Division of fraction.
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Division of fraction into natural number.
Definition.
To divide fraction into whole number, it is necessary to multiply denominator by a whole number, and to leave without modifications a numerator. Simplify the fraction if needed.Examples of dividing of fractions into integer
Example 1.
Find the quotient of the fraction into integer:
| 3 | : 2 | = | 3 | = | 3 |
| 7 | 7 · 2 | 14 |
Example 2.
Find the quotient of the fraction into integer:
| 6 | : 3 | = | 6 | = | 2 · 3 | = | 2 |
| 11 | 11 · 3 | 11 · 3 | 11 |
Definition.
To get the reciprocal of a fraction, just turn it upside down. In other words swap over the Numerator and Denominator.
| 3 | - reciprocal fraction | 7 |
| 7 | 3 |
Division of natural number into fraction.
Definition.
To divide natural number into fraction, it is necessary to multiply natural number by reciprocal of fraction.Examples of dividing of integer into fraction
Example 3.
Find the quotient of the integer into fraction:
| 2: | 7 | = | 2· | 2 | = | 4 |
| 2 | 7 | 7 |
Example 4.
Find the quotient of the integer into fraction:
| 2: | 4 | = | 2· | 5 | = | 2 · 5 | = | 2 · 5 | = | 5 | = | 2 · 2 + 1 | = 2 | 1 |
| 5 | 4 | 4 | 2 · 2 | 2 | 2 | 2 |
Division of fraction.
Definition.
To divide fractions, it is necessary to multiply first fraction by reciprocal of second fraction.Examples of dividing of two fractions
Example 5.
Find the quotient of the two fractions:
| 3 | : | 4 | = | 3 | · | 5 | = | 3 · 5 | = | 15 |
| 7 | 5 | 7 | 4 | 7 · 4 | 28 |
Example 6.
Find the quotient of the two fractions:
| 6 | : | 4 | = | 6 | · | 7 | = | 6 · 7 | = | 3 · 2 | = | 3 | = | 2 + 1 | = 1 | 1 |
| 7 | 7 | 7 | 4 | 7 · 4 | 2 · 2 | 2 | 2 | 2 |
Division of mixed numbers.
Definition.
- To divide mixed numbers:
- converting mixed numbers to improper fractions;
- to multiply first fraction by reciprocal of second fraction;
- simplify the fraction;
- if this fraction is improper then convert fraction to a mixed number.
Examples of dividing of two mixed numbers
Example 7.
Find the quotient of the two mixed numbers:
| 1 | 1 | : | 2 | 2 | = | 1 · 2 + 1 | : | 2 · 3 + 2 | = | 3 | : | 8 | = | 3 | · | 3 | = | 3 · 3 | = | 9 |
| 2 | 3 | 2 | 3 | 2 | 3 | 2 | 8 | 2 · 8 | 16 |
Example 8.
Find the quotient of the mixed number into fraction:
| 2 | 1 | : | 3 | = | 2 · 7 + 1 | : | 3 | = | 15 | · | 5 | = | 15 · 5 | = | 25 | = 3 | 4 |
| 7 | 5 | 7 | 5 | 7 | 3 | 7 · 3 | 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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