Multiplication of common fractions
To multiply a fraction by a fraction, you need to multiply the numerator of the first fraction by the numerator of the second - this will be the numerator of the result, and multiply the denominator of the first fraction by the denominator of the second - this will be the denominator of the result.
Example 3. Calculate the product
.
3/7
*
5/11
=
3*5/7*11
=
15/77
.
Example 4. Calculate the product
.
, Let's reduce this fraction by 3 and by 5, we get
Multiplying mixed fractions
To multiply a mixed fraction by a mixed fraction, you need to write both fractions as improper fractions and multiply them according to the rule for multiplying fractions.
Example 5. Calculate the product
.
1
1/2
* 3
2/3
=
3/2
*
11/3
=
33/6
=
11/2
= 5
1/2
.
Example 6. Calculate the product
.
5
1/4
* 2
3/5
=
21/4
*
13/5
=
273/20
= 13
13/20
.
Division of common fractions
To divide one fraction by another, you need to multiply the numerator of the first fraction by the denominator of the second - this will be the numerator of the result, and multiply the denominator of the first by the numerator of the second - this will be the denominator of the result. Thus, dividing fractions comes down to multiplication.
Example 7. Calculate the value of an expression
.
, let's reduce the resulting fraction by 3:
.
Example 8. Calculate the value of an expression
.
3
2/7
: 2
1/7
=
23/7
:
15/7
=
23*7/7*15
, let's reduce the resulting fraction by 7:
23*7/7*15
=
23/15
= 1
8/15
.
Example 9. Calculate the value of an expression
.
15 : 2
1/2
=
15/1
:
5/2
=
15*2/1*5
, let's reduce this fraction by 5:
.
Example 10. Calculate the value of an expression
.
7
2/9
: 13 =
65/9
:
13/1
=
65*1/9*13
, let's reduce this fraction by 13:
.
