# 4.8 Exercise supplement

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This module is from Fundamentals of Mathematics by Denny Burzynski and Wade Ellis, Jr. This module is an exercise supplement for the chapter "Introduction to Fractions and Multiplication and Division of Fractions" and contains many exercise problems. Odd problems are accompanied by solutions.

## Fractions of whole numbers ( [link] )

For Problems 1 and 2, name the suggested fraction.

$\frac{2}{6}$ or $\frac{1}{3}$

For problems 3-5, specify the numerator and denominator.

$\frac{4}{5}$

numerator, 4; denominator, 5

$\frac{5}{\text{12}}$

$\frac{1}{3}$

numerator, 1; denominator, 3

For problems 6-10, write each fraction using digits.

Three fifths

Eight elevenths

$\frac{8}{\text{11}}$

Sixty-one forty firsts

Two hundred six-thousandths

$\frac{\text{200}}{6,\text{000}}$

zero tenths

For problems 11-15, write each fraction using words.

$\frac{\text{10}}{\text{17}}$

ten seventeenths

$\frac{\text{21}}{\text{38}}$

$\frac{\text{606}}{\text{1431}}$

six hundred six, one thousand four hundred thirty-firsts

$\frac{0}{8}$

$\frac{1}{\text{16}}$

one sixteenth

For problems 16-18, state each numerator and denominator and write each fraction using digits.

One minute is one sixtieth of an hour.

In a box that contains forty-five electronic components, eight are known to be defective. If three components are chosen at random from the box, the probability that all three are defective is fifty-six fourteen thousand one hundred ninetieths.

numerator, 56; denominator, 14,190

About three fifths of the students in a college algebra class received a “B” in the course.

For problems 19 and 20, shade the region corresponding to the given fraction.

$\frac{1}{4}$

$\frac{3}{7}$

## Proper fraction, improper fraction, and mixed numbers ( [link] )

For problems 21-29, convert each improper fraction to a mixed number.

$\frac{\text{11}}{4}$

$2\frac{3}{4}$

$\frac{\text{15}}{2}$

$\frac{\text{51}}{8}$

$6\frac{3}{8}$

$\frac{\text{121}}{\text{15}}$

$\frac{\text{356}}{3}$

$\text{118}\frac{2}{3}$

$\frac{3}{2}$

$\frac{5}{4}$

$1\frac{1}{4}$

$\frac{\text{20}}{5}$

$\frac{9}{3}$

3

For problems 30-40, convert each mixed number to an improper fraction.

$5\frac{2}{3}$

$\text{16}\frac{1}{8}$

$\frac{\text{129}}{8}$

$\text{18}\frac{1}{3}$

$3\frac{1}{5}$

$\frac{\text{16}}{5}$

$2\frac{9}{\text{16}}$

$\text{17}\frac{\text{20}}{\text{21}}$

$\frac{\text{377}}{\text{21}}$

$1\frac{7}{8}$

$1\frac{1}{2}$

$\frac{3}{2}$

$2\frac{1}{2}$

$8\frac{6}{7}$

$\frac{\text{62}}{7}$

$2\frac{9}{2}$

Why does $0\frac{1}{\text{12}}$ not qualify as a mixed number?

because the whole number part is zero

Why does 8 qualify as a mixed number?

## Equivalent fractions, reducing fractions to lowest terms, and raising fractions to higher term ( [link] )

For problems 43-47, determine if the pairs of fractions are equivalent.

$\frac{1}{2}$ , $\frac{\text{15}}{\text{30}}$

equivalent

$\frac{8}{9}$ , $\frac{\text{32}}{\text{36}}$

$\frac{3}{\text{14}}$ , $\frac{\text{24}}{\text{110}}$

not equivalent

$2\frac{3}{8}$ , $\frac{\text{38}}{\text{16}}$

$\frac{\text{108}}{\text{77}}$ , $1\frac{5}{\text{13}}$

not equivalent

For problems 48-60, reduce, if possible, each fraction.

$\frac{\text{10}}{\text{25}}$

$\frac{\text{32}}{\text{44}}$

$\frac{8}{\text{11}}$

$\frac{\text{102}}{\text{266}}$

$\frac{\text{15}}{\text{33}}$

$\frac{5}{\text{11}}$

$\frac{\text{18}}{\text{25}}$

$\frac{\text{21}}{\text{35}}$

$\frac{3}{5}$

$\frac{9}{\text{16}}$

$\frac{\text{45}}{\text{85}}$

$\frac{9}{\text{17}}$

$\frac{\text{24}}{\text{42}}$

$\frac{\text{70}}{\text{136}}$

$\frac{\text{35}}{\text{68}}$

$\frac{\text{182}}{\text{580}}$

$\frac{\text{325}}{\text{810}}$

$\frac{\text{65}}{\text{162}}$

$\frac{\text{250}}{\text{1000}}$

For problems 61-72, determine the missing numerator or denominator.

$\frac{3}{7}=\frac{?}{\text{35}}$

15

$\frac{4}{\text{11}}=\frac{?}{\text{99}}$

$\frac{1}{\text{12}}=\frac{?}{\text{72}}$

6

$\frac{5}{8}=\frac{\text{25}}{?}$

$\frac{\text{11}}{9}=\frac{\text{33}}{?}$

27

$\frac{4}{\text{15}}=\frac{\text{24}}{?}$

$\frac{\text{14}}{\text{15}}=\frac{?}{\text{45}}$

42

$\frac{0}{5}=\frac{?}{20}$

$\frac{\text{12}}{\text{21}}=\frac{\text{96}}{?}$

168

$\frac{\text{14}}{\text{23}}=\frac{?}{\text{253}}$

$\frac{\text{15}}{\text{16}}=\frac{\text{180}}{?}$

192

$\frac{\text{21}}{\text{22}}=\frac{\text{336}}{?}$

For problems 73-95, perform each multiplication and division.

$\frac{4}{5}\cdot \frac{\text{15}}{\text{16}}$

$\frac{3}{4}$

$\frac{8}{9}\cdot \frac{3}{\text{24}}$

$\frac{1}{\text{10}}\cdot \frac{5}{\text{12}}$

$\frac{1}{\text{24}}$

$\frac{\text{14}}{\text{15}}\cdot \frac{7}{5}$

$\frac{5}{6}\cdot \frac{\text{13}}{\text{22}}\cdot \frac{\text{11}}{\text{39}}$

$\frac{5}{\text{36}}$

$\frac{2}{3}÷\frac{\text{15}}{7}\cdot \frac{5}{6}$

$3\frac{1}{2}÷\frac{7}{2}$

1

$2\frac{4}{9}÷\frac{\text{11}}{\text{45}}$

$\frac{8}{\text{15}}\cdot \frac{3}{\text{16}}\cdot \frac{5}{\text{24}}$

$\frac{1}{\text{48}}$

$\frac{8}{\text{15}}÷3\frac{3}{5}\cdot \frac{9}{\text{16}}$

$\frac{\text{14}}{\text{15}}÷3\frac{8}{9}\cdot \frac{\text{10}}{\text{21}}$

$\frac{4}{\text{35}}$

$\text{18}\cdot 5\frac{3}{4}$

$3\frac{3}{7}\cdot 2\frac{1}{\text{12}}$

$\frac{\text{50}}{7}=7\frac{1}{7}$

$4\frac{1}{2}÷2\frac{4}{7}$

$6\frac{1}{2}÷3\frac{1}{4}$

2

$3\frac{5}{\text{16}}÷2\frac{7}{\text{18}}$

$7÷2\frac{1}{3}$

3

$\text{17}÷4\frac{1}{4}$

$\frac{5}{8}÷1\frac{1}{4}$

$\frac{1}{2}$

$2\frac{2}{3}\cdot 3\frac{3}{4}$

$\text{20}\cdot \frac{\text{18}}{4}$

90

$0÷4\frac{1}{8}$

$1÷6\frac{1}{4}\cdot \frac{\text{25}}{4}$

1

## Applications involving fractions ( [link] )

Find $\frac{8}{9}$ of $\frac{\text{27}}{2}$ .

What part of $\frac{3}{8}$ is $\frac{\text{21}}{\text{16}}$ ?

$\frac{7}{2}$ or $3\frac{1}{2}$

What part of $3\frac{1}{5}$ is $1\frac{7}{\text{25}}$ ?

Find $6\frac{2}{3}$ of $\frac{9}{\text{15}}$ .

4

$\frac{7}{\text{20}}$ of what number is $\frac{\text{14}}{\text{35}}$ ?

What part of $4\frac{1}{\text{16}}$ is $3\frac{3}{4}$ ?

$\frac{\text{12}}{\text{13}}$

Find $8\frac{3}{\text{10}}$ of $\text{16}\frac{2}{3}$ .

$\frac{3}{\text{20}}$ of what number is $\frac{\text{18}}{\text{30}}$ ?

4

Find $\frac{1}{3}$ of 0.

Find $\frac{\text{11}}{\text{12}}$ of 1.

$\frac{\text{11}}{\text{12}}$

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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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