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← Mixed and Decimal Numbers

Reference

Converting Between Different Forms of Numbers

Method

Converting a Decimal Number Into a Fraction

It is possible to convert a decimal number into a fraction and the other way around. Consider the following decimal number.

0.56

A decimal number can be rewritten as a fraction in three steps.

Count the Number of Decimal Places

n

The number $0.56$ can be read as $56$ hundredths. There are two decimal places.

Write as a Fraction With the Denominator of

1 0^{n}

The number has

2

decimal places. This means that

0.56

can be written it as a fraction with a numerator of

56

and with a denominator of

1 0^{2} .

0.56 = \frac{5 6}{1 0 ^{2}} ⇓ 0.56 = \frac{5 6}{1 0 0}

Simplify the Fraction

Next, check whether

\frac{5 6}{1 0 0}

can be simplified. Start by splittting the numerator and denominator into prime factors.

56100 = 2 \cdot 2 \cdot 2 \cdot 7 = 2 \cdot 2 \cdot 5 \cdot 5

The numbers share two common factors. Their product is the GCF of

56

and

100 .

GCF (56, 100) = 2 \cdot 2 = 4

Finally, divide both the numerator and denominator by

4 .

\frac{5 6}{1 0 0}

ReduceFrac

$\frac{a}{b} = \frac{a / 4}{b / 4}$

\frac{5 6 \div 4}{1 0 0 \div 4}

CalcQuot

Calculate quotient

\frac{1 4}{2 5}

The fractions

\frac{1 4}{2 5}

and

\frac{5 6}{1 0 0}

are equivalent and they both correspond to the decimal

0.56 .

Extra

Interact With an Applet That Converts Decimals to Fractions

Submit a decimal number between

1

and

0.001

with no more than

3

digits after the decimal point. Then, the process of converting that decimal into a fraction will be shown.

$The submitted decimal is converted to a fraction$

Method

Converting a Fraction Into a Decimal Number

It is possible to convert a fraction into a decimal number and the other way around. Consider the following fraction.

\frac{1 6}{2 5}

Divide the numerator of

16

by the denominator of

25

by using the long division to rewrite the fraction as a decimal.

The result is

0.64 .

This is the decimal number that corresponds to the fraction

\frac{1 6}{2 5} .

Extra

Rewriting Fractions With the Denominators That Are Powers of

10

A fraction can have a denominator that is a power of $10 .$ Consider a few examples.

Fraction	$\frac{7}{1 0}$	$\frac{2 6}{1 0 0}$	$\frac{7 8 2}{1 0 0 0}$

In that case, the procedure of the long division of the numerator by the denominator is not the best way to go. Instead, the fraction can be rewritten directly as a decimal. First, count how many zeros each denominator has.

Fraction	$\frac{7}{1 0}$	$\frac{2 6}{1 0 0}$	$\frac{7 8 2}{1 0 0 0}$
Number of Zeros	$1$	$2$	$3$

Then, move the decimal point of the numerator to the left the number of times equal to the number of zeros in the denominator. For example, in the case of

\frac{7}{1 0},

there is one zero. This indicates that the decimal point of

7

will be moved one place to the left.

The rest of the fractions can be rewritten into decimal numbers in a similar manner.

Fraction	$\frac{7}{1 0}$	$\frac{2 6}{1 0 0}$	$\frac{7 8 2}{1 0 0 0}$
Number of Zeros	$1$	$2$	$3$
Decimal	$0.7$	$0.26$	$0.782$

Method

Converting a Mixed Number Into an Improper Fraction

Improper fractions and mixed numbers are two different ways of writing numbers that can have the same value. Sometimes, it is useful to convert between them. Consider the following mixed number.

5 \frac{2}{9}

This mixed number can be rewritten as an improper fraction in three steps.

Multiply the Integer Part by the Denominator

First, identify the integer part of the mixed number. This is the integer number written before the fraction.

5 is the integer part of the mixed number 5 and 2/9

Next, multiply the integer part by the denominator of the fraction. In this case, the denominator of the fraction is

9 .

5 \times 9 = 45

Add the Numerator

Add the numerator of the fraction to the number from the previous step. In the given mixed number, the numerator of the fraction is

2 .

45 + 2 = 47

This is the numerator of the improper fraction.

5 \frac{2}{9} = \frac{4 7}{?}

Write the Denominator

Write the numerator of the fraction part as the denominator of the improper fraction. The denominator in the fraction of the given mixed number is

9 .

Therefore, this is also the denominator of the improper fraction.

5 \frac{2}{9} = \frac{4 7}{9}

Extra

Interact With an Applet that Converts Different Mixed Numbers Into Improper Fractions

Submit the values of the integer part, numerator and denominator between

1

and

15,

inclusively. Then, the process of converting the mixed number into an improper fraction will be illustrated.

$Mixed number is rewritten as a fraction$

Method

Converting an Improper Fraction Into a Mixed Number

Improper fractions and mixed numbers are two different ways of writing numbers that can have the same value. Converting an improper fraction into a mixed number can help to estimate the actual value of the fraction. Consider the following improper fraction.

\frac{2 1}{4}

This improper fraction can be rewritten as a mixed number in three steps.

Divide the Numerator by the Denominator

Start by dividing the numerator of the improper fraction by the denominator. Note that the quotient must be an integer number.

Applet to compute the division of two numbers, 21 and 4

Here, the result of the division of

21

4

is the quotient of

5

with a reminder of

1 .

Write the Integer Part

Recall that a mixed number consists of an integer part and a proper fraction. The integer part is equal to the quotient of the improper fraction. In this case, it is $5 .$

$Mixed number with the integer of 5 and an unknown proper fraction$

Write the Fraction Part

Now the numerator and denominator of the fraction part will be identified. The numerator is equal to the remainder of the division from the first step. In this case, the reminder is $1$ and becomes the numerator of the fraction part.

$Mixed number with the integer of 5 and the proper fraction with the numerator of 1$

Note that the numerator must be less than the denominator since the fraction part of a mixed number is a proper fraction. The denominator is the same as the denominator of the improper fraction. Therefore, its value is $4 .$

$Mixed number with the integer of 5 and the proper fraction of 1 over 4$

The numerator is less than the denominator, so the fraction is indeed a proper fraction. Finally, finding the mixed number corresponding to $\frac{2 1}{4}$ is complete.

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