Multiplication and Division of Decimals

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Fractions Units

Multiplication and Division of fractions are relatively easier tasks than addition and subtraction. Multiplication of fractions is often applied in many everyday calculations and in many situations it amounts to simple cancelling out of numbers. Both multiplications and division of fractions are difficult to understand concepts but the skills and methods to solve them are not hard to learn. In this unit we will look at the methods required in solving these problems.

Multiplication

Follow these steps in solving multiplication of fractions problem:

Write all fraction terms as numerators and denominators
Cancel out those terms that can be simplified
Multiply numerator with numerator
Multiply denominator with denominator
Re-write the fraction or the term as the answer

See Example 1

Division

Follow these steps in solving division problems in fraction

Write all fraction terms as numerators and denominators and use to separate fraction terms.
Change the symbol to X and re-write the fraction term on the right hand of the symbol in reverse order( numerator becomes denominator and vice versa)
Simplify the fraction terms as a simple multipliction
Re-write the resulting fraction or term as the answer

See Example 2

Examples

Example 1

First we will cancel out terms 9 and 3 by dividing by 3 and then simplify the terms

Comments:

This problem is already written with all terms in fractions. But, the term 9 from first fraction can be cancelled out with term 3 from second fraction by dividing both numerator and denominator by 3.

This simplifies to

Now, numerators multiply each other and denominators multiply each other

Example 2

Re-write the terms using the X symbol instead of and simplify the resulting fraction terms

Comments:
This is simple problem and requires simple steps:

The problem is:

changing the division sign to a multiplication sign and reversing the fration terms on the right we get:

It is now easy to simplify this problem by cancelling out 4 by 2 and 9 by 3.

Have a Go

Problem 1

Problem 2

Problem 3

Problem 4

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Practice Questions

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Solution 1

To solve this problem first we re-write the terms as fractions

Now, since the number 5 is part of both numerator and denominator, we can cancel this out by dividing both top and bottom parts with number 5:

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Solution 2

In this problem there are many terms that can be simplified. First, look at numbers 11 and 77, they can be simplified by dividing both numerator and denominator by 11

In the same way numbers 48 and 24 can be simplified as:

Even, 35 and 7 can be simplified as:

Next, simplify 4 and 2 as:

Even, 2 and 18 can be further reduced as:

You can see that this multi-step cancellation and simplification could have been done in fewer steps, but once you know the method, practice it doing in fewer steps.

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Solution 3

Re-write the terms in simple form

Now, change the division sign into multiply and inverse the second fraction

Simplify these terms by dividing both 50 and 15 with 5

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Solution 4

Re-write the fraction in simple form as

Now, change the division sign to multiply and inverse the second fraction

Simplify this by dividing both 25 and 5 with 5 and reducing the fraction

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