Division of Fractions | Why sign of Division is changed to Multiplication?? | जानिए हर सवाल का जवाब

Division of Fractions | Why sign of Division is changed to Multiplication?? | जानिए हर सवाल का जवाब | Concept Clarification

This video helps to clarify concept about why sign of division is changed to Multiplication within seconds.This video Helps you to Clear your doubts / Concept related with these type of Questions and helpful in Basic Calculations

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Dividing Fractions
Multiplication and division are inverse operations. When we divide by 2, we could also solve the same problem by multiplying by ½ .

Think about 36 ÷ 2, which is equal 18. Half of 36, or 36 x ½ is also 18.

We can use this property to help us divide fractions.

Method 1:

Multiply by the reciprocal, also sometimes referred to as "Keep, Change, Flip."

Here is how it works. You rewrite the division question as a multiplication question by flipping the second fraction over.

Example #1:

Rewrite this question as

So

Example #2:

Rewrite this question as

So

Example #3:

Rewrite the whole number as a fraction first. 6

Then change the question to

Next, keep the first number, change the division to multiplication and then flip the second fraction over.





Example #4:

Start by writing 5 as a fraction. 5

Now we can rewrite the question as a multiplication problem.



So

There are other methods for dividing fractions if you cannot remember these steps.

Method 2:

Get common denominators and then divide the numerators.

Example #5:

Start by rewriting the problem with common denominators. The best denominator is 6.





Now that we have common denominators we can just divide the numerators.



Let's go through the steps one more time.

Example #6:

The lowest common denominator for this example would be 40.





Now we are ready to divide.



This method does work, but it requires common denominators before you can solve. This first option does not require common denominators, but you do have to remember to flip the second fraction and change the problem to multiplication.





When we multiply fractions, we multiply their numerators to find the numerator of the result, and we multiply their denominators to find the denominator of the result.

\frac34\times\frac17
​4
​
​3
​​ ×
​7
​
​1
​​

\frac{3\times1}{4\times7}
​4×7
​
​3×1
​​

\frac{3}{28}
​28
​
​3
​​

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When we divide fractions, we actually turn the division problem into a multiplication problem by turning the divisor (the second fraction) upside down (switching its numerator with its denominator) and changing the division symbol to a multiplication symbol at the same time. We call this process “multiplying by the reciprocal.” The reciprocal of a fraction a/ba/b is the fraction b/ab/a (where the numerator and denominator are flipped.

\frac34\div\frac17
​4
​
​3
​​ ÷
​7
​
​1
​​

\frac34\times\frac71
​4
​
​3
​​ ×
​1
​
​7
​​

\frac{3\times7}{4\times1}
​4×1
​
​3×7
​​

\frac{21}{4}
​4
​
​21
​​

It’s okay that in this last fraction, the numerator is larger than the denominator. When that’s the case, the fraction is called an “improper” fraction.

To do division with fractions, we turn the second fraction upside down and change the division symbol to a multiplication symbol at the same time.

\frac23\times\frac{11}{4}
​3
​
​2
​​ ×
​4
​
​11
​​

Then we treat this as a multiplication problem, by multiplying the numerators and the denominators separately.

\frac{2\times11}{3\times4}
​3×4
​
​2×11
​​

\frac{22}{12}
​12
​
​22
​​

We always like to give our answer in lowest terms, so we’ll simplify this fraction by canceling a 22 from the numerator and denominator.

\frac{22}{12}=\frac{2\cdot11}{2\cdot6}
​12
​
​22
​​ =
​2⋅6
​
​2⋅11
​​
\frac22\cdot\frac{11}{6}
​2
​
​2
​​ ⋅
​6
​
​11
​​

1\cdot\frac{11}{6}1⋅
​6
​
​11
​​

\frac{11}{6}
​6
​
​11
​
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