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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