4.1 Fractions of whole numbers

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Sample set a

The diagrams in the following problems are illustrations of fractions.

The fraction $\frac{1}{3}$ is read as "one third."

The fraction $\frac{3}{5}$ "is read as "three fifths."

The fraction $\frac{6}{7}$ is read as "six sevenths."

When the numerator and denominator are equal, the fraction represents the entire quantity, and its value is 1.

$\frac{\text{nonzero whole number}}{\text{same nonzero whole number}}=1$

Practice set a

Specify the numerator and denominator of the following fractions.

$\frac{4}{7}$

4, 7

$\frac{5}{8}$

5, 8

$\frac{\text{10}}{\text{15}}$

10, 15

$\frac{1}{9}$

1, 9

$\frac{0}{2}$

0, 2

In order to properly translate fractions from word form to number form, or from number form to word form, it is necessary to understand the use of the hyphen .

Use of the hyphen

One of the main uses of the hyphen is to tell the reader that two words not ordinarily joined are to be taken in combination as a unit. Hyphens are always used for numbers between and including 21 and 99 (except those ending in zero).

Sample set b

Write each fraction using whole numbers.

Fifty three-hundredths. The hyphen joins the words three and hundredths and tells us to consider them as a single unit. Therefore,
fifty three-hundredths translates as $\frac{\text{50}}{\text{300}}$

Fifty-three hundredths. The hyphen joins the numbers fifty and three and tells us to con­sider them as a single unit. Therefore,
fifty-three hundredths translates as $\frac{\text{53}}{\text{100}}$

Four hundred seven-thousandths. The hyphen joins the words seven and thousandths and tells us to consider them as a single unit. Therefore,
four hundred seven-thousandths translates as $\frac{\text{400}}{\text{7,000}}$

Four hundred seven thousandths. The absence of hyphens indicates that the words seven and thousandths are to be considered individually.
four hundred seven thousandths translates as $\frac{\text{407}}{\text{1000}}$

Write each fraction using words.

$\frac{\text{21}}{\text{85}}$ translates as twenty-one eighty-fifths.

$\frac{\text{200}}{\text{3,000}}$ translates as two hundred three-thousandths. A hyphen is needed between the words three and thousandths to tell the reader that these words are to be considered as a single unit.

$\frac{\text{203}}{\text{1,000}}$ translates as two hundred three thousandths.

Practice set b

Write the following fractions using whole numbers.

one tenth

$\frac{1}{\text{10}}$

eleven fourteenths

$\frac{\text{11}}{\text{14}}$

sixteen thirty-fifths

$\frac{\text{16}}{\text{35}}$

eight hundred seven-thousandths

$\frac{\text{800}}{7,\text{000}}$

Write the following using words.

$\frac{3}{8}$

three eighths

$\frac{1}{\text{10}}$

one tenth

$\frac{3}{\text{250}}$

three two hundred fiftieths

$\frac{\text{114}}{\text{3,190}}$

one hundred fourteen three thousand one hundred ninetieths

Name the fraction that describes each shaded portion.

$\frac{3}{8}$

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

In the following 2 problems, state the numerator and denominator, and write each fraction in words.

The number $\frac{5}{9}$ is used in converting from Fahrenheit to Celsius.

5, 9, five ninths

A dime is $\frac{1}{\text{10}}$ of a dollar.

1, 10, one tenth

Exercises

For the following 10 problems, specify the numerator and denominator in each fraction.

$\frac{3}{4}$

numerator, 3; denominator, 4

$\frac{9}{\text{10}}$

$\frac{1}{5}$

numerator, 1; denominator, 5

$\frac{5}{6}$

$\frac{7}{7}$

numerator, 7; denominator, 7

$\frac{4}{6}$

$\frac{0}{\text{12}}$

numerator, 0; denominator, 12

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

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

numerator, 18; denominator, 1

$\frac{0}{\text{16}}$

For the following 10 problems, write the fractions using whole numbers.

four fifths

$\frac{4}{5}$

two ninths

fifteen twentieths

$\frac{\text{15}}{\text{20}}$

forty-seven eighty-thirds

ninety-one one hundred sevenths

$\frac{\text{91}}{\text{107}}$

twenty-two four hundred elevenths

six hundred five eight hundred thirty-fourths

$\frac{\text{605}}{\text{834}}$

three thousand three forty-four ten-thousandths

ninety-two one-millionths

$\frac{\text{92}}{1,\text{000},\text{000}}$

one three-billionths

For the following 10 problems, write the fractions using words.

$\frac{5}{9}$

five ninths

$\frac{6}{\text{10}}$

$\frac{8}{\text{15}}$

eight fifteenths

$\frac{\text{10}}{\text{13}}$

$\frac{\text{75}}{\text{100}}$

seventy-five one hundredths

$\frac{\text{86}}{\text{135}}$

$\frac{\text{916}}{\text{1,014}}$

nine hundred sixteen one thousand fourteenths

$\frac{\text{501}}{\text{10,001}}$

$\frac{\text{18}}{\text{31,608}}$

eighteen thirty-one thousand six hundred eighths

$\frac{1}{\text{500,000}}$

For the following 4 problems, name the fraction corresponding to the shaded portion.

$\frac{1}{2}$

$\frac{4}{7}$

For the following 4 problems, shade the portion corresponding to the given fraction on the given figure.

$\frac{3}{5}$

$\frac{1}{8}$

$\frac{6}{6}$

$\frac{0}{3}$

State the numerator and denominator and write in words each of the fractions appearing in the state­ments for the following 10 problems.

A contractor is selling houses on $\frac{1}{4}$ acre lots.

Numerator, 1; denominator, 4; one fourth

The fraction $\frac{\text{22}}{7}$ is sometimes used as an approximation to the number $\pi$ . (The symbol is read “pi.")

The fraction $\frac{4}{3}$ is used in finding the volume of a sphere.

Numerator, 4; denominator, 3; four thirds

One inch is $\frac{1}{\text{12}}$ of a foot.

About $\frac{2}{7}$ of the students in a college statistics class received a “B” in the course.

Numerator, 2; denominator, 7; two sevenths

The probability of randomly selecting a club when drawing one card from a standard deck of 52 cards is $\frac{\text{13}}{\text{52}}$ .

In a box that contains eight computer chips, five are known to be good and three are known to be defective. If three chips are selected at random, the probability that all three are defective is $\frac{1}{\text{56}}$ .

Numerator, 1; denominator, 56; one fifty-sixth

In a room of 25 people, the probability that at least two people have the same birthdate (date and month, not year) is $\frac{\text{569}}{\text{1000}}$ .

The mean (average) of the numbers 21, 25, 43, and 36 is $\frac{\text{125}}{4}$ .

Numerator, 125; denominator, 4; one hundred twenty-five fourths

If a rock falls from a height of 20 meters on Jupiter, the rock will be $\frac{\text{32}}{\text{25}}$ meters high after $\frac{6}{5}$ seconds.

Exercises for review

( [link] ) Use the numbers 3 and 11 to illustrate the commutative property of addition.

$3+\text{11}=\text{11}+3=\text{14}$

( [link] ) Find the quotient. $\text{676}÷\text{26}$

( [link] ) Write $7\cdot 7\cdot 7\cdot 7\cdot 7$ using exponents.

${7}^{5}$

( [link] ) Find the value of $\frac{8\cdot \left(6+\text{20}\right)}{8}+\frac{3\cdot \left(6+\text{16}\right)}{\text{22}}$ .

( [link] ) Find the least common multiple of 12, 16, and 18.

144

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