## Prepare for compound fraction exam

**Introduction**

**:**

A certain part of the whole is called as fractions. The fractions can be denoted as `a/b` , Where a, b are integers. We can multiply two or more fractions.There are three types of fraction in math.

1) Proper fraction

2) Improper fraction

3) Compound fraction

In this article we are going to see how to prepare the compound fraction exam, example and solved problems on prepare for compound fraction exam .

Prepare for compound fraction exam :

**Proper fraction:**

A fraction is of the form `a/b` , where b > a

**Improper fraction:**

A fraction is of the form` a/b` , where a > b

**Compound fraction:**

A fraction is of the form a `b/c` . Here a = Quotient.

b = Remainder

c = Divisor.

Problems on prepare for compound fraction exam :

**Problem 1:**

Write the compound fraction for the following fraction `13 / 3`

**Solution:**

Given, Fraction `13/3`

We need to find the compound fractions for `13/3`

To find compound fraction, divided 13 by 3.

_____

3 ) 13 ( 4 ------------- > Quotient

12

1 ------------- > Remainder

The compound fraction for `13/3` = Quotient `"Remainder "/ "Divisor"` = 4 `1/3 `

**Verification:**

We can verify the answer as shown in below,

Quotient `"Remainder" / "Divisor"` = `"(quotient * Divisor ) + Remainder " / " Divisor"`

`4 1 / 3` = ( ( 4 *3) + 1 ) / 3

= `(12+1) / 3`

**Problem 2:**

Find compound fractions for the decimal 7.5

**Solution:**

Given, decimal number 7.5

We need to find two mixed numbers,

Multiply and divide 7.5 by 10,

7.5 = `7.5 xx ( 10/10)`

= `(7.5 xx 10) / 10`

= `75 / 10`

Now divide 75 by 10 ,

____

10) 75 ( 7

70

5

The compound fraction of 7.5 = `75 / 10` is 7 `5/10`

**Problem 3:**

Dividing the compound fractions `8 5/12` ÷ `4 5/6`

**Solution:**

Given , two compound fractions `8 5/12` , `4 5/6`

We need to dividing the above fractions.

First we convert it into fractions.

`8 5/ 12` = `(( 12 * 8 ) + 5 ) / 12`

= `101 / 12`

`4 5/6` = `(( 4 * 6) + 5 ) / 6`

= `29 / 6`

`8 5/12` ÷` 4 5/6` = `101 / 12` ÷ `29 / 6`

Take a reciprocal for `29 / 6`

Reciprocal of `29 / 6` = `6 / 29`

Now multiply it with `101/12`

`8 5/12` ÷ `4 5/6` = `101 / 12` ÷ `29 / 6` = `101 / 12` * `6 / 29 `

`101 / 12 xx 6 / 29` = `( 101 xx 6) / ( 12 xx 29)`

= `606 / 348 `

We can simplify it further.

Divide by 6 on both numerator and denominator,

`606 / 348` = `( 606 / 6 ) / ( 348 / 6)`

= `101 / 58`

**Answer:**`8 5/12` ÷ `4 5/6` = `101 / 58`

**Problem 4:**

Add the following two compound fractions

**`4 2/3 + 5 6/7 `**

**Solution:**

Given , `4 2/3 + 5 6/7 `

We need to find the addition of given fraction,

4` 2/3 + 5 6/7` = `4 + 2 /3 + 5 + 6/7`

= `9 + 2/3 + 6/7`

We need to find the least common denominator,

lcd = 3 * 7 = 21

`9 + 2/3 + 6/7` = `189 / 21 + 14 / 21 + 18 / 21`

= `( 189 + 14 + 18 ) / 21`

= `221 / 21`

**Answer:**4 `2/3` + 5 `6/7` = `221 / 21`