.
24 + (3 + 5) × 5 + (6 – 3)² ______________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
24 + (3 + 5) × 5 + (6 – 3)² = ?
First solve the parts that are inside parenthesis.
24 + 8 × 5 + 3² = ?
Second solve the parts that have exponents.
24 + 8 × 5 + 9 = ?
Third perform multiplication operation.
24 + 40 + 9 = ?
Fourth perform Addition operation.
24 + 40 + 9 = 73
So, the expression 24 + (3 + 5) × 5 + (6 – 3)²  is equal to 73.

Question 12.
33 – (4 – 2)³ + 6 × 2 + (5)² – 3 ______________
Answer:
We have to calculate the above given expression in order. The order of operation is PEMDAS. These letters stands for Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.
33 – (4 – 2)³ + 6 × 2 + (5)² – 3 = ?
First solve the parts that are inside parenthesis.
33 – 2³ + 6 × 2 + (5)² – 3= ?
Second solve the parts that have exponents.
33 – 8 + 6 × 2 + 25 – 3= ?
Third perform multiplication operation.
33 – 8 + 12 + 25 – 3 = ?
Fourth perform Addition and subtraction operation from left to right.
33 – 8 + 12 + 25 – 3 = ?
25 + 12 + 25 – 3 = ?
37 + 25 – 3 = ?
62 – 3 = 59
So, the expression 33 – (4 – 2)³ + 6 × 2 + (5)² – 3 is equal to 59.

What number property does each expression display?

Question 13.
3 + 4 + 5 = 5 + 4 + 3 ______________
Answer:
The expression 3 + 4 + 5 = 5 + 4 + 3 is commutative property of addition.
Explanation:
The commutative property of addition states that the addends are added in any order without changing the sum.
3 + 4 + 5 = 12
5 + 4 + 3 = 12

Question 14.
3(4 + 6) = 3(4) + 3(6) _______________
Answer:
The expression 3(4 + 6) = 3(4) + 3(6) is Distributive property of multiplication over addition.
Explanation:
The Distributive property of multiplication over addition states that when we multiply numbers, we have to multiply the numbers each separately and then add their products.
3(4 + 6) = 30
3(4) + 3(6) = 30

Question 15.
(15 + 16) + 18 = 15 + (16 + 18) ________________
Answer:
The expression (15 + 16) + 18 = 15 + (16 + 18) is Associative property of addition.
Explanation:
The Associative property of addition states that the addends are grouped in any way without changing the sum.
(15 + 16) + 18 = 49
15 + (16 + 18) = 49

Question 16.
34(1) = 34 _______________
Answer:
The expression 34(1) = 34 is Multiplication Identity property of 1.
Explanation:
In multiplication, the identity element is 1. Any factor or factors multiplying with 1 the product will not change.
34(1) = 34

Question 17.
3 + 0 = 3 _____________
Answer:
The expression 3 + 0 = 3 is Zero Identity of Addition.
Explanation:
In addition, the identity element is 0. Any addend + 0 will not change the total.
3 + 0 = 3

Question 18.
16(5 – 3) = (16 × 5) – (16 × 3) ______________
Answer:
The expression 16(5 – 3) = (16 × 5) – (16 × 3) is Distributive property of multiplication over subtraction.
Explanation:
The Distributive property of multiplication over subtraction states that when we multiply numbers, we have to multiply the numbers each separately and then subtract their products.
16(5 – 3) = 16(2) = 32
(16 × 5) – (16 × 3) = 80 – 48 = 32

Question 19.
15 × 5 = 5 × 15 _______________
Answer:
The expression 15 × 5 = 5 × 15 is commutative property of multiplication.
Explanation:
The commutative property of multiplication states that the numbers are multiplied in any order without changing the product.
15 × 5 = 75
5 × 15 = 75

Question 20.
33(0) + (33 + 0) = 0 + 33 = 33 ______________
Answer:
The expression 33(0) + (33 + 0) = 0 + 33 = 33 is Zero property of addition and multiplication.
Explanation:
Zero property of addition and multiplication states that any addend + 0 will not change the total and any number multiplied with 0 is equal to 0.
33(0) + (33 + 0) = 0 + 33 = 33

Question 21.
(7 × 4) × 20 = 7 × (4 × 20) _____________
Answer:
The expression (7 × 4) × 20 = 7 × (4 × 20) is Associative property of Multiplication.
Explanation:
The Associative property of multiplication states that the numbers are grouped in any way without changing the product.
(7 × 4) × 20 = 560
7 × (4 × 20) = 560

Solve for x.

Question 22.
4 + x = 7
Answer:
Given equation is 4 + x = 7.
To calculate x value we need to subtract both sides of the equation with 4.
x + 4 – 4= 7 – 4
x = 3

Question 23.
x – 5 = 12
Answer:
Given equation is x – 5 = 12
To calculate x value we need to add both sides of the equation with 5.
x – 5 + 5 = 12 + 5
x = 17

Question 24.
29 – x = 25
Answer:
Given equation is 29 – x = 25
To calculate x value we need to subtract both sides of the equation with 29.
29 – x – 29 = 25 – 29
– x = -4
x = 4

Question 25.
x + 30 = 90
Answer:
Given equation is x + 30 = 90
To calculate x value we need to subtract both sides of the equation with 30.
x + 30 – 30= 90 – 30
x = 60

Question 26.
4x + 5 = 13
Answer:
Given equation is 4x + 5 = 13
To calculate x value first we need to perform subtraction operation and then division operation.
Subtract 5 from 13 the difference is equal to 8.
4x = 13 – 5
4x = 8
x = 8/4
x = 2

Question 27.
3x – 5 = 13
Answer:
Given equation is 3x – 5 = 13
To calculate x value first we need to perform addition operation and then division operation.
Add 13 with 5 the sum is equal to 18
3x = 13 + 5
3x = 18
x = 18/3
x = 6

Question 28.
5x + 4 = 39
Answer:
Given equation is 5x + 4 = 39
To calculate x value first we need to perform subtraction operation and then division operation.
Subtract 4 from 39 the difference is equal to 35.
5x = 39 – 4
5x = 35
x = 35/5
x = 7

Question 29.
3x + 4 = 28
Answer:
Given equation is 3x + 4 = 28
To calculate x value first we need to perform subtraction operation and then division operation.
Subtract 4 from 28 the difference is equal to 24.
3x = 28 – 4
3x = 24
x = 24/3
x = 8

Question 30.
-4x + 4 = -28
Answer:
Given equation is -4x + 4 = -28
To calculate x value first change all numbers to one sides and variable to another side.
28 + 4 = 4x
Second perform addition operation and then division operation.
32 = 4x
32/4 = x
x = 8

Question 31.
\(\frac{x}{4}\) + 5 = 25
Answer:
Given equation is \(\frac{x}{4}\) + 5 = 25
To calculate x value first we have to perform subtraction operation and then multiplication operation.
\(\frac{x}{4}\) = 25 – 5
\(\frac{x}{4}\) = 20
x = 20 x 4
x = 80

Question 32.
\(\frac{x}{2}\) – 5 = 30
Answer:
Given equation is \(\frac{x}{2}\) – 5 = 30
To calculate x value first we have to perform addition operation and then multiplication operation.
\(\frac{x}{2}\) = 30 + 5
\(\frac{x}{2}\) = 35
x = 35 x 2
x = 70

Question 33.
\(\frac{2}{3}\)x – 4 = 26
Answer:
Given equation is \(\frac{2}{3}\)x – 4 = 26
To calculate x value first we have to perform addition operation, second multiplication operation and then division operation.
\(\frac{2}{3}\)x = 26 + 4
\(\frac{2}{3}\)x = 30
2x = 30 x 3
2x = 90
x = 90/2
x = 45

Find all the factors.

Question 34.
24
Answer:
The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Explanation:
The numbers that divide 24 exactly without leaving a remainder are the factors of 24. The number 24 is an even number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.

Question 35.
15
Answer:
The factors of 15 are 1, 3, 5 and 15.
Explanation:
The numbers that divide 15 exactly without leaving a remainder are the factors of 15. The number 15 is an odd number. The factors of 15 are 1, 3, 5 and 15.

Question 36.
20
Answer:
The factors of 20 are 1, 2, 4, 5, 10 and 20.
Explanation:
The numbers that divide 20 exactly without leaving a remainder are the factors of 20. The number 20 is an even number. The factors of 20 are 1, 2, 4, 5, 10 and 20.

Question 37.
8
Answer:
The factors of 8 are 1, 2, 4 and 8.
Explanation:
The numbers that divide 8 exactly without leaving a remainder are the factors of 8. The number 8 is an even number. The factors of 8 are 1, 2, 4 and 8.

Question 38.
13
Answer:
The factors of 13 are 1, 13.
Explanation:
The numbers that divide 13 exactly without leaving a remainder are the factors of 13. The number 13 is an odd number. The factors of 13 are 1,13.

Question 39.
21
Answer:
The factors of 21 are 1, 3, 7 and 21.
Explanation:
The numbers that divide 21 exactly without leaving a remainder are the factors of 21. The number 21 is an odd number. The factors of 21 are 1, 3, 7 and 21.

List the first five multiples.

Question 40.
5
Answer:
The first five multiples of 5 are 5,10,15, 20, 25.

Question 41.
3
Answer:
The first five multiples of 3 are 3, 6, 9, 12, 15.

Question 42.
7
Answer:
The first five multiples of 7 are 7,14, 21, 28, 35.

Question 43.
11
Answer:
The first five multiples of 11 are 11, 22, 33, 44, 55.

Solve the inequalities.

Question 44.
2x ≤ 14
Answer:
The given equation is 2x ≤ 14.
Divide both sides of the equation by 2.
2x/2 ≤ 14/2
x ≤ 7
The value of x should be less than or equal to 7.

Question 45.
x + 8 ≥ 2
Answer:
The given equation is x + 8 ≥ 2.
Subtract both sides of the equation with 8.
x + 8 – 8 ≥ 2 – 8
x ≥ – 6
The value of x should be greater than or equal to -6.

Question 46.
3 < \(\frac{x}{6}\)
Answer:
The given equation is 3 < \(\frac{x}{6}\).
Multiply both sides of the equation with 6.
3 x 6 < \(\frac{x}{6}\) x 6
18 < x
The value of x should be greater than 18.

Question 47.
x – 7 > 4
Answer:
The given equation is x – 7 > 4.
Add both sides of the equation with 7.
x – 7 + 7 > 4 + 7
x > 11
The value of x should be greater than 11.

Question 48.
x + 3x > 16
Answer:
The given equation is x + 3x > 16.
4x > 16
Divide both sides of the equation by 4.
4x/4 > 16/4
x > 4
The value of x should be greater than 4.

Question 49.
Elba has four tiles marked 1, 2, 3, and 4. If she needs to choose a tile that solves the equation x – 1 > 2, which one will she choose?
Answer:
Elba has four tiles marked 1, 2, 3, and 4.
If she choose a tile 1 then the equation becomes 0 > 2. So, she will not choose tile 1.
If she choose a tile 2 then the equation becomes 1 > 2. So, she will not choose tile 2.
If she choose a tile 3 then the equation becomes 2 > 2. So, she will not choose tile 3.
If she choose a tile 4 then the equation becomes 3 > 2. So, she will choose tile 4.

Question 50.
Vicki’s mother tells her to pack at least 4 shirts for a trip. Write an inequality that expresses that command, using the letter x for the number of shirts.
Answer:
Vicki’s mother tells her to pack at least 4 shirts for a trip. Which means 4 shirts or more.
The inequality that expresses the command is x ≥ 4.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 4.3 Absolute Value will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 4.3 Absolute Value

Exercises
Solve

Question 1.
|-3| = ____
Answer:
The absolute value of |-3| = 0.

Explanation:
The absolute value is the distance between a number and zero.
The distance between −3 and 0 is 3 .

Question 2.
|-26| = ____
Answer:
The absolute value  of |-26| = 26.

Explanation:
The absolute value is the distance between a number and zero.
The distance between -26 and 0 is 26. .

Question 3.
|423| = ____
Answer:
The absolute value of |423| = 423.

Explanation:
The absolute value is the distance between a number and zero.
The distance between 423  and 0 is 423 .

Question 4.
|-.7| = ____
Answer:
The absolute value of |-.7| = .7.

Explanation:
The absolute value is the distance between a number and zero.
The distance between -.7 and 0 = .7.

Question 5.
|-\(\frac{5}{6}\)| = ____
Answer:
The absolute value of |-\(\frac{5}{6}\)| = \(\frac{5}{6}\).

Explanation:
The absolute value is the distance between a number and zero.
The distance between –\(\frac{5}{6}\) and 0 = \(\frac{5}{6}\) .

Question 6.
|\(\frac{2}{3}\)| = ____
Answer:
The absolute value of |\(\frac{2}{3}\)| = \(\frac{2}{3}\).

Explanation:
The absolute value is the distance between a number and zero.
The distance between \(\frac{2}{3}\) and 0 =  \(\frac{2}{3}\).

Compare using <, >, or =.

Question 7.
|—6| ____ |—7|
Answer:
|—6| < |—7|

Explanation:
|—6| = 6.
|—7| = 7.
6 is lesser than 7.

Question 8.
|21| ___ |—21|
Answer:
|21| = |—21|

Explanation:
|21| = 21.
|—21| = 21.
|21| is equal to  |—21|.

Question 9.
|—8| ___ |—4|
Answer:
|—8| > |—4|

Explanation:
|—8| = 8.
|—4| = 4.
8 is greater than 4.

Question 10.
|—5| ___ |7|
Answer:
|—5| < |7|

Explanation:
|—5| = 5.
|7| = 7.
5 is lesser than 7.

Question 11.
|10| ______ |—12|
Answer:
|10| < |—12|

Explanation:
|10| = 10.
|—12| = 12.
10 is lesser than 12.

Question 12.
|423| ______ |425|
Answer:
|423| < |425|

Explanation:
|423| = 423.
|425| = 425.
423 is lesser than 425.

Question 13.
If Elena’s bank account balance is -$53.86, how much would she need to deposit in order to bring her balance to $10.00? ________
Answer:
$63.86 she needs to deposit in order to bring her balance to $10.00.

Explanation:
Amount of Elena’s bank account = -$53.86.
Amount of Elena’s needs to get the balance to $10.00:
-$53.86 + ?? = $10.
=> ?? = $10 + $53.86
=> ?? = $63.86.

Question 14.
If the temperature was 4 degrees lower than normal on Tuesday and 6 degrees higher than normal on Wednesday, which day’s temperature was more different than normal?
Answer:
Tuesday’s temperature was more different than normal because its decreasing than normal temperature.

Explanation:
Let the normal temperature be x.
Temperature on Tuesday = x – 4.
Temperature on Wednesday = x  + 6.

Question 15.
Vivian’s bank account balance is -$3.46. Evelyn’s bank account balance is -$2.98. Who has the greater debt? _______________________
Answer:
Amount of Vivian’s bank account has greater debt than Amount of Evelyn’s bank account which say his debt are more.

Explanation:
Amount of Vivian’s bank account = -$3.46.
Amount of Evelyn’s bank account = -$2.98.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 5.1 Plotting Ordered Pairs will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 5.1 Plotting Ordered Pairs

Exercises Give Ordered Pairs

Question 1.
Give the ordered pair for each point on the graph.

Answer:

Explanation:
Ordered pairs of points in the graph:
A = (1,2)
B = (3,-3)
C = (-5,-5)
D = (5,5)
E = (4,-5)
F = (1,1)
G = (-1,1)
H = (-4,4)
I = (8,8)
J = (-5,6)

Exercises
Plot Ordered Pairs

Plot the ordered pairs on the graph.

Question 1.
A(2, 3)
Answer:

Explanation:
A(2, 3) represents (x, y) axis points in the graph.

Question 2.
B(4, -4)
Answer:

Explanation:
B(4, -4)represents (x, y) axis points in the graph.

Question 3.
C(4, 4)
Answer:

Explanation:
C(4, 4) represents C(x, y) axis points in the graph.

Question 4.
D(-4, 4)
Answer:

Explanation:
D(-4, 4) represents D(x, y) axis points in the graph.

Question 5.
E(-4, 4)
Answer:

Explanation:
E(-4, 4) represents E(x, y) axis points in the graph.

Question 6.
F(5, 2)
Answer:

Explanation:
F(5, 2) represents F(x, y) axis points in the graph.

Question 7.
G(8, 2)
Answer:

Explanation:
G(8, 2) represents G(x, y) axis points in the graph.

Question 8.
H(8, 6)
Answer:

Explanation:
H(8, 6) represents H(x, y) axis points in the graph.

Question 9.
J(-5, 6)
Answer:

Explanation:
J(-5, 6) represents J(x, y) axis points in the graph.

Question 10.
K(3, -4)
Answer:

Explanation:
K(3, -4)represents K(x, y) axis points in the graph.

Question 11.
L(-2, -2)
Answer:

Explanation:
L(-2, -2) represents L(x, y) axis points in the graph.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 5.2 Distance will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 5.2 Distance

Exercises
Find The Distance Between The Points

Question 1.
(2, 5) and (2, 8) _________
Answer:

Explanation:
1. coordinates points = (2,5)
2. coordinates points = (2,8)
Distance between the two points = 3.

Question 2.
(-2, 1) and (-2, 3) _________
Answer:

Explanation:
1. coordinates points = (-2, 1)
2. coordinates points = (-2, 3)
Distance between the two points = 2.

Question 3.
(1, -4) and (1, 1) _________
Answer:

Explanation:
1. coordinates points = (1, -4)
2. coordinates points = (1, 1)
Distance between the two points = 5.

Question 4.
(3, 2) and (6, 2) _____
Answer:

Explanation:
1. coordinates points = (3, 2)
2. coordinates points = (6, 2)
Distance between the two points = 3.

Question 5.
(2, 3) and (-2, 3) _____
Answer:

Explanation:
1. coordinates points = (2,3)
2. coordinates points = (-2, 3)
Distance between the two points = 4.

Question 6.
(-4, -1) and (3, -1) _____
Answer:

Explanation:
1. coordinates points = (-4, -1)
2. coordinates points = (3, -1)
Distance between the two points = 7.

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 6.1 Changing Improper Fractions to Mixed Numbers will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 6.1 Changing Improper Fractions to Mixed Numbers

Exercises
Change to Mixed Numbers

Question 1.
\(\frac{22}{7}\)
Answer:
Mixed fraction of \(\frac{22}{7}\) = 3\(\frac{1}{7}\)

Explanation:
\(\frac{22}{7}\) = 3 + \(\frac{1}{7}\)
= 3\(\frac{1}{7}\)

Question 2.
\(\frac{35}{4}\)
Answer:
Mixed fraction of \(\frac{35}{4}\) = 8\(\frac{3}{4}\)

Explanation:
\(\frac{35}{4}\) = 8 + \(\frac{3}{4}\)
= 8 \(\frac{3}{4}\)

Question 3.
\(\frac{73}{10}\)
Answer:
Mixed fraction of \(\frac{73}{10}\) = 7\(\frac{3}{10}\)

Explanation:
\(\frac{73}{10}\) = 7 + \(\frac{3}{10}\)
= 7\(\frac{3}{10}\)

Question 4.
\(\frac{47}{3}\)
Answer:
Mixed fraction of \(\frac{47}{3}\) = 15\(\frac{2}{3}\)

Explanation:
\(\frac{47}{3}\) = 15 + \(\frac{2}{3}\)
= 15\(\frac{2}{3}\)

Question 5.
\(\frac{87}{11}\)
Answer:
Mixed fraction of \(\frac{87}{11}\) = 7\(\frac{10}{11}\)

Explanation:
\(\frac{87}{11}\) = 7 + \(\frac{10}{11}\)
= 7\(\frac{10}{11}\)

Question 6.
\(\frac{35}{6}\)
Answer:
Mixed fraction of \(\frac{35}{6}\) = 5\(\frac{5}{6}\)

Explanation:
\(\frac{35}{6}\) = 5 + \(\frac{5}{6}\)
= 5\(\frac{5}{6}\)

Question 7.
\(\frac{26}{5}\)
Answer:
Mixed fraction of \(\frac{26}{5}\) = 5\(\frac{1}{5}\)

Explanation:
\(\frac{26}{5}\) = 5 + \(\frac{1}{5}\)
= 5\(\frac{1}{5}\)

Question 8.
\(\frac{111}{8}\)
Answer:
Mixed fraction of latex]\frac{111}{8}[/latex] = 13\(\frac{7}{8}\)

Explanation:
latex]\frac{111}{8}[/latex] = 13 + latex]\frac{7}{8}[/latex]
= 13\(\frac{7}{8}\)

Question 9.
\(\frac{32}{3}\)
Answer:
Mixed fraction of \(\frac{32}{3}\) = 10\(\frac{2}{3}\)

Explanation:
\(\frac{32}{3}\) = 10 + \(\frac{2}{3}\)
= 10\(\frac{2}{3}\)

Question 10.
\(\frac{66}{5}\)
Answer:
Mixed fraction of \(\frac{66}{5}\) = 13\(\frac{1}{5}\)

Explanation:
\(\frac{66}{5}\) = 13 + \(\frac{1}{5}\)
= 13\(\frac{1}{5}\)

Question 11.
\(\frac{211}{11}\)
Answer:
Mixed fraction of \(\frac{211}{11}\) = 19\(\frac{2}{11}\)

Explanation:
\(\frac{211}{11}\) = 19 + \(\frac{2}{11}\)
= 19\(\frac{2}{11}\)

Question 12.
\(\frac{21}{4}\)
Answer:
Mixed fraction of \(\frac{21}{4}\) = 5\(\frac{1}{4}\)

Explanation:
\(\frac{21}{4}\) = 5 + \(\frac{1}{4}\)
= 5\(\frac{1}{4}\)

Question 13.
\(\frac{78}{7}\)
Answer:
Mixed fraction of \(\frac{78}{7}\) = 11\(\frac{1}{7}\)

Explanation:
\(\frac{78}{7}\) = 11 + \(\frac{1}{7}\)
= 11\(\frac{1}{7}\)

Question 14.
\(\frac{82}{9}\)
Answer:
Mixed fraction of \(\frac{82}{9}\) = 9\(\frac{1}{9}\)

Explanation:
latex]\frac{82}{9}[/latex] = 9 + \(\frac{1}{9}\)
= 9\(\frac{1}{9}\)

Question 15.
\(\frac{13}{2}\)
Answer:
Mixed fraction of \(\frac{13}{2}\) = 6\(\frac{1}{2}\)

Explanation:
\(\frac{13}{2}\) = 6 + \(\frac{1}{2}\)
= 6\(\frac{1}{2}\)

Question 16.
\(\frac{67}{4}\)
Answer:
Mixed fraction of \(\frac{67}{4}\) = 16\(\frac{3}{4}\)

Explanation:
\(\frac{67}{4}\) = 16 + \(\frac{3}{4}\)
= 16\(\frac{3}{4}\)

Question 17.
\(\frac{11}{8}\)
Answer:
Mixed fraction of \(\frac{11}{8}\) = 1\(\frac{3}{8}\)

Explanation:
\(\frac{11}{8}\) = 1 + \(\frac{3}{8}\)
= 1\(\frac{3}{8}\)

Question 18.
\(\frac{43}{14}\)
Answer:
Mixed fraction of \(\frac{43}{14}\) = 3\(\frac{1}{14}\)

Explanation:
\(\frac{43}{14}\) = 3 + \(\frac{1}{14}\)
= 3\(\frac{1}{14}\)

Question 19.
\(\frac{137}{13}\)
Answer:
Mixed fraction of \(\frac{137}{13}\) = 10\(\frac{7}{13}\)

Explanation:
\(\frac{137}{13}\) = 10 + \(\frac{7}{13}\)
= 10\(\frac{7}{13}\)

Question 20.
\(\frac{45}{2}\)
Answer:
Mixed fraction of \(\frac{45}{2}\) = 22\(\frac{1}{2}\)

Explanation:
\(\frac{45}{2}\) = 22 + \(\frac{1}{2}\)
= 22\(\frac{1}{2}\)

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 6.2 Changing Mixed Numbers to Improper Fractions will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 6.2 Changing Mixed Numbers to Improper Fractions

Exercises
Change to Improper Fractions

Question 1.
2\(\frac{2}{3}\)
Answer:
Improper fraction of 2\(\frac{2}{3}\) = \(\frac{8}{3}\)

Explanation:
2\(\frac{2}{3}\) = [(2 × 3) + 2] ÷ 3
= (6 + 2) ÷ 3
= \(\frac{8}{3}\)

Question 2.
5\(\frac{4}{7}\)
Answer:
Improper fraction of 5\(\frac{4}{7}\) = \(\frac{39}{7}\)

Explanation:
5\(\frac{4}{7}\) = [(5 × 7) + 4)] ÷ 7
= (35 + 4) ÷ 7
= \(\frac{39}{7}\)

Question 3.
21\(\frac{3}{5}\)
Answer:
Improper fraction of 21\(\frac{3}{5}\) = \(\frac{108}{5}\)

Explanation:
21\(\frac{3}{5}\) = [(21 × 5) + 3)] ÷ 5
= (105 + 3) ÷ 5
= \(\frac{108}{5}\)

Question 4.
5\(\frac{3}{8}\)
Answer:
Improper fraction of 5\(\frac{3}{8}\) =

Explanation:
5\(\frac{3}{8}\) = [(5 × 8) + 3] ÷ 8
= (40 + 3) ÷ 8
= \(\frac{43}{8}\)

Question 5.
22\(\frac{6}{7}\)
Answer:
Improper fraction of 22\(\frac{6}{7}\) = \(\frac{160}{7}\)

Explanation:
22\(\frac{6}{7}\) = [(22 × 7) + 6] ÷ 7
= (154 + 6) ÷ 7
= \(\frac{160}{7}\)

Question 6.
15\(\frac{4}{11}\)
Answer:
Improper fraction of 5\(\frac{4}{11}\) = \(\frac{59}{11}\)

Explanation:
5\(\frac{4}{11}\) = [(5 × 11) + 4] ÷ 11
= (55 + 4) ÷ 11
= \(\frac{59}{11}\)

Question 7.
13\(\frac{2}{3}\)
Answer:
Improper fraction of 13\(\frac{2}{3}\) = \(\frac{41}{3}\)

Explanation:
13\(\frac{2}{3}\) = [(13 × 3) + 2] ÷ 3
= (39 + 2) ÷ 3
= \(\frac{41}{3}\)

Question 8.
3\(\frac{11}{17}\)
Answer:
Improper fraction of 3\(\frac{11}{17}\) = \(\frac{62}{17}\)

Explanation:
3\(\frac{11}{17}\) = [(3 × 17) + 11] ÷ 17
= (51 + 11) ÷ 17
= \(\frac{62}{17}\)

Question 9.
2\(\frac{4}{19}\)
Answer:
Improper fraction of 2\(\frac{4}{19}\) = \(\frac{42}{19}\)

Explanation:
2\(\frac{4}{19}\) = [(2 × 19) + 4] ÷ 19
= (38 + 4) ÷ 19
= \(\frac{42}{19}\)

Question 10.
6\(\frac{3}{4}\)
Answer:
Improper fraction of 6\(\frac{3}{4}\) = \(\frac{27}{4}\)

Explanation:
6\(\frac{3}{4}\) = [(6 × 4) + 3] ÷ 4
= (24 + 3) ÷ 4
= \(\frac{27}{4}\)

Question 11.
1\(\frac{1}{51}\)
Answer:
Improper fraction of 1\(\frac{1}{51}\) = \(\frac{52}{51}\)

Explanation:
1\(\frac{1}{51}\) = [(1 × 51) + 1] ÷ 51
= (51 + 1) ÷ 51
= \(\frac{52}{51}\)

Question 12.
55\(\frac{1}{2}\)
Answer:
Improper fraction of 55\(\frac{1}{2}\) = \(\frac{111}{2}\)

Explanation:
55\(\frac{1}{2}\) = [(55 × 2) + 1] ÷ 2
= (110 + 1) ÷ 2
= \(\frac{111}{2}\)

Question 13.
10\(\frac{2}{23}\)
Answer:
Improper fraction of 10\(\frac{2}{23}\) = \(\frac{232}{23}\)

Explanation:
10\(\frac{2}{23}\) = [(10 × 23) + 2] ÷ 23
= (230 + 2) ÷ 23
= \(\frac{232}{23}\)

Question 14.
6\(\frac{4}{7}\)
Answer:
Improper fraction of 6\(\frac{4}{7}\) = \(\frac{46}{7}\)

Explanation:
6\(\frac{4}{7}\) = [(6 × 7) + 4] ÷ 4
= (42 + 4) ÷ 4
= \(\frac{46}{7}\)

Question 15.
13\(\frac{2}{7}\)
Answer:
Improper fraction of 13\(\frac{2}{7}\) = \(\frac{93}{7}\)

Explanation:
13\(\frac{2}{7}\) = [(13 × 7) + 2] ÷ 7
= [91 + 2) ÷ 7
= \(\frac{93}{7}\)

Question 16.
42\(\frac{1}{3}\)
Answer:
Improper fraction of 42\(\frac{1}{3}\) = \(\frac{127}{3}\)

Explanation:
42\(\frac{1}{3}\) = [(42 × 3) + 1] ÷ 3
= (126 + 1) ÷ 3
= \(\frac{127}{3}\)

Question 17.
5\(\frac{1}{19}\)
Answer:
Improper fraction of 5\(\frac{1}{19}\) = \(\frac{96}{19}\)

Explanation:
5\(\frac{1}{19}\) = [(5 × 19) + 1] ÷ 19
= (95 + 1) ÷ 19
= \(\frac{96}{19}\)

Question 18.
12\(\frac{2}{3}\)
Answer:
Improper fraction of 12\(\frac{2}{3}\) = \(\frac{38}{3}\)

Explanation:
12\(\frac{2}{3}\) = [(12 × 3) + 2] ÷ 3
= (36 + 2) ÷ 3
= \(\frac{38}{3}\)

Question 19.
2\(\frac{3}{4}\)
Answer:
Improper fraction of 2\(\frac{3}{4}\) = \(\frac{11}{4}\)

Explanation:
2\(\frac{3}{4}\) = [(2 × 4) + 3] ÷ 4
= (8 + 3) ÷ 4
= \(\frac{11}{4}\)

Question 20.
200\(\frac{33}{100}\)
Answer:
Improper fraction of 200\(\frac{33}{100}\) = \(\frac{20033}{100}\)

Explanation:
200\(\frac{33}{100}\) = [(200 × 100) + 33] ÷ 100
= (20000 + 33) ÷ 100
= \(\frac{20033}{100}\)

Practice questions available in McGraw Hill Math Grade 6 Answer Key PDF Lesson 25.1 Measures of Central Tendency (Mean, Median, Range) will engage students and is a great way of informal assessment.

McGraw-Hill Math Grade 6 Answer Key Lesson 25.1 Measures of Central Tendency (Mean, Median, Range)

Exercise

CALCULATE

Question 1.
What is the range for this set of numbers?
1, 8, 14, 22, 13, 19
Answer:
Given data is 1, 8, 14, 22, 13, 19
lowest number = 1
highest number = 22
range = high – low
range = 22 – 21
So, the range of the number is 21

Question 2.
What is the average for this set of numbers?
2, 2, 3, 3, 4, 6, 6, 10
Answer:
Given data is 2, 2, 3, 3, 4, 6, 6, 10
lowest number = 2
highest number = 10
Range = 10 – 2 = 8
So, the range of the number is 8.

Question 3.
What is the mode of this set of numbers?
2, 5, 10, 15, 6, 5, 6, 2, 5
Answer:
Given data is 2, 5, 10, 15, 6, 5, 6, 2, 5
2 – 2 times
5 – 3 times
6 – 2 times
10 – 1 time
15 – 1 time
The number 5 is repeated 3 times.
So, the mode is 5.

Question 4.
What is the median for this set of numbers?
3, 7, 2, 8, 9, 4, 6
Answer:
Given data 3, 7, 2, 8, 9, 4, 6
Set the numbers in the ascending or descending order.
2, 3, 4, 6, 7, 8, 9
The Median is the middle number.
Here 6 is in the middle.
So, the median is 6.

Question 5.
What is the range for this set of numbers?
2, 4, 9, 34, 35, 42, 15, 14
Answer:
Given data is 2, 4, 9, 34, 35, 42, 15, 14
Low number = 2
Highest number = 42
Range = 42 – 2
Range = 40
So, the range of the numbers is 40.

Question 6.
What is the mean for this set of numbers?
10, 20, 30, 69, 79, 89, 3
Answer:
Given data is 10, 20, 30, 69, 79, 89, 3
Mean = sum of observations/number of observations
Mean = (10 + 20 + 30 + 69 + 79 + 89 + 3)/7
Mean = 42.8
So, the mean of the set of numbers is 42.8

Question 7.
George earns tips of $10 for Sunday, $15 for Monday, and $35 for Tuesday. What is the average of his tips for the three days?
Answer:
Given data,
George earns tips of $10 for Sunday, $15 for Monday, and $35 for Tuesday.
Average = (10 + 15 + 35)/3
Average = 60/3
Average = 20
Therefore the average of his tips for the three days is $20.

Question 8.
If a group of 20 students in a class has an average age of 13 years, what would happen to the average if a student who was 12 years old was replaced with a student who was 14 years old?
Answer:
The average age of 20 students is 13.
sum/20 = 13
sum = 13 × 20
sum = 260
average = (12 + 14)/2 = 13
If 12 years old was replaced with a student who was 14 years old
average = (14 + 14)/2 = 14
So, the average becomes 14.

All the solutions provided in McGraw Hill Math Grade 1 Answer Key PDF Chapter 6 Lesson 1 Counting from 100 to 120 by 1s as per the latest syllabus guidelines.

McGraw-Hill Math Grade 1 Answer Key Chapter 6 Lesson 1 Counting from 100 to 120 by 1s

Count

Write the missing numbers.

Question 1.
Count from 100 to 103.
100 101 102 103
Explanation:
The given pattern is skip by ones
In skip by ones we add one to it

Question 2.
Count from 106 to 108.
___ ___ ____
Answer:
106 107 108
Explanation:
The given pattern is skip by ones
In skip by ones we add one to it

Question 3.
Count from 111 to 113.
___ ___ ____
Answer:
111 112 113
Explanation:
The given pattern is skip by ones
In skip by ones we add one to it

Question 4.
Count from 112 to 114.
___ ___ ____
Answer:
112 113 114
Explanation:
The given pattern is skip by ones
In skip by ones we add one to it

Question 5.
Count from 105 to 107.
___ ___ ____
Answer:
105 106 107
Explanation:
The given pattern is skip by ones
In skip by ones we add one to it

Question 6.
Count from 102 to 104.
___ ___ ____
Answer:
102 103 104
Explanation:
The given pattern is skip by ones
In skip by ones we add one to it

All the solutions provided in McGraw Hill Math Grade 1 Answer Key PDF Chapter 6 Lesson 2 Counting from 0 to 120 by 10s as per the latest syllabus guidelines.

McGraw-Hill Math Grade 1 Answer Key Chapter 6 Lesson 2 Counting from 0 to 120 by 10s

Count

Count by tens out loud. Write the missing numbers.

Question 1.
Count from 10 to 40 by 10s.
10 20 30 40
Explanation:
The given pattern is skip by tens
In skip by tens we have  to add ten to it

Question 2.
Count from 80 to 110 by 10s.
80 90 ___ ___
Answer:
80 90 100 110
Explanation:
The given pattern is skip by tens
In skip by tens we have to  add ten to it

Question 3.
Count from 20 to 50 by 10s.
____ ____ ___ ___
Answer:
20 30 40 50
Explanation:
The given pattern is skip by tens
In skip by tens we have to  add ten to it

Question 4.
Count from 80 to 110 by 10s.
___ ____ ___ ___
Answer:
80 90 100 110
Explanation:
The given pattern is skip by tens
In skip by tens we have to  add ten to it

Question 5.
Count from 0 to 30 by 10s.
___ ___ ___ ___
Answer:
0 10 20 30
Explanation:
The given pattern is skip by tens
In skip by tens we have to  add ten to it

Question 6.
Count from 50 to 80 by 10s.
___ ___ ____ ____
Answer:
50 60 70 80
Explanation:
The given pattern is skip by tens
In skip by tens we have to  add ten to it

All the solutions provided in McGraw Hill Math Grade 1 Answer Key PDF Chapter 6 Lesson 3 Counting from 0 to 100 by 5s as per the latest syllabus guidelines.

McGraw-Hill Math Grade 1 Answer Key Chapter 6 Lesson 3 Counting from 0 to 100 by 5s

Çount

Count by 5s. Write the numbers.

Question 1.
Count from 5 to 20 by 5s.
5 10 15 20
Explanation:
The given pattern is skip by fives
In skip by fives we have to add five to it

Question 2.
Count from 30 to 45 by 5s.
30 35 ____ ____
Answer:
30 35 40 45
Explanation:
The given pattern is skip by fives
In skip by fives we have to add five to it

Question 3.
Count from 55 to 70 by 5s.
55 60 ____ ___
Answer:
55 60 65 70
Explanation:
The given pattern is skip by fives
In skip by fives we have to add five to it

Question 4.
Count from 35 to 50 by 5s.
___ ___ ___ ____
Answer:
35 40 45 50
Explanation:
The given pattern is skip by fives
In skip by fives we have to add five to it

Question 5.
Count from 60 to 75 by 5s.
___ ___ ___ ____
Answer:
60 65 70 75
Explanation:
The given pattern is skip by fives
In skip by fives we have to add five to it

Question 6.
Count from 80 to 95 by 5s.
___ ___ ___ ____
Answer:
80 85 90 95
Explanation:
The given pattern is skip by fives
In skip by fives we have to add five to it