Multiplication of fractions
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Multiplication of fraction and whole number.
Definition.
To multiply fraction by a whole number, it is necessary to multiply numerator by a whole number, and to leave without modifications a denominator. Simplify the fraction if needed.Examples of multiplication fraction and integer
Example 1.
Find the product of fraction and natural number:
| 3 | · 2 | = | 3 · 2 | = | 6 |
| 7 | 7 | 7 |
Example 2.
Find the product of fraction and natural number:
| 1 | · 4 | = | 4 | = | 2·2 | = | 2 |
| 2 | 2 | 2 |
Multiplication of fractions.
Definition.
- To multiply fractions
- multiply the numerators and multiply the denominators;
- simplify the fraction if needed.
Examples of multiplication of fractions
Example 3.
Find the product of two fractions:
| 3 | · | 2 | = | 3 · 2 | = | 6 |
| 7 | 5 | 7 · 5 | 35 |
Example 4.
Find the product of two fractions:
| 10 | · | 3 | = | 10 · 3 | = | 2 · 5 · 3 | = | 5 | = | 5 |
| 9 | 4 | 9 · 4 | 2 · 2 · 3 · 3 | 2 · 3 | 6 |
Multiplication of mixed numbers.
Definition.
- To multiply mixed numbers:
- converting mixed numbers to improper fractions;
- multiply the numerators and multiply the denominators;
- simplify the fraction;
- if this fraction is improper then convert fraction to a mixed number.
Examples of multiplication of mixed numbers
Example 5.
Find the product of two mixed numbers:
| 2 | 1 | · | 1 | 2 | = | 2 · 2 + 1 | · | 1 · 3 + 2 | = | 5 | · | 5 | = | 5 · 5 | = | 25 | = | 6 · 4 + 1 | = 4 | 1 |
| 2 | 3 | 2 | 3 | 2 | 3 | 2 · 3 | 6 | 6 | 6 |
Example 6.
Find the product of mixed number and integer:
| 4 | 1 | · | 6 | = | 4 · 3 + 1 | · | 6 | = | 13 · 6 | = | 26 |
| 3 | 3 | 3 |
Example 7.
Find the product of mixed number and fraction:
| 2 | 1 | · | 3 | = | 2 · 7 + 1 | · | 3 | = | 15 | · | 3 | = | 15 · 3 | = | 3 · 3 | = | 9 | = | 7 + 2 | = 1 | 2 |
| 7 | 5 | 7 | 5 | 7 | 5 | 7 · 5 | 7 | 7 | 7 | 7 |
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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