# How do I find 2/3 of a whole number?

Feb 11, 2017

To find $\frac{2}{3}$ of a whole number, you need to multiply the number by the numerator $2$ and divide that product by the denominator $3$.

#### Explanation:

If you represent any whole number by $n$;

then $\frac{2}{3}$ of that number is $\frac{2}{3} n$, or $\frac{2 n}{3}$

Looking at the last form you can see that you are multiplying the number $n$ by $2$ and dividing the product by $3$.

Example if: $n = 666$

$\frac{2}{3} \times n = \frac{2}{3} \times \left(6666\right) = \frac{13332}{3} = 4444$

Similarly if: $n = 1$

$\frac{2}{3} \times \left(1\right) = \frac{2}{3}$

Feb 11, 2017

Divide the number by 3 to find 'one-third,, then multiply by 2 to find 'two-thirds'.
$\frac{2}{3}$ of a number = $n \div 3 \times 2$

#### Explanation:

It is important to understand what two-thirds actually means...

Working with 'thirds' means you have started with a number or a quantity of something (like sweets) and divided it into THREE EQUAL parts, each part being 'one third' of the original amount.

$\frac{1}{3}$ of 12 means $12 \div 3 = 4 \text{ } \rightarrow 4 + 4 + 4 = 12$

$\frac{1}{3}$ of 30 means $30 \div 3 = 10 \text{ } \rightarrow 10 + 10 + 10 = 30$

$\frac{1}{3}$ of 15 means $15 \div 3 = 5 \text{ } \rightarrow 5 + 5 + 5 = 15$

Now, to find 'two-thirds", simply means use 2 of the parts.

(SO, divide by 3 and then multiply by 2)

$\frac{2}{3}$ of 12 means: $12 \div 3 \times 2 = 4 \times 2 = 8$

$\frac{2}{3}$ of 30 means:$30 \div 3 \times 2 = 10 \times 2 = 20$

$\frac{2}{3}$ of 15 means: $15 \div 3 \times 2 = 5 \times 2$

So for a number, let's call it $n ,$ can write this as:

$\frac{2}{3} \times n , \text{ or " (2xxn)/3" or "ndiv3xx2" or } n \times 2 \div 3$

It does not matter whether you multiply or divide first.

Dividing first makes the numbers smaller and easier to work with.

Finding $\frac{2}{3}$ of $63$. Compare the numbers:

$63 \div 3 \times 2 = 21 \times 2 = 42$

and

$63 \times 2 \div 3 = 126 \div 3 = 42$