How do you solve #\frac { 4} { 5} \div \frac { 1} { 2}#?

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Answer 1 · 2016-10-22T01:52:41

#8/5 = 1 3/5#

Write the problem as a complex fractions and then simplify by using the multiplicative inverse.

The fraction sign literally means to divide. So the problem is one fraction divided by a second fraction. The problem can be written

# (4/5)/(1/2) # This is called a complex fraction

To simplify the fraction multiply both sides by the inverse of the bottom fraction

# (1/2) xx (2/1) = (2/2) = (1/1)# By multiplying by the inverse the bottom term or fraction disappears.

The fairness principal states that what ever you do to one side must be done to the other side. ( The multiplication property of equality)

So both top fraction and the bottom fraction must be multiplied by the inverse # 2/1# This gives

#{ ( 4/5) xx ( 2/1)} /{ (1/2) xx (2/1)}# The bottom fraction turns to #(1/1)#

Giving this

#{ (4 xx 2)/(5xx1)}/ (1/1) = 8/5#

#8/5 = 1 3/5#

The key to dividing fractions is to use the inverse of the second fraction which becomes the denominator of the complex fraction.

Answer 2 · 2016-10-22T07:44:04

#8/5 = 1 3/5#

Dividing by any number is the same as multiplying by its reciprocal.

For example, saying "10 divided by 2", is the same as "half of 10"

In Maths:

#10 color(red)(div 2) = 10 color(red)(xx 1/2)#

Dividing by a fraction is exactly the same. Multiply by its reciprocal.

#4/5 color(red)(div 1/2)#
#color(white)(.x)darr#
#4/5 color(red)(xx 2/1)" "larr# no cancelling to be done. Multiply across

=#8/5#

=#1 3/5#