Deep knowledge of dividing fractions!
Dividing fractions is not hard. Instead, it is very straightforward once you know how to multiply fractions.
It is important to explain some important terms or concepts before showing you how to divide fractions.
2/3 is a simple fraction and in the lesson about fractions, we called 2 the numerator and 3 the denominator. You can also call 2 the dividend and 3 the divisor.
Dividend and divisor are mostly used when doing long division. When we divide complex fractions, these terms can be used as well to describe the problem. If you need to know more about complex fractions, check this lesson about
complex fractions for a more comprehensive coverage. First, study this example.
More examples showing how dividing fractions work. Study carefully the following three fractions problems well.
Example #1:
3/4 ÷ 1/8
Invert the divisor, change division into multiplication, and multiply.
3/4 ÷ 1/8 = 3/4 × 8/1
3/4 ÷ 1/8 = (3 × 8) / (4 × 1)
3/4 ÷ 1/8 = 24 / 4
3/4 ÷ 1/8 = 6
Did you notice that this is the same problem as the one in the figure above? Here though, we write the fraction with a '/' called 'slash' instead of a horizontal fraction bar.
Moreover, what you have is a fraction divided by another fraction.
Whenever a fraction is divided by another, we call this a complex fraction. This is a very simple example of complex fraction. Complex fractions can look a lot more complicated than this.
Here with this complex fraction, the dividend is 3/4 and the divisor is 1/8.
When you divide a fraction by another, invert the divisor and multiply the inverted divisor by the dividend. The inverted divisor is called the reciprocal.
Inverting a fraction means that your numerator will become your denominator and your denominator will become your numerator.
For example, when inverting 2/3, we get 3/2.
Example #2:
2/5 ÷ 4/3
2/5 ÷ 4/3 = 2/5 × 3/4
2/5 ÷ 4/3 = (2 × 3)/(5 × 4)
2/5 ÷ 4/3 = 6/20
To simplify 6/20, get the greatest common factor of 6 and 20.
GCF(6,20) = 2
Divide both numerator and denominator by 2.
You get 3/10
Example #3:
3/8 ÷ 3/4
3/8 ÷ 3/4 = 3/8 × 4/3
3/8 ÷ 3/4 = (3 × 4)/(8 × 3)
3/8 ÷ 3/4 = 12/24
3/8 ÷ 3/4 = 1/2
Take the dividing fractions quiz to see how well you can divide fractions.
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