McGraw Hill Math

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 18.1 Customary Units of Length existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 18.1 Customary Units of Length

Exercises
CALCULATE
Question 1.
12.5 feet is how many yards?
Answer:
12.5 feet is equal to 4.16 yards.

Explanation:
Conversion:
1 yard = 3 feet.
?? yards = 12.5 feet
=> 12.5 × 1 = 3 × ??
=> 12.5 ÷ 3 = ??
=> 4.16 yards.

Question 2.
1 mile is how many feet?
Answer:
1 mile is equal to 5280 feet.

Explanation:
Conversion:
1 mile = 5280 feet.
1 mile = ?? feet
=> 1 × ?? = 5280 × 1
=> ?? = 5280 feet.

Question 3.
144 inches is how many yards?
Answer:
144 inches is equal tp 4 yards.

Explanation:
Conversion:
1 yard = 36 inches.
?? yards = 144 inches.
=> 144 × 1 = 36 × ??
=> 144 ÷ 36 = ??
=> 4 yards.

Question 4.
3 miles is how many yards?
Answer:
3 miles is equal to 5,280 yards.

Explanation:
Conversion:
1 mile = 1760 yards.
3 miles = ?? yards.
=> 1 × ?? = 1760 × 3
=> ?? = 5,280 yards.

Question 5.
128 inches is how many feet?
Answer:
128 inches is equal to 10.66 feet.

Explanation:
Conversion:
1 feet = 12 inches.
?? feet = 128 inches.
=> 1 × 128 = 12 × ??
=> 128 ÷ 12 = ??
=> ?? = 10.66 feet.

Question 6.
10,560 yards is how many miles?
Answer:
10,560 yards is equal to  6 miles.

Explanation:
Conversion:
1 mile = 1,760 yards.
?? miles = 10,560 yards
=> 1 × 10,560 = 1760 × ??
=> 10,560  ÷ 1,760 = ??
=> 6 miles = ??

Question 7.
15.5 yards is how many feet?
Answer:
15.5 yards is equal to 46.5 feet.

Explanation:
Conversion:
1 yard = 3 feet.
15.5 yards = ?? feet
=> 1 × ?? = 3 × 15.5
=> ?? = 46.5 feet.

Question 8.
3.25 miles is how many inches?
Answer:
3.25 miles is equal to 2,05,920 inches.

Explanation:
Conversion:
1 miles = 63360 inches.
3.25 miles = ?? inches.
=> 1 × ?? = 63360 × 3.25
=> ?? = 2,05,920 inches.

Question 9.
31.5 yards is how many inches?
Answer:
31.5 yards is equal to 1,134 inches.

Explanation:
Conversion:
1 yard = 36 inches.
31.5 yards = ?? inches.
=> 1 × ?? = 36 × 31.5
=> ?? = 1,134 inches.

Question 10.
25 miles is how many yards?
Answer:
25 miles is equal to 44,000 miles.

Explanation:
Conversion:
1 mile = 1760 yards.
25 miles = ?? yards.
=> 1 × ?? = 1760 × 25
=> ?? = 44,000 miles.

Question 11.
42,931 feet is how many miles?
Answer:
42,931 feet is equal to 8.13 miles.

Explanation:
Conversion:
1 mile = 5,280 feet.
?? miles = 42,931 feet.
=> 1 × 42,931 = 5,280 × ??
=> 42,931 ÷ 5,280 = ??
=> 8.13 miles = ??

Question 12.
52 feet is how many inches?
Answer:
52 feet is equal to 624 inches.

Explanation:
Conversion:
1 feet = 12 inches.
52 feet = ?? inches.
=> 1 × ?? = 12 × 52
=> ?? = 624 inches.

Question 13.
345 yards is how many feet?
Answer:
345 yards is equal to 1,035 feet.

Explanation:
Conversion:
1 yard = 3 feet.
345 yards = ?? feet.
=> 1 × ?? = 3 × 345
=> ?? = 1,035 feet.

Question 14.
63,360 inches is how many miles?
Answer:
63,360 inches is equal to 1 mile.

Explanation:
Conversion:
1 mile = 63360 inches.
?? miles = 63360 inches.
=> 1 × 63360 = ?? × 63360
=> 63360 ÷ 63360 = ??
=> 1 mile = ??

Question 15.
31,680 inches is how many miles?
Answer:
31,680 inches is equal to 0.5 miles.

Explanation:
Conversion:
1 mile = 63,360 inches.
?? miles = 31,680 inches
=> 1 × 31,680 = 63,360 × ??
=> 31,680 ÷ 63,360 = ??
=> 0.5 miles = ??

Question 16.
7,000 yards is how many inches?
Answer:
7,000 yards is equal to 2,52,000 inches.

Explanation:
Conversion:
1 yard = 36 inches.
7,000 yards = ?? inches
=> 1 × ?? = 36 × 7,000
=> ?? = 2,52,000 inches.

Question 17.
1,590 feet is how many yards?
Answer:
1,590 feet is equal to 530 yards.

Explanation:
Conversion:
1 yard = 3 feet.
?? yards = 1,590 feet.
=> 1 × 1590 = 3 × ??
=> 1590 ÷ 3 = ??
=> 530 yards = ??

Question 18.
500 miles is how many yards?
Answer:
500 miles is equal to 8,80,000 yards.

Explanation:
Conversion:
1 mile = 1,760 yards.
500 miles = ?? yards
=> 1 × ?? = 1,760 × 500
=> ?? = 8,80,000 yards.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 17.4 Solving Equations and Inequalities by Multiplication and Division existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 17.4 Solving Equations and Inequalities by Multiplication and Division

Exercises

SOLVE

Question 1.
2y + 15 = 25
Answer:
Given equation is 2y + 15 = 25
Subtract 15 from both sides of the equation.
2y + 15 – 15 = 25 – 15
2y = 10
To solve above multiplication equation we need to divide both sides of the equation by 2 to find y.
2y/2 = 10/2
y = 5
The value of y is equal to 5.

Question 2.
5 + 5p < 70
Answer:
Given inequality is 5 + 5p < 70
Subtract 5 from both sides of the inequality.
5 + 5p – 5 < 70 – 5
5p < 65
To solve above multiplication inequality we need to divide both sides of the inequality by 5 to find p.
5p/5 < 65/5
p < 13
The value of p is less than 13.

Question 3.
8c + 8 > 224
Answer:
Given inequality is 8c + 8 > 224
Subtract 8 from both sides of the inequality.
8c + 8 – 8 > 224 – 8
8c > 216
To solve above multiplication inequality we need to divide both sides of the inequality by 8 to find c.
8c/8 > 216/8
c > 27
The value of c is greater than 27.

Question 4.
17 + \(\frac{w}{3}\) = 45
Answer:
Given equation is 17 + \(\frac{w}{3}\) = 45
Subtract 17 from both sides of the equation.
17 + \(\frac{w}{3}\) – 17= 45 – 17
\(\frac{w}{3}\) = 28
To solve above division equation we need to multiply both sides of the equation by 3 to find w.
\(\frac{w}{3}\) x 3 = 28 x 3
w = 84
The value of w is equal to 84.

Question 5.
34 = 10 + 4q
Answer:
Given equation is 34 = 10 + 4q
Subtract 10 from both sides of the equation.
34 – 10 = 10 + 4q -10
24 = 4q
To solve above multiplication equation we need to divide both sides of the equation by 4 to find q.
24/4 = 4q/4
6 = q
The value of q is equal to 6.

Question 6.
42 = 7 + \(\frac{z}{5}\)
Answer:
Given equation is 42 = 7 + \(\frac{z}{5}\)
Subtract 7 from both sides of the equation.
42 – 7 = 7 + \(\frac{z}{5}\) – 7
35 = \(\frac{z}{5}\)
To solve above division equation we need to multiply both sides of the equation by 5 to find z.
35 x 5= \(\frac{z}{5}\) x 5
175 = z
The value of z is equal to 175.

Question 7.
232 ≤ 8 + 8x
Answer:
Given inequality is 232 ≤ 8 + 8x
Subtract 8 from both sides of the inequality.
232 – 8 ≤ 8 + 8x – 8
224 ≤ 8x
To solve above multiplication inequality we need to divide both sides of the inequality by 8 to find x.
224/8 ≤ 8x/8
28 ≤ x
The value of x is greater than or equal to 28.

Question 8.
63 = 3 + 4g
Answer:
Given equation is 63 = 3 + 4g
Subtract 3 from both sides of the equation.
63 – 3 = 3 + 4g – 3
60 = 4g
To solve above multiplication equation we need to divide both sides of the equation by 4 to find g.
60/4 = 4g/4
15 = g
The value of g is equal to 15.

Question 9.
12 = \(\frac{g}{9}\)
Answer:
Given equation is 12 = \(\frac{g}{9}\)
To solve above division equation we need to multiply both sides of the equation by 9 to find g.
12 x 9 = \(\frac{g}{9}\) x 9
108 = g
The value of g is equal to 108.

Question 10.
3k + 5 > 56
Answer:
Given inequality is 3k + 5 > 56
Subtract 5 from both sides of the inequality.
3k + 5 – 5 > 56 – 5
3k > 51
To solve above multiplication inequality we need to divide both sides of the inequality by 3 to find k.
3k/3 > 51/3
K > 17
The value of k is greater than 17.

Question 11.
49 ≥ 10 + \(\frac{p}{5}\)
Answer:
Given inequality is 49 ≥ 10 + \(\frac{p}{5}\)
Subtract 10 from both sides of the inequality.
49 – 10 ≥ 10 + \(\frac{p}{5}\) – 10
39 ≥ \(\frac{p}{5}\)
To solve above division equation we need to multiply both sides of the equation by 5 to find p.
39 x 5 ≥ \(\frac{p}{5}\) x 5
195 ≥ p
The value of p is less than or equal to 195.

Question 12.
2y + 5 = 74
Answer:
Given equation is 2y + 5 = 74
Subtract 5 from both sides of the equation.
2y + 5 – 5 = 74 – 5
2y = 69
To solve above multiplication equation we need to divide both sides of the equation by 2 to find y.
2y/2 = 69/2
y = 34.5
The value of y is equal to 34.5.

Question 13.
8d + 130 = 210
Answer:
Given equation is 8d + 130 = 210
Subtract 130 from both sides of the equation.
8d + 130 – 130 = 210 – 130
8d = 80
To solve above multiplication equation we need to divide both sides of the equation by 8 to find d.
8d/8 = 80/8
d = 10
The value of d is equal to 10.

Question 14.
33 + \(\frac{1}{3}\)c ≤ 66
Answer:
Given inequality is 33 + \(\frac{1}{3}\)c ≤ 66
Subtract 33 from both sides of the inequality.
33 + \(\frac{1}{3}\)c – 33 ≤ 66 – 33
\(\frac{1}{3}\)c ≤ 33
To solve above division inequality we need to multiply both sides of the inequality by 3 to find c.
\(\frac{1}{3}\)c x 3 ≤ 33 x 3
c ≤ 99
The value of c is less than or equal to 99.

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McGraw-Hill Math Grade 7 Answer Key Lesson 17.3 Solving Equations and Inequalities by Addition and Subtraction

Exercises

SOLVE

Solve for the variable shown in the expression.

Question 1.
x + 6 = 17
Answer:
Given equation is x + 6 = 17
Subtract 6 from both sides of the equation to find x.
x + 6 – 6 = 17 – 6
x = 11

Question 2.
17 = s + 9
Answer:
Given equation is 17 = s + 9
Subtract 9 from both sides of the equation to find s.
17 – 9 = s + 9 – 9
8 = s

Question 3.
14 + z = 49
Answer:
Given equation is 14 + z = 49
Subtract 14 from both sides of the equation to find z.
14 + z – 14 = 49 – 14
z = 35

Question 4.
17 – f < 14
Answer:
Given inequality is 17 – f < 14
Subtract 14 from 17 to find f.
17 – 14 < f
3 < f

Question 5.
c – 11 > 11
Answer:
Given inequality is c – 11 > 11
Add 11 to both sides of the inequality to find c.
c – 11 + 11 > 11 + 11
c > 22

Question 6.
y + 23 = 25
Answer:
Given equation is y + 23 = 25
Subtract 23 from both sides of the equation to find y.
y + 23 – 23 = 25 – 23
y = 2

Question 7.
107 = 5 + l
Answer:
Given equation is 107 = 5 + I
Subtract 5 from both sides of the equation to find I.
107 – 5 = 5 + I – 5
102 = I

Question 8.
k + 36 = 64
Answer:
Given equation is k + 36 = 64
Subtract 36 from both sides of the equation to find k.
k + 36 – 36 = 64 – 36
k = 28

Question 9.
15 + u ≤ 43
Answer:
Given inequality is 15 + u ≤ 43
Subtract 15 from both sides of the inequality to find u.
15 + u – 15 ≤ 43 – 15
u ≤ 28

Question 10.
59 – t = 22
Answer:
Given equation is 59 – t = 22
Subtract 59 from both sides of the equation to find the value of t.
59 – t – 59 = 22 – 59
– t = – 37
t = 37

Question 11.
9 – a = 3
Answer:
Given equation is 9 – a = 3
Subtract 9 from both sides of the equation to find the value of a.
9 – a – 9 = 3 – 9
– a = -6
a = 6

Question 12.
75 + b > 101
Answer:
Given inequality is 75 + b > 101
Subtract 75 from both sides of the inequality to find b.
75 + b – 75 > 101 – 75
b > 26

Question 13.
49 – e = 24
Answer:
Given equation is 49 – e = 24
Subtract 49 from both sides of the equation to find the value e.
49 – e – 49 = 24 – 49
– e = – 25
e = 25

Question 14.
16 + d ≥ 39
Answer:
Given inequality is 16 + d ≥ 39
Subtract 16 from both sides of the inequality to find d.
16 + d – 16 ≥ 39 – 16
d ≥ 23

Question 15.
w + 15 ≤ 81
Answer:
Given inequality is w + 15 ≤ 81
Subtract 15 from both sides of the inequality to find w.
w + 15 – 15 ≤ 81 – 15
w ≤ 66

Question 16.
q – 23 = 35
Answer:
Given equation is q – 23 = 35
Add 23 to both sides of the equation to find q.
q – 23 + 23 = 35 + 23
q = 58

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McGraw-Hill Math Grade 7 Answer Key Lesson 17.2 Understanding Inequalities

Exercises

EXPLAIN

Put into words what each expression is describing.

Question 1.
3x < 6
Answer:
The given expression 3x < 6 describes three times a number is less than six.

Question 2.
p – 1 > 5
Answer:
The given expression p – 1 > 5 describes a number minus one is greater than five.

Question 3.
y ≤ 4
Answer:
The given expression y ≤ 4 describes a number is less than or equal to four.

Question 4.
s² ≥ 25
Answer:
The given expression s² ≥ 25 describes a square of a number is greater than or equal to twenty-five.

Question 5.
\(\frac{f}{5}\) < 63
Answer:
The given expression \(\frac{f}{5}\) < 63 describes a number divided by five is less than sixty-three.

Question 6.
w + 9 < 12
Answer:
The given expression w + 9 < 12 describes a number plus nine is less than twelve.

Question 7.
643 < d + g
Answer:
The given expression 643 < d + g describes six hundred forty-three is less than the sum of two numbers.

Question 8.
z + 2 ≤ 15
Answer:
The given expression z + 2 ≤ 15 describes a number plus two is less than or equal to fifteen.

Question 9.
4h > 17
Answer:
The given expression 4h > 17 describes four times a number is greater than seventeen.

Question 10.
1 – n ≥ -63
Answer:
The given expression 1 – n ≥ -63 describes one minus number is greater than or equal to negative sixty-three.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 17.1 Understanding Variable Expressions existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 17.1 Understanding Variable Expressions

Exercises

EXPLAIN

Put into words what each expression is describing.

Question 1.
\(\frac{a}{4}\)
Answer:
The given expression \(\frac{a}{4}\) describes a number is divided by four.

Question 2.
y + 3
Answer:
The given expression y + 3 describes a number plus three.

Question 3.
4b + 8
Answer:
The given expression 4b + 8 describes four times a number plus eight.

Question 4.
.9q – 7
Answer:
The given expression .9q – 7 describes nine tenths of a number minus seven.

Question 5.
\(\frac{(x-3)}{25}\)
Answer:
The given expression \(\frac{(x-3)}{25}\) describes a number minus three, then divided by twenty-five.

Question 6.
8(2g + 6)
Answer:
The given expression 8(2g + 6) describes eight times the sum of two times a number plus six.

Question 7.
2n – 5
Answer:
The given expression 2n – 5 describes two times a number minus five.

Question 8.
12(r – 14)
Answer:
The given expression 12(r – 14) describes twelve times the result of a number minus fourteen.

Question 9.
\(\frac{7}{h}\)
Answer:
The given expression \(\frac{7}{h}\) describes seven is divided by a number.

Question 10.
\(\frac{11+b}{16}\)
Answer:
The given expression \(\frac{11+b}{16}\) describes the sum of eleven plus a number, then divided by sixteen.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 16.3 Scientific Notation existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 16.3 Scientific Notation

Exercises

CONVERT

If the expression is in scientific notation, convert it to a number. If it is a number, convert it to scientific notation. Round all numbers to 6 places to the right of the decimal point when converting to scientific notation.

Question 1.
5 × 10⁵ = ____________
Answer:
5 × 10⁵ = 500,000
Explanation:
The given expression is in scientific notation. To convert it into a number first we have to solve 10⁵. Here base is 10 and exponent is 5.  So, we have to multiply the base 10 by itself as five times the product is equal to 100,000. Multiply 5 with 100,000 the product is equal to 500,000.

Question 2.
478.23 = _____________
Answer:
478.23 = 4.7823 x 10²
Explanation:
There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved two place values. So, the count is 10². The number 478.23 in scientific notation as 4.7823 x 10².

Question 3.
89,786 = _____________
Answer:
89,786 = 8.9786 x 10⁴
Explanation:
Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved four place values. So, the count is 10⁴. The number 89,786 in scientific notation as 8.9786 x 10⁴.

Question 4.
6.721 × 10⁶ = ____________
Answer:
6.721 × 10⁶ = 6,721,000
Explanation:
The given expression is in scientific notation. To convert it into a number first we have to solve 10⁶. Here base is 10 and exponent is 6. So, we have to multiply the base 10 by itself as six times the product is equal to 1,000,000. Multiply 6.721 with 1,000,000 the product is equal to 6,721,000.

Question 5.
2.9731 × 10^-2 = ______________
Answer:
2.9731 × 10^-2 = 0.029731
Explanation:
The given expression is in scientific notation. To convert it into a number first we have to solve 10^-2. Here base is 10 and exponent is -2. So, we have to multiply the base 10 by itself as two times the product is equal to 0.01. Multiply 2.9731 with 0.01 the product is equal to 0.029731.

Question 6.
691,273 = _____________
Answer:
691,273 = 6.91273 x 10⁵
Explanation:
Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved five place values. So, the count is 10⁵. The number 691,273 in scientific notation as 6.91273 x 10⁵.

Question 7.
5,9178 × 10^-3 = ____________
Answer:
5,9178 × 10^-3 = 0.0059178
Explanation:
The given expression is in scientific notation. To convert it into a number first we have to solve 10^-3. Here base is 10 and exponent is -3. So, we have to multiply the base 10 by itself as three times the product is equal to 0.001. Multiply 5,9178 with 0.001 the product is equal to 0.0059178.

Question 8.
8.72345 × 10¹⁰ = ______________
Answer:
8.72345 × 10¹⁰ = 87,234,500,000
Explanation:
The given expression is in scientific notation. To convert it into a number first we have to solve 10¹⁰. Here base is 10 and exponent is 10. So, we have to multiply the base 10 by itself as ten times. Multiply 8.72345 with 10¹⁰ the product is equal to 87,234,500,000.

Question 9.
6,664,475 = _____________
Answer:
6,664,475 = 6.664475 x 10⁶
Explanation:
Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved six place values. So, the count is 10⁶. The number 6,664,475 in scientific notation as 6.664475 x 10⁶.

Question 10.
.0005123 = ______________
Answer:
.0005123= 5.123 x 10^-4
Explanation:
There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the right, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved four place values to left . So, the count is 10^-4. The number .0005123 in scientific notation as 5.123 x 10^-4.

Question 11.
8.9 = ______________
Answer:
8.9 = 8.9 x 10⁰
Explanation:
There is a decimal point to the right of the given number. The number 8 is greater than 1 and less than 10. Here I moved zero place values to right . So, the count is 10⁰. The number 8.9 in scientific notation as 8.9 x 10⁰.

Question 12.
100.235 = _______________
Answer:
100.235 = 1.00235 x 10²
Explanation:
There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved two place values. So, the count is 10². The number 100.235 in scientific notation as 1.00235 x 10².

Question 13.
963,764 = _____________
Answer:
963,764 = 9.63764 x 10⁵
Explanation:
Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved five place values. So, the count is 10⁵. The number 963,764 in scientific notation as 9.63764 x 10⁵.

Question 14.
4.6554 = _____________
Answer:
4.6554 = 4.6554 x 10⁰
Explanation:
There is a decimal point to the right of the given number. The number 4 is greater than 1 and less than 10. Here I moved zero place values to right . So, the count is 10⁰. The number 4.6554 in scientific notation as 4.6554 x 10⁰.

Question 15.
789.23 = _______________
Answer:
789.23 = 7.8923 x 10²
Explanation:
There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved two place values. So, the count is 10². The number 789.23 in scientific notation as 7.8923 x 10².

Question 16.
15,896,000,000,000 = ______________
Answer:
15,896,000,000,000 = 1.5896 x 10¹³
Explanation:
Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved thirteen place values. So, the count is 10¹³. The number 15,896,000,000,000 in scientific notation as 1.5896 x 10¹³.

Question 17.
8,999,345,000 = ________________
Answer:
8,999,345,000 = 8.999345 x 10⁹
Explanation:
Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.
We have to stop the process when the number is greater than 1 and less than 10. Here I moved nine place values. So, the count is 10⁹. The number 8,999,345,000 in scientific notation as 8.999345 x 10⁹.

Question 18.
1.697324 × 10⁴ = ______________
Answer:
1.697324 × 10⁴ = 16,973.24
Explanation:
The given expression is in scientific notation. To convert it into a number first we have to solve 10⁴. Here base is 10 and exponent is 4. So, we have to multiply the base 10 by itself as four times the product is equal to 10,000. Multiply 1.697324 with 10,000 the product is equal to 16,973.24.

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McGraw-Hill Math Grade 7 Answer Key Lesson 16.2 Square Roots

Exercises

CALCULATE

Identify the square root.

Question 1.
\(\sqrt{36}\) ______________
Answer:
\(\sqrt{36}\) = 6
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{36}\) is equal to 6 because 6 x 6 is equal to 36.

Question 2.
\(\sqrt{144}\) ______________
Answer:
\(\sqrt{144}\) = 12
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{144}\) is equal to 12 because 12 x 12 is equal to 144.

Question 3.
\(\sqrt{81}\) ______________
Answer:
\(\sqrt{81}\) = 9
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{81}\) is equal to 9 because 9 x 9 is equal to 81.

Question 4.
\(\sqrt{25}\) ______________
Answer:
\(\sqrt{25}\) = 5
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{25}\) is equal to 5 because 5 x 5 is equal to 25.

Question 5.
\(\sqrt{169}\) ______________
Answer:
\(\sqrt{169}\) = 13
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{169}\) is equal to 13 because 13 x 13 is equal to 169.

Question 6.
\(\sqrt{9}\) ______________
Answer:
\(\sqrt{9}\) = 3
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{9}\) is equal to 3 because 3 x 3 is equal to 9.

Question 7.
\(\sqrt{1}\) ______________
Answer:
\(\sqrt{1}\) = 1
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{1}\) is equal to 1 because 1 x 1 is equal to 1.

Question 8.
\(\sqrt{49}\) ______________
Answer:
\(\sqrt{49}\) = 7
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{49}\) is equal to 7 because 7 x 7 is equal to 49.

Question 9.
\(\sqrt{4}\) ______________
Answer:
\(\sqrt{4}\) = 2
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{4}\) is equal to 2 because 2 x 2 is equal to 4.

Question 10.
\(\sqrt{100}\) ______________
Answer:
\(\sqrt{100}\) = 10
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{100}\) is equal to 10 because 10 x 10 is equal to 100.

Question 11.
\(\sqrt{16}\) ______________
Answer:
\(\sqrt{16}\) = 4
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{16}\) is equal to 4 because 4 x 4 is equal to 16.

Question 12.
\(\sqrt{121}\) ______________
Answer:
\(\sqrt{121}\) = 11
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{121}\) is equal to 11 because 11 x 11 is equal to 121.

Question 13.
\(\sqrt{64}\) ______________
Answer:
\(\sqrt{64}\) = 8
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{64}\) is equal to 8 because 8 x 8 is equal to 64.

Question 14.
\(\sqrt{225}\) ______________
Answer:
\(\sqrt{225}\) = 15
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. The \(\sqrt{225}\) is equal to 15 because 15 x 15 is equal to 225.

Estimate.

Question 15.
\(\sqrt{12}\) is between ___________ and __________
Answer:
\(\sqrt{12}\) is between 3 and 4
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. We know that 3 x 3 = 9 and 4 x 4 = 16. The \(\sqrt{12}\) is in between 3 and 4.

Question 16.
\(\sqrt{41}\) is between ___________ and __________
Answer:
\(\sqrt{41}\) is between 6 and 7
Explanation:
The square root of a number is the number that, when multiplied by itself is equal to that number. We know that 6 x 6 = 36 and 7 x 7 = 49. The \(\sqrt{41}\) is in between 6 and 7.

Excel in your academics by accessing McGraw Hill Math Grade 7 Answer Key PDF Lesson 16.1 Exponents existing for free of cost.

McGraw-Hill Math Grade 7 Answer Key Lesson 16.1 Exponents

Exercises

CALCULATE

Question 1.
12² = _____________
Answer:
12² = 12 x 12 = 144
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 12 and exponent is 2.  So, we have to multiply the base 12 by itself as two times the product is equal to 144.

Question 2.
10⁴ = _____________
Answer:
10⁴ = 10 x 10 x 10 x 10 = 10,000
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 10 and exponent is 4.  So, we have to multiply the base 10 by itself as four times the product is equal to 10,000.

Question 3.
7³ = _____________
Answer:
7³ = 7 x 7 x 7 = 343
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 7 and exponent is 3.  So, we have to multiply the base 7 by itself as three times the product is equal to 343.

Question 4.
2³ = _____________
Answer:
2³ = 2 x 2 x 2 = 8
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 2 and exponent is 3.  So, we have to multiply the base 2 by itself as three times the product is equal to 8.

Question 5.
4⁴ = _____________
Answer:
4⁴ = 4 x 4 x 4 x 4 = 256
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 4 and exponent is 4.  So, we have to multiply the base 4 by itself as four times the product is equal to 256.

Question 6.
5³ = _____________
Answer:
5³ = 5 x 5 x 5 = 125
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 5 and exponent is 3.  So, we have to multiply the base 5 by itself as three times the product is equal to 125.

Question 7.
41² = _____________
Answer:
41² = 41 x 41= 1,681
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 41 and exponent is 2.  So, we have to multiply the base 41 by itself as two times the product is equal to 1,681.

Question 8.
5⁵ = _____________
Answer:
5⁵ = 5 x 5 x 5 x 5 = 3,125
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 5 and exponent is 5.  So, we have to multiply the base 5 by itself as five times the product is equal to 3,125.

Question 9.
6⁷ = _____________
Answer:
6⁷ = 6 x 6 x 6 x 6 x 6 x 6 x 6 = 279,936
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 6 and exponent is 7.  So, we have to multiply the base 6 by itself as seven times the product is equal to 279,936.

Question 10.
17⁴ = _____________
Answer:
17⁴ = 17 x 17 x 17 x 17 = 83,521
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 17 and exponent is 4.  So, we have to multiply the base 17 by itself as four times the product is equal to 83,521.

Question 11.
0¹⁰ = _____________
Answer:
0¹⁰ = 0
Explanation:
The exponent number tells how many times we have to multiply the base by itself.  Here base is 0 and exponent is 10.  So, we have to multiply the base 0 by itself as ten times the product is equal to 0.

Question 12.
101⁰ = _____________
Answer:
101⁰ = 1
A base raised to the zero power is equal to 1. So, 101⁰ is equal to 1.

Question 13.
12¹ = _____________
Answer:
12¹ = 12
A base raised to the first power is equal to the base. So, 12¹ is equal to 12.

Question 14.
24⁰ = _____________
Answer:
24⁰ = 1
A base raised to the zero power is equal to 1. So, 24⁰ is equal to 1.

Question 15.
33¹ = _____________
Answer:
33¹ = 33
A base raised to the first power is equal to the base. So, 33¹ is equal to 33.

MULTIPLY OR DIVIDE

Question 1.
2³ ÷ 2^-5 = _____________
Answer:
2³ ÷ 2^-5 = 2^{(3 – (-5))}  = 2⁸ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 2⁸.

Question 2.
5⁵ × 5^-6 = _____________
Answer:
5⁵ × 5^-6 = 5^{(5 + (-6))}  = 5^-1 = 1/5   
Explanation:
If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 5^-1.

Question 3.
11¹¹ ÷ 11⁴ = _____________
Answer:
11¹¹ ÷ 11⁴ = 11^{(11 – 4)}  = 11⁷ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 11⁷.

Question 4.
54⁴ ÷ 54^-2 = _____________
Answer:
54⁴ ÷ 54^-2 = 54^{(4 – (-2))} = 54^{(4 + 2)}= 54⁶ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 54⁶.

Question 5.
3² ÷ 3⁰ = _____________
Answer:
3² ÷ 3⁰ = 3^{(2 – 0)} = 3² 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 3².

Question 6.
8¹ × 8⁸ = _____________
Answer:
8¹ × 8⁸ = 8^{(1 + 8)}  = 8⁹    
Explanation:
If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 8⁹.

Question 7.
15⁵ ÷ 15⁴ = _____________
Answer:
15⁵ ÷ 15⁴ = 15^{(5 – 4)} = 15¹ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 15.

Question 8.
8⁶ ÷ 8² = _____________
Answer:
8⁶ ÷ 8² = 8^{(6 – 2)} = 8⁴ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 8⁴.

Question 9.
18⁷ × 18²¹ = _____________
Answer:
18⁷ × 18²¹ = 18^{(7 + 21)}  = 18²⁸    
Explanation:
If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 18²⁸.

Question 10.
81¹⁰ ÷ 81⁷ = _____________
Answer:
81¹⁰ ÷ 81⁷ = 81^{(10 – 7)} = 81³ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 81³.

Question 11.
19¹⁹ × 19¹⁶ = _____________
Answer:
19¹⁹ × 19¹⁶ = 19^{(19 + 16)}  = 19³⁵    
Explanation:
If we want to multiply a base raised to a power by the same base raised to a power then we have to add the exponents. Here both the bases are same. After adding the exponents the result is equal to 19³⁵.

Question 12.
21² ÷ 21³ = _____________
Answer:
21² ÷ 21³ = 21^{(2 – 3)} = 21^-1 = 1/21 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 1/21.

Question 13.
15^-5 ÷ 15⁶ = _____________
Answer:
15^-5 ÷ 15⁶ = 15^{(-5 – 6)} = 15^-11 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 15^-11.

Question 14.
10^-8 ÷ 10^-12 = _____________
Answer:
10^-8 ÷ 10^-12 = 10^{(-8 – (-12))} =10^{(-8 + 12)}= 10⁴ 
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 10,000.

Question 15.
17¹⁵ ÷ 17²² = _____________
Answer:
17¹⁵ ÷ 17²² = 17^{(15 – 22)} = 17^-7 = 1/17⁷
Explanation:
If we want to divide a base raised to a power by the same base raised to a power then we have to subtract the exponents. Here both the bases are same. After subtracting the exponents the result is equal to 17^-7.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.2 Multiplying Two Fractions: Reciprocals to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.2 Multiplying Two Fractions: Reciprocals

Exercises Multiply

Question 1.
\(\frac{3}{2}\) × \(\frac{4}{9}\)
Answer:
\(\frac{2}{3}\),

Explanation:
When we multiply \(\frac{3}{2}\) X \(\frac{4}{9}\), We get \(\frac{3 X 4}{2 X 9}\) = \(\frac{12}{18}\) both goes by 6 we get  \(\frac{6 X 2}{6 X 3}\) = \(\frac{2}{3}\).

Question 2.
\(\frac{5}{9}\) × \(\frac{12}{30}\)
Answer:
\(\frac{2}{9}\),

Explanation:
When we multiply \(\frac{5}{9}\) X \(\frac{12}{30}\) we get \(\frac{5 X 12}{9 X 30}\) = \(\frac{60}{270}\) both goes by 30, So \(\frac{2 X 30}{9 X 30}\) = \(\frac{2}{9}\).

Question 3.
\(\frac{15}{21}\) × \(\frac{6}{25}\)
Answer:
\(\frac{6}{35}\),

Explanation:
When we multiply \(\frac{15}{21}\) X \(\frac{6}{25}\) we get
\(\frac{15 X 6}{21 X 25}\) = \(\frac{90}{525}\) both goes by 15, So \(\frac{6 X 15}{35 X 15}\) = \(\frac{6}{35}\),

Question 4.
\(\frac{1}{2}\) × \(\frac{1}{2}\)
Answer:
\(\frac{1}{4}\),

Explanation:
When we multiply \(\frac{1}{2}\) X \(\frac{1}{2}\) we get \(\frac{1 X 1}{2 X 2}\) = \(\frac{1}{4}\).

Question 5.
\(\frac{2}{3}\) × \(\frac{3}{4}\)
Answer:
\(\frac{1}{2}\),

Explanation:
When we multiply \(\frac{2}{3}\) X \(\frac{3}{4}\) we get
\(\frac{2 X 3}{3 X 4}\) = \(\frac{6}{12}\) both goes by 6, So
\(\frac{1 X 6}{2 X 6}\) = \(\frac{1}{2}\).

Question 6.
\(\frac{5}{4}\) × \(\frac{16}{35}\)
Answer:
\(\frac{4}{7}\),

Explanation:
When we multiply \(\frac{5}{4}\) X \(\frac{16}{35}\) we get
\(\frac{5 X 16}{4 X 35}\) = \(\frac{80}{140}\) both goes by 20, So
\(\frac{4 X 20}{7 X 20}\) = \(\frac{4}{7}\),

Question 7.
\(\frac{5}{18}\) × \(\frac{9}{25}\)
Answer:
\(\frac{1}{10}\),

Explanation:
When we multiply \(\frac{5}{18}\) X \(\frac{9}{25}\) we get \(\frac{5 X 9}{18 X 25}\) = \(\frac{45}{450}\) both goes by 45, So
\(\frac{1 X 45}{10 X 45}\) = \(\frac{1}{10}\).

Question 8.
\(\frac{4}{14}\) × \(\frac{28}{64}\)
Answer:
\(\frac{1}{8}\),

Explanation:
When we multiply \(\frac{4}{14}\) X \(\frac{28}{64}\) we get
\(\frac{4 X 28}{14 X 64}\) = \(\frac{112}{896}\) both goes by 112, So \(\frac{1}{8}\).

Question 9.
\(\frac{13}{22}\) × \(\frac{11}{13}\)
Answer:
\(\frac{1}{2}\),

Explanation:
When we multiply \(\frac{13}{22}\) X \(\frac{11}{13}\) we get
\(\frac{13 X 11}{22 X 13}\) = \(\frac{143}{286}\) both goes by 143,
So \(\frac{1 X 143}{2 X 286}\).

Question 10.
\(\frac{12}{13}\) × \(\frac{52}{72}\)
Answer:
\(\frac{2}{3}\),

Explanation:
When we multiply \(\frac{12}{13}\) X \(\frac{52}{72}\) we get
\(\frac{12 X 52}{13 X 72}\) = \(\frac{624}{936}\) both goes by 312,
So \(\frac{2 X 312}{3 X 312}\) = \(\frac{2}{3}\).

Question 11.
\(\frac{2}{15}\) × \(\frac{2}{15}\)
Answer:
\(\frac{4}{225}\),

Explanation:
When we multiply \(\frac{2}{15}\) X \(\frac{2}{15}\) we get
\(\frac{2 X 2}{15 X 15}\) = \(\frac{4}{225}\).

Question 12.
\(\frac{21}{24}\) × \(\frac{8}{35}\)
Answer:
\(\frac{1}{5}\),

Explanation:
When we multiply \(\frac{21}{24}\) X \(\frac{8}{35}\) we get
\(\frac{21 X 8}{24 X 35}\) = \(\frac{168}{840}\) both goes by 168, \(\frac{1}{5}\).

Question 13.
\(\frac{48}{21}\) × \(\frac{42}{64}\)
Answer:
\(\frac{3}{2}\),

Explanation:
When we multiply \(\frac{48}{21}\) X \(\frac{42}{64}\) we get
\(\frac{48 X 42}{21 X 64}\) = \(\frac{2016}{1344}\) both goes by 672, So \(\frac{3}{2}\).

Question 14.
\(\frac{7}{9}\) × \(\frac{9}{14}\)
Answer:
\(\frac{1}{2}\),

Explanation:
When we multiply \(\frac{7}{9}\) X \(\frac{9}{14}\) we get
\(\frac{7 X 9}{9 X 14}\) = \(\frac{63}{126}\) both goes by 63, So \(\frac{1 x 63}{2 X 63}\) = \(\frac{1}{2}\).

Question 15.
\(\frac{15}{18}\) × \(\frac{9}{25}\)
Answer:
\(\frac{3}{10}\),

Explanation:
When we multiply \(\frac{15}{18}\) X \(\frac{9}{25}\) we get \(\frac{15 X 9}{18 X 25}\) = \(\frac{135}{450}\) both goes by 45, So \(\frac{3 X 45}{10 X 45}\) = \(\frac{3}{10}\).

Question 16.
\(\frac{10}{13}\) × \(\frac{26}{45}\)
Answer:
\(\frac{4}{9}\),

Explanation:
When we multiply \(\frac{10}{13}\) X \(\frac{26}{45}\) we get
\(\frac{10 X 26}{13 X 45}\) = \(\frac{260}{585}\) both goes by 65,
So \(\frac{4 X 65}{9 X 65}\) = \(\frac{4}{9}\).

Question 17.
Daisy runs on an oval track that is \(\frac{1}{4}\) of a mile long. If she runs \(\frac{5}{16}\) of the way around the track, how far did she run?
Answer:
\(\frac{5}{64}\) mile long Daisy ran on an oval track,

Explanation:
When Daisy runs we multiply \(\frac{1}{4}\) mile long track with  \(\frac{5}{16}\) way Daisy ran around the track  we get \(\frac{1 X 5}{4 X 16}\) = \(\frac{5}{64}\) mile long Daisy ran.

Question 18.
Bart’s family’s motorboat uses \(\frac{22}{6}\) gallons of gas every hour. If they run the boat for \(\frac{1}{3}\) of an hour, how much gas will they be using?
Answer:
\(\frac{11}{9}\) gallons of gas will be used every hour,

Explanation:
When we multiply Bart’s family’s motorboat uses  \(\frac{22}{6}\) gallons of gas is used every hour by Barts family’s boat  \(\frac{1}{3}\) of an hour, we get \(\frac{22 X 1}{6 X 3}\) = \(\frac{22}{18}\) both goes by 2 we get \(\frac{11 X 2}{9 X 2}\) =  \(\frac{11}{9}\) gallons of gas would be used for every hour.

Practice the questions of McGraw Hill Math Grade 8 Answer Key PDF Lesson 4.1 Multiplying Fractions and Whole Numbers to secure good marks & knowledge in the exams.

McGraw-Hill Math Grade 8 Answer Key Lesson 4.1 Multiplying Fractions and Whole Numbers

Exercises Multiply

Question 1.
13 × \(\frac{1}{4}\)
Answer:
\(\frac{13}{4}\),

Explanation:
When 13 is multiplied by \(\frac{1}{4}\) we get \(\frac{13 X 1}{4}\) = \(\frac{13}{4}\).

Question 2.
15 × \(\frac{2}{7}\)
Answer:
\(\frac{30}{7}\),

Explanation:
When 15 is multiplied by \(\frac{2}{7}\) we get \(\frac{15 X 2}{7}\) = \(\frac{15}{7}\).

Question 3.
22 × \(\frac{3}{8}\)
Answer:
\(\frac{33}{4}\),

Explanation:
When 22 is multiplied by \(\frac{3}{8}\) we get \(\frac{22 X 3}{8}\) = \(\frac{33}{4}\).

Question 4.
24 × \(\frac{3}{4}\)
Answer:
\(\frac{72}{4}\) = 18,

Explanation:
When 24 is multiplied by \(\frac{3}{4}\) we get \(\frac{24 X 3}{4}\) = \(\frac{72}{4}\) = 18.

Question 5.
18 × \(\frac{7}{20}\)
Answer:
\(\frac{63}{10}\),

Explanation:
When 18 is multiplied by \(\frac{7}{20}\) we get \(\frac{18 X 7}{20}\) = \(\frac{63}{10}\).

Question 6.
31 × \(\frac{2}{17}\)
Answer:
\(\frac{62}{17}\),

Explanation:
When 31 is multiplied by \(\frac{2}{17}\) we get \(\frac{31 X 2}{17}\) = \(\frac{62}{17}\).

Question 7.
6 × \(\frac{7}{24}\)
Answer:
\(\frac{7}{4}\),

Explanation:
When 6 is multiplied by \(\frac{7}{24}\) we get \(\frac{6 X 7}{24}\) = \(\frac{7}{4}\).

Question 8.
14 × \(\frac{10}{11}\)
Answer:
\(\frac{140}{11}\),
Explanation:
When 14 is multiplied by \(\frac{10}{11}\) we get \(\frac{14 X 10}{11}\) = \(\frac{140}{11}\).

Question 9.
16 × \(\frac{5}{36}\)
Answer:
\(\frac{20}{9}\),

Explanation:
When 16 is multiplied by \(\frac{5}{36}\) we get \(\frac{16 X 5}{36}\) = \(\frac{20}{9}\).

Question 10.
7 × \(\frac{2}{3}\)
Answer:
\(\frac{14}{3}\),

Explanation:
When 7 is multiplied by \(\frac{2}{3}\) we get \(\frac{7 X 2}{3}\) = \(\frac{14}{3}\).

Question 11.
16 × \(\frac{3}{5}\)
Answer:
\(\frac{48}{5}\),

Explanation:
When 16 is multiplied by \(\frac{3}{5}\) we get \(\frac{16 X 3}{5}\) = \(\frac{48}{5}\).

Question 12.
14 × \(\frac{11}{28}\)
Answer:
\(\frac{11}{2}\),

Explanation:
When 14 is multiplied by \(\frac{11}{28}\) we get \(\frac{14 X 11}{28}\) = \(\frac{154}{28}\) both goes by 14 as \(\frac{14 X 1 X 11}{14 X 2}\) = \(\frac{11}{2}\).

Question 13.
44 × \(\frac{6}{7}\)
Answer:
\(\frac{264}{7}\),

Explanation:
When 44 is multiplied by \(\frac{6}{7}\) we get \(\frac{44 X 6}{7}\) = \(\frac{264}{7}\).

Question 14.
20 × \(\frac{23}{40}\)
Answer:
\(\frac{23}{2}\),

Explanation:
When 20 is multiplied by \(\frac{23}{40}\) we get \(\frac{20 X 23}{40}\) = \(\frac{460}{40}\) both goes by 20 we get \(\frac{20 X 1 X 23}{20 X 1 X 2}\) = \(\frac{1 X 23}{1 X 2}\) = \(\frac{23}{2}\).

Question 15.
33 × \(\frac{6}{11}\)
Answer:
\(\frac{198}{11}\) = 18,

Explanation:
When 33 is multiplied by \(\frac{6}{11}\) we get \(\frac{33 X 6}{11}\) = \(\frac{11 X 3 X 6}{11}\) = 3 X 6 = 18.

Question 16.
25 × \(\frac{16}{45}\)
Answer:
\(\frac{80}{9}\),

Explanation:
When 25 is multiplied by \(\frac{16}{45}\) we get \(\frac{25 X 16}{45}\) = \(\frac{400}{45}\) both goes in 5 as \(\frac{80 X 5}{9 X 5}\) = \(\frac{80}{9}\).

Question 17.
Before setting out on a bike ride, each rider was given \(\frac{5}{8}\) gallons of water to carry with them on the trip. If there are 28 people on the bike, ride, how much water was dispensed?
Answer:
\(\frac{35}{2}\) gallons of water,

Explanation:
When 28 people on the bike is multiplied by \(\frac{5}{8}\) gallons of water to carry with them on the trip we get \(\frac{28 X 5}{8}\) = \(\frac{140}{8}\) both goes by 4 so \(\frac{35}{2}\). Therefore \(\frac{35}{2}\) water was dispensed before setting out on a bike ride.

Question 18.
Norbert estimates that it takes 1\(\frac{2}{7}\) hours to complete one load of laundry. If Norbert’s dad has 8 loads of laundry to do, how long will it take him to finish?
Answer:
\(\frac{72}{7}\) or 10\(\frac{2}{7}\),

Explanation:
Given Norbert estimates that it takes 1\(\frac{2}{7}\) hours to complete one load of laundry. Then 1\(\frac{2}{7}\) hours = \(\frac{1 X 7 + 2}{7}\)
= \(\frac{9}{7}\) now long it will take Norbet to finish the work is \(\frac{9}{7}\) X 8 = \(\frac{9 X 8}{7}\) = \(\frac{72}{7}\) as numerator
is greater than denominator we write in mixed fraction as \(\frac{10 X 7 + 2}{7}\) = 10\(\frac{2}{7}\).