Multiply or divide fractions calculator

Result:
Calculation path:

This calculator can be used to divide or multiply fractions or mixed numbers. The result is displayed including the calculation path.

Multiplying fractions

If you want to multiply 2 fractions, multiply the numerator of one fraction by the numerator of the other fraction and write the result in the numerator of the resulting fraction. Then multiply the denominator of one fraction by the denominator of the other fraction and write the result in the denominator of the resulting fraction.

Example:

3
4
and
5
7
are to be multiplied.

3
4
∙
5
7
=
3∙5
4∙7
=
15
28

Dividing fractions

If you want to divide a fraction by another fraction, multiply the first fraction by the reciprocal of the second fraction. The reciprocal is formed by interchanging the numerator and the denominator.

Example:

3
4
is to be divided by
5
7
.

3
4
:
5
7
=
3
4
∙
7
5
=
3∙7
4∙5
=
21
20

Multiplying or dividing mixed numbers

If you want to multiply or divide mixed numbers, you must first convert them to fractions. If you want the result to be a mixed number again, then you can convert the resulting fraction back to a mixed number.

Example:

2
3
4
should be divided by 1
5
7
.

First, the mixed numbers are converted to fractions:

2
3
4
:1
5
7
=
2∙4 + 3
4
:
1∙7 + 5
7
=
11
4
:
12
7

Then the division is performed by multiplying the first fraction and the reciprocal of the second fraction:

11
4
:
12
7
=
11
4
∙
7
12
=
11∙7
4∙12
=
77
48

Finally, the fraction is converted back to a mixed number:

77
48
=1
29
48

Reducing before multiplying

Large numbers in the fractions make it difficult to multiply the fractions, to use the result for further calculations, and to reduce the resulting fraction after multiplying. Therefore, it is often useful to reduce the fractions before multiplying, if this is possible.

If for example
111
555
and
49
56
are to be multiplied, then the result is
5439
31080
. Just doing the multiplication without a calculator is time-consuming. And then you might want to shorten the fraction.

It is easier to find out that the first fraction can be shortened by 111 and the second by 7. After reducing the fractions, you get:
111
555
∙
49
56
=
1
5
∙
7
8

If you perform the multiplication, you get as result
7
40
. Much simpler.

Cross simplification:

Before multiplying, however, fractions may be reduced not only if the numerator and denominator from the same fraction have a common divisor, but also if the numerator from one fraction and the denominator from the other fraction have a common divisor.

Example:

33
56
∙
49
55

The numerator of the first fraction and the denominator of the second fraction are both divisible by 11. Thus, the numerator of the first fraction and the denominator of the second fraction may be divided by 11.

33
56
∙
49
55
=
3
56
∙
49
5

The denominator of the first fraction and the numerator of the second fraction can both be divided by 7:

3
56
∙
49
5
=
3
8
∙
7
5

Now the multiplication is much easier:

3
8
∙
7
5
=
21
40

Cross simplification may only be used if there is a multiplication sign between the two fractions. In this case, both the numerator from the first fraction and the denominator from the second, as well as the denominator from the first fraction and the numerator from the second fraction were able to be simplified. However, it would have been legitimate as well if only one of the two combinations could have been simplified.

good explanatory videos on YouTube:

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