Question

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

Answer 1

To find `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 `2/3` of that number is `2/3 n`, or `(2n)/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`

`2/3 xx n = 2/3 xx(6666) = 13332/3 = 4444`

Similarly if: `n = 1`

`2/3 xx (1) = 2/3`

Answer 2

Divide the number by 3 to find 'one-third,, then multiply by 2 to find 'two-thirds'.
`2/3` of a number = `n div 3 xx2`

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.

`1/3` of 12 means `12 div 3 = 4" "rarr 4 + 4+ 4 = 12`

`1/3` of 30 means `30 div 3 = 10" "rarr 10+10+10=30`

`1/3` of 15 means `15 div 3 = 5" "rarr 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)

`2/3` of 12 means: `12 div 3 xx 2 = 4xx 2 = 8`

`2/3` of 30 means:`30 div 3 xx 2= 10xx2 = 20`

`2/3` of 15 means: `15 div 3 xx2= 5xx2`

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

`2/3 xx n, " or " (2xxn)/3" or "ndiv3xx2" or "nxx2div3`

It does not matter whether you multiply or divide first.

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

Finding `2/3` of `63`. Compare the numbers:

`63 div 3 xx 2 = 21 xx 2 = 42`

and

`63 xx2 div 3 = 126 div 3 = 42`