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# Decimals: Multiplying and Dividing

### Decimals: Multiplying and Dividing

Multiplying and dividing decimals can be achieved in a similar way to regular numbers.

Multiplying and dividing decimals is best achieved by moving the decimal point first.

When multiplying, move the decimal point to the right until both numbers are whole numbers. Then, when you have your answer, move the decimal point to the left by the same amount.

Let's try $2.1 \times 3.4$

Change these to whole numbers

$2.1 \times 3.4 \rightarrow21 \times 34$

Multiply these numbers

$21 \times 34=714$

Move the decimal point back

To make whole numbers, we moved the decimal point one place to the right for each number. Now, we need to move it the same amount of places to the left: $714 \rightarrow7.14$

So our answer is $7.14$

Nice! 👍

Check that this is reasonable

Round your numbers to $2$ and $3.4$. $2 \times 3.4=6.8$, so our answer of $7.14$looks like it is in the right area!

Find $1.44 \times 1.2$

Find $45.6 \times 3.2$

When dividing, we move the decimal points the same number of places to the right for each number and then do the division with whole numbers. We do **not** need to do anything to the answer.

Let's have a go at $\dfrac{3.15}{0.45}$

Make the numerator a whole number

This means moving 2 places to the left. $3.15\rightarrow315$

Adjust the denominator in the same way

We moved the numerator 2 places, so we should also move the denominator 2 places to the left. $0.45\rightarrow 45$

Divide the two whole numbers

$\dfrac{315}{45}=7$

Nice! 🙌

The answer is $7$ - no need to move the decimal place again. This is because the numerator and denominator stay in the same **ratio**.

What is $\dfrac{3.4}{0.17}$?