**Applying multiplication and division of rational numbers :**

To solve many problems in math, often we may have to use multiplication and division of rational numbers.

In this section, we are going to learn how to multiply and divide rational numbers.

**Note : **

Rational numbers are usually denoted in the form "a/b".

That is, fraction form.

**Stuff 1 :**

To multiply a proper or improper fraction by another proper or improper fraction, we have to multiply the numerators and denominators.

For example,

2/3 x 4/5 = 8/15

1/3 x 7/11 = 7/33

**Stuff 2 :**

To multiply a proper or improper fraction by a whole number, we have to multiply the numerator of the fraction by the whole number.

For example,

(2/3) x 4 = 8/3

3 x 7/11 = 21/33

**Example 1 :**

Find 1/5 of 3/8

**Solution : **

1/5 of 3/8 = 1/5 x 3/8

1/5 of 3/8 = 3/40

**Example 2 :**

Find 2/9 x 3/2

**Solution : **

2/9 x 3/2 = 1/3

**Example 3 :**

Find 2/5 x 5 2/3

**Solution : **

2/5 x 5 2/3 = 2/5 x 17/3

2/5 x 5 2/3 = 34/15

2/5 x 5 2/3 = 2 4/15

**Example 4 :**

Find 6 3/4 x 7/10

**Solution : **

6 3/4 x 7/10 = 27/4 x 7/10

6 3/4 x 7/10 = (27x7) / (4x10)

6 3/4 x 7/10 = 189 / 40

6 3/4 x 7/10 = 4 29/40

**Example 5 :**

Lily reads 1/4 th of a book in 1 hour. How much of the book will she read in 3 1/2 hours ?

**Solution : **

The part of the book read by Lily in 1 hour = 1/4

So, the part of the book read by Lily in 3 1/2 hours is

= 3 1/2 x 1/4

= 7/2 x 1/4

= (7x1) / (2x4)

= 7/8

Hence, Lily reads 7/8 part of the book in 3 1/2 hours.

**Example 6 :**

David ate 1/3 of the pizza and gave 3/4 th of the remaining to his friend. What is the part of the pizza did David give his friend ?

**Solution : **

The part of the pizza eaten by David = 1/3

So, the remaining pizza = 2/3

The part of the given to his friend is

= 3/4 of the remaining

= 3/4 of 2/3

= 3/4 x 2/3

= 1/2

Hence, he gave 1/2 of the pizza to his friend.

**Step 1 :**

When we divide a fraction by another fraction, first we have to change the division sign as multiplication.

**Step 2 :**

Take reciprocal of the second fraction.

**Step 3 :**

Multiply the two fractions. (Numerator times numerator and denominator times denominator).

**Example 1 : **

Simplify : 2/5 ÷ 6/7

**Solution : **

Using the method explained above, we have

2/5 ÷ 6/7 = 2/5 x 7/6

2/5 ÷ 6/7 = (2x7) / (5x6)

2/5 ÷ 6/7 = 7/15

**Example 2 :**

Simplify : 7/5 ÷ 3/2

**Solution : **

Using the method explained above, we have

7/5 ÷ 3/2 = 7/5 x 2/3

7/5 ÷ 3/2 = (7x2) / (5x3)

7/5 ÷ 3/2 = 14/15

**Example 3 :**

Simplify : 5/12 ÷ 20/13

**Solution : **

Using the method explained above, we have

5/12 ÷ 20/13 = 5/12 ÷ 20/13

5/12 ÷ 20/13 = 5/12 x 13/20

5/12 ÷ 20/13 = (5x13) / (12x20)

5/12 ÷ 20/13 = 13/48

**Example 4 :**

Simplify : 2/19 ÷ 6 1/2

**Solution : **

First, let us convert the mixed number 6 1/2 in to improper fraction.

6 1/2 = 13/2

Now,m we have 2/19 ÷ 6 1/2 = 2/19 ÷ 13/2

Using the method explained above, we have

2/19 ÷ 13/2 = 2/19 x 13//2

2/19 ÷ 13/2 = (2x13) / (19x2)

2/19 ÷ 13/2 = 13 / 19

**Example 5 :**

David can make one pizza in 1/2 hour. How many pizzas can he make in 5/2 hours ?

**Solution : **

Time taken to make one pizza = 1/2 hour

No. of pizzas made in 5/2 hours = 5/2 ÷ 1/2

No. of pizzas made in 5/2 hours = 5/2 x 2/1

No. of pizzas made in 5/2 hours = (5x2) / (2x1)

No. of pizzas made in 5/2 hours = 5

After having gone through the stuff given above, we hope that the students would have understood "Applying multiplication and division of rational numbers".

Apart from the stuff given above, if you want to know more about "Applying multiplication and division of rational numbers", please click here

Apart from "Applying multiplication and division of rational numbers", if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**