Dividing fractions

Contenido

What is the division of fractions?

Unlike the mathematical operation that we know as division, in the division of fractions a distribution is not made but a multiplication, which is a cross multiplication between the numerators and denominators of both fractions.

Learn more about: "Division" →

Symbol or sign of the division of fractions

The division of fractions is represented with the symbol of a diagonal "/" or an orbelo "÷", in some cases it is represented with two dots ":", the symbol of the division is known as "between".

Learn more about: "Operations with Fractions" →

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How to dividing fractions?

To obtain the numerical value in the form of fractions, in the division of fractions there are 2 recommended methods, there are other methods but they can be confusing with other fraction operations.

1 / 4

÷

1 / 2

=

2 / 4

Method 1 of the division of fractions: Multiply in cross

It consists of multiplying the numerator of the first fraction by the denominator of the second fraction and the result of the multiplication corresponds to the numerator of the result, on the other hand, to obtain the result of the denominator you must multiply the denominator of the first fraction by the numerator of the second fraction.

For example, fractions 1/3 are divided by 2/6, the following steps are performed:

• 1. The numerator of the first fraction is multiplied with the denominator of the second fraction.

  1

  / 3

  ÷

  2 /

  6

  =

  ? /  
• 2. The result of the multiplication is placed in the position of the numerator.
  1 / 3

  ÷

  2 / 6

  =

  6 /  
• 3. Now the denominator of the first fraction is multiplied by the numerator of the second fraction.
  1 /

  3

  ÷

  2

  / 6

  =

  6 / ?
• 4. The result of the multiplication is placed in the position of the denominator.
  1 / 3

  ÷

  2 / 6

  =

  6 / 6
Therefore, we can summarize the procedure in one step, where the blue mark indicates the result of the numerator and the red mark the result of the denominator:

1

/ 3

÷

2 /

6

=

1 x 6 / 3 x 2

=

6 / 6
The result of division can be simplified because both numerator and denominator have the same value. Thus, 6/6 = 1.

Examples:

2 / 3
÷
4 / 3
=
2 x 3 / 3 x 4
=
6 / 12
5 / 2
÷
6 / 2
=
5 x 2 / 2 x 6
=
10 / 12
5 / 6
÷
4 / 3
=
5 x 3 / 6 x 4
=
15 / 24
8 / 3
÷
2 / 4
=
8 x 4 / 3 x 2
=
32 / 6

From the previous examples you can simplify 6/12 = 1/2, 10/12 = 5/6 and 15/24 = 5/8 and 32/6 = 16/3.

Exercise:

A)
5 / 3
÷
3 / 3
= ?
B)
9 / 2
÷
5 / 2
= ?
C)
6 / 5
÷
4 / 3
= ?
D)
6 / 8
÷
2 / 2
= ?
See result

Method 2 of division of fractions: Multiply internal numbers and external numbers

It consists of accommodating a fraction over another and subsequently multiplying the external numbers of the accommodation to obtain the numerator result, then we must multiply the internal numbers to obtain the result of the denominator.

In the following example, fractions 2/3 will be divided by 1/4, to carry out the division of fractions by this method the following steps are performed:

• 1. The external numbers are multiplied.

  2

  / 3 1

  4

  =

  ? /  
• 2. The result of the multiplication is placed in the position of the numerator.
  2 / 3 1 4

  =

  8 /  
• 3. The internal numbers are multiplied.
  2 /

  3

  1

  4

  =

  8 / ?
• 4. The result of the multiplication is placed in the position of the denominator.
  2 / 3 1 4

  =

  8 / 3

Note: For method two the arrangement of the fractions is very important, it is recommended to learn method 2.

Example:

4 / 3 4 6
=
24 / 12
3 / 4 7 6
=
18 / 28
5 / 3 4 5
=
25 / 12
7 / 4 7 3
=
21 / 28

From the previous examples it can be simplified 24/12 = 2, 18/28 = 9/14 and 21/28 = 3/4.

Ejercicios:

A)
3 / 5 4 7
= ?
B)
4 / 6 9 2
= ?
C)
2 / 4 7 3
= ?
D)
7 / 4 3 4
= ?
See result

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Division of mixed fractions

In the division of mixed fractions, it is necessary that the whole part be expressed as a fraction with the same denominator as in the fractional part that accompanies it. For example, to perform the following mixed multiplication:

6

5 / 3

÷ 3

4 / 5

1.- The entire part is multiplied by the denominator of the accompanying fraction.
6 x 3 = 18 3 x 5 = 15

2.- The result of the multiplication is added with the numerator of the accompanying fraction.
18 + 5 / 3
÷
15 + 4 / 5

3.- Once the mixed fractions are converted, the division can be made.
23 / 3
÷
19 / 5
=
23 x 5 / 3 x 19
=
115 / 57

Learn more about: “Mixed fraction” →