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Mathematics LibreTexts

4.6: Applications Involving Fractions

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Learning Objectives
  • be able to solve missing product statements
  • be able to solve missing factor statements

Multiplication Statements

Statement, Multiplication Statement
A statement is a sentence that is either true or false. A mathematical statement of the form

product = (factor 1) ⋅ (factor 2)

is a multiplication statement. Depending on the numbers that are used, it can be either true or false.

Omitting exactly one of the three numbers in the statement will produce exactly one of the following three problems. For convenience, we'll represent the omitted (or missing) number with the letter M (M for Missing).

  1. M = (factor 1) ⋅ (factor 2) Missing product statement.
  2. M ⋅ (factor 2) = product Missing factor statement.
  3. (factor 1) ⋅ M = product Missing factor statement.

We are interested in developing and working with methods to determine the missing number that makes the statement true. Fundamental to these methods is the ability to translate two words to mathematical symbols. The word

of translates to times
is translates to equals

Missing Products Statements

The equation M=84 is a missing product statement. We can find the value of M that makes this statement true by multiplyingthe known factors.

Missing product statements can be used to determine the answer to a question such as, "What number is fraction 1 of fraction 2?

Sample Set A

Find 34 of 89. We are being asked the question, "What number is 34 of 89?" We must translate from words to mathematical symbols.

Two statements in a row. Each element is aligned with something above it. First, what number is three-fourths of eight-ninths, becomes. Second, M equals three-fourths times eight-ninths, multiply.  M is the missing product, and three-fourths and eight-ninths are known factors.

M=13412893=1213=23

Thus, 34 of 89 is 23.

Two statements in a row. Each element is aligned with something above it. First, what number is three-fourths of twenty-four. Second, M equals three-fourths times twenty-four.  M is the missing product, and three-fourths and eight-ninths are known factors.

M=3416241=3611=181=18

Thus, 18 is 34 of 24.

Practice Set A

Find 38 of 1615.

Answer

25

Practice Set A

What number is 910 of 56?

Answer

34

Practice Set A

1116 of 833 is what number?

Answer

16

Missing Factor Statements

The equation 8M=32 is a missing factor statement. We can find the value of M that makes this statement true by dividing (since we know that 32÷8=4.

The expression 8 times M equals 32 means that M equals thirty-two divided by eight. M is the missing factor, thirty-two is the product, and eight is the known factor.

Finding the Missing Factor
To find the missing factor in a missing factor statement, divide the product by the known factor.
missing factor = (product) ÷ (known factor)

Missing factor statements can be used to answer such questions as

38 of what number is 94?
What part of 127 is 11314?

Sample Set B

Three eighths of what number is nine fourths? This is the same as three eighths times M equals nine fourths. Three eighths is the known factor, M is the missing factor, and nine-fourths is the product.

Now, using

missing factor = (product) ÷ (known factor)

We get

M=94÷38=9483=39412831=3211=6

Check the work: is three eighths times six equal to nine fourths? Cancel out the six and the eight by dividing each by two. This can be simplified to find out that yes, they are equal.

Thus, 38 of 6 is 94.

What part of 1 and two-sevenths is 1 and thirteen-fourteenths? This is equivalent to M times 1 and two-sevenths equals 1 and thirteen-fourteenths. M is the missing factor, 1 and two-sevenths is the known factor, and 1 and thirteen-fourteenths is the product.

For convenience, let's convert the mixed numbers to improper fractions.

M97=2714

Now, using

missing factor = (product) ÷ (known factor)

we get

M=2714÷97=271479=3271421791=3121=32

Check: is three halves times nine sevenths equal to twenty-seven fourteenths? Yes.

Thus, 32 of 127 is 11314.

Practice Set B

35 of what number is 920?

Answer

34

Practice Set B

334 of what number is 229?

Answer

1627

Practice Set B

What part of 35 is 910?

Answer

112

Practice Set B

What part of 114 is 178?

Answer

112

Exercises

Exercise 4.6.1

Find 23 of 34.

Answer

12

Exercise 4.6.2

Find 58 of 110.

Exercise 4.6.3

Find 1213 of 1336.

Answer

13

Exercise 4.6.4

Find 14 of 47.

Exercise 4.6.5

310 of 154 is what number?

Answer

98 or 118

Exercise 4.6.6

1415 of 2021 is what number?

Exercise 4.6.7

344 of 1112 is what number?

Answer

116

Exercise 4.6.8

13 of 2 is what number?

Exercise 4.6.9

14 of 3 is what number?

Answer

34

Exercise 4.6.10

110 of 1100 is what number?

Exercise 4.6.11

1100 of 110 is what number?

Answer

11,000

Exercise 4.6.12

159 of 247 is what number?

Exercise 4.6.13

1718 of 415 is what number?

Answer

1027

Exercise 4.6.14

118 of 11116 is what number?

Exercise 4.6.15

Find 23 of 16 of 92.

Answer

12

Exercise 4.6.16

Find 58 of 920 of 49.

Exercise 4.6.17

512 of what number is 56?

Answer

2

Exercise 4.6.18

314 of what number is 67?

Exercise 4.6.19

103 of what number is 59?

Answer

16

Exercise 4.6.20

157 of what number is 2021?

Exercise 4.6.21

83 of what number is 179?

Answer

23

Exercise 4.6.22

13 of what number is 13?

Exercise 4.6.23

16 of what number is 16?

Answer

1

Exercise 4.6.24

34 of what number is 34?

Exercise 4.6.25

811 of what number is 811?

Answer

1

Exercise 4.6.26

38 of what number is 0?

Exercise 4.6.27

23 of what number is 1?

Answer

32 or 112

Exercise 4.6.28

315 of what number is 1?

Exercise 4.6.29

1912 of what number is 514?

Answer

3

Exercise 4.6.30

3125 of what number is 2815?

Exercise 4.6.31

What part of 23 is 119?

Answer

53 or 123

Exercise 4.6.32

What part of 910 is 335?

Exercise 4.6.33

What part of 89 is 35?

Answer

2740

Exercise 4.6.34

What part of 1415 is 730?

Exercise 4.6.35

What part of 3 is 15?

Answer

115

Exercise 4.6.36

What part of 8 is 23?

Exercise 4.6.37

What part of 24 is 9?

Answer

38

Exercise 4.6.38

What part of 42 is 26?

Exercise 4.6.39

Find 1213 of 3940.

Answer

910

Exercise 4.6.40

1415 of 1221 is what number?

Exercise 4.6.41

815 of what number is 225?

Answer

92=412

Exercise 4.6.42

1115 of what number is 2235?

Exercise 4.6.43

1116 of what number is 1?

Answer

1611 or 1511

Exercise 4.6.44

What part of 2340 is 3920?

Exercise 4.6.45

435 of 3922 is what number?

Answer

3077

Exercises for Review

Exercise 4.6.46

Use the numbers 2 and 7 to illustrate the commutative property of addition.

Exercise 4.6.47

Is 4 divisible by 0?

Answer

no

Exercise 4.6.48

Expand 37. Do not find the actual value.

Exercise 4.6.49

Convert 3512 to an improper fraction.

Answer

4112

Exercise 4.6.50

Find the value of 38 \div \dfrac{9}{16} \cdot \dfrac{6}{5}\).


This page titled 4.6: Applications Involving Fractions is shared under a CC BY license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) via source content that was edited to the style and standards of the LibreTexts platform.

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