# How do you find the quotient of 4.8 divided by 6.75?

##### 1 Answer
Apr 29, 2016

$\frac{32}{45} \to 0.7111 \overline{\textcolor{w h i t e}{.} 1 \textcolor{w h i t e}{.}}$

#### Explanation:

You $\underline{\text{do not state}}$ the quotient is to be derived $\underline{\text{without}}$ a calculator.
Write as: $\frac{4.8}{6.75}$

Multiply by 1 but in the form of $1 = \frac{100}{100}$

$\frac{4.8 \times 100}{6.75 \times 100} \equiv \frac{480}{675}$

The numerator end in 0 and the denominator ends in 5. So 5 is a common factor.

$\frac{480 \div 5}{675 \div 5} \equiv \frac{96}{135}$

9+6=15 which is divisible by 3 and 1+3+5 =9 which is also divisible by 3 so 3 is a common factor.

$\frac{96 \div 3}{135 \div 3} = \frac{32}{45}$ This is the quotient but in fraction form
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If you wish to convert this to decimal you divide 45 into 32

By calculator $\to 32 \div 45 = 0.7111 \overline{\textcolor{w h i t e}{.} 1 \textcolor{w h i t e}{.}}$

The bar means that the 1's go on repeating for ever