Five-sevenths plus three twenty-firsts equals what?
These fractions have different denominators. Before we can add them, we need to find a common denominator. Seven multiplied by three is 21. 21 is a multiple of seven. So we could make both fractions into twenty-firsts.
To get from seven to 21, we had to multiply by three. Three times seven is 21. So we need to do the same to the numerator. We need to multiply five by three. Five-sevenths is equal to fifteen twenty-firsts. Now we can add fifteen twenty-firsts and three twenty-firsts, which gives us a total of eighteen twenty-firsts.
We need to simplify this fraction. Which number could we divide 18 and 21 by? Both these numbers are multiples of three. 18 divided by three is six, and 21 divided by three is seven. Five-sevenths plus three twenty-firsts equals six-sevenths. We chose to add the fractions as twenty-firsts.
We could also change these fractions into sevenths and add the sevenths. So the first thing we need to do is work out how many sevenths three twenty-firsts is. To get from 21 to seven, we need to divide by three. So we have to do the same to the numerator. Three divided by three is one. Now we can add five-sevenths and one-seventh, which makes six-sevenths. Both methods give us the same answer of six-sevenths.