Equivalent Fractions,

Decimals and Fractions

#13

= =12

24

48

Fractions that represent the same value are

equivalent fractions. So are

equivalent fractions.

Vocabulary

Example 1

Find two equivalent fractions for .4

6__

Example 2: Multiplying and Dividing to Find Equivalent Fractions

Find the missing number that makes the fractions equivalent.

35__

20___=

Example 3

Find the missing number that makes the fraction equivalent.

39__

27___=

Every fraction has one equivalent fraction that is called the simplest form of the fraction. A fraction is in simplest form when the GCF of the numerator and the denominator is 1.

Vocabulary

Example 4: Writing Fractions in Simplest Form

Write each fraction in simplest form.

20 48___

Example 5: Writing Fractions in Simplest Form

Write the fraction in simplest form.

710___

Example 6

Write each fraction in simplest form.

1216___

1216___

A number that contains both a whole number greater than 0 and a fraction, such as 1 , is called a mixed number.

34

__

__41

1 1__21

1 __43

2 __41

2 __21

Mixed numbers12

14

34

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5

Vocabulary

Example 7: Writing Decimals as Fractions or Mixed Numbers

Write each decimal as a fraction or mixed number.

0.67

Example 8: Writing Decimals as Fractions or Mixed Numbers

Write each decimal as a fraction or mixed number.

5.9

Example 9

Write each decimal as a fraction or mixed number.

3.07

Example 10: Writing Fractions as Decimals

Write each fraction or mixed number as a decimal.

20____ 3

Example 11: Writing Fractions as Decimals

3 __ 1

6

Write each fraction or mixed number as a decimal.

A terminating decimal, such as 0.75, has a finite number of decimal places. A repeating decimal, such as 0.666…, has a block of one or more digits that repeat continuously

0.80.750.60.60.50.40.30.250.2

Common Fractions and Equivalent Decimals1

3__1

5__ 1

4__ 2

5__ 1

2__ 3

5__ 2

3__ 3

4__ 4

5__

Vocabulary

Example 12: Comparing and Ordering Fractions and Decimals

Order the fractions and decimal from least to greatest.

, 0.8, 7 __10

3__4

Example 13

Order the fractions and decimal from least to greatest.

0.3, 3__5

, 0.53