Comparing fractions.
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Comparing fractions with a common denominator
Definition.
To compare fraction with the common denominators (bottom number of a fraction) you need to compare numerators and to see which fraction is greater.Example of comparing fractions with the common denominators:
Example 1.
| 3 | < | 4 |
| 7 | 7 |
Example 2.
| 7 | > | 6 |
| 11 | 11 |
Comparing fractions with a common numerator
Definition.
The fraction with the smallest denominator is the larger fraction if the numerators are the same.Example of comparing fractions with the common numerator:
Example 3.
| 4 | > | 4 |
| 7 | 9 |
Example 4.
| 1 | < | 1 |
| 31 | 20 |
Comparing fractions
Definition.
To compare fractions with different denominators you need to make them the same finding the least common multiple (LCM) of the denominators (which is called the Least Common Denominator). Then to compare numerators and to see which fraction is greater.Example of comparing fractions:
Example 5.
| 8 | ? | 5 |
| 9 | 6 |
to reduce fractions to a common denominator
| 16 | ? | 15 |
| 18 | 18 |
as 16 > 15, then
| 8 | > | 5 |
| 9 | 6 |
Example 6.
| 3 | ? | 9 |
| 7 | 20 |
to reduce fractions to a common denominator
| 60 | ? | 63 |
| 140 | 140 |
as 60 < 63, then
| 3 | < | 9 |
| 7 | 20 |
Fraction
Forms of fractions (vulgar fraction, proper fraction, improper fractions, mixed numbers, decimals)
The basic property of fraction
Simplifying fractions
Least common denominator of fractions
Converting improper fractions (composed fractions) to mixed numbers
Converting mixed numbers to improper fractions (composed fractions)
Addition and Subtraction of fractions
Multiplication of fractions
Division of fractions
Comparing fractions
Convert Decimals to Common Fractions
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