Finding the whole

Hello, and welcome to Myriora Maths! Two sevenths of a number is twelve. What's the whole number? This is working backwards, and a bar makes it easy. Let's draw it!

Draw a bar, and cut it into seven equal parts. Two of the parts are twelve. So one part is twelve divided by two: six. And seven parts are seven times six: forty-two!

So here's the method. Divide by the top to find one part. Then multiply by the bottom to find the whole. And always check: two sevenths of forty-two is twelve.

Three quarters of a class are eighteen children. How many children are in the class? Eighteen divided by three is six in each quarter. Four quarters is twenty-four children!

Here's a harder one. A shop sells one quarter of its apples, and has thirty apples left. How many did it start with? If one quarter is sold, three quarters are left. So three quarters is thirty, one quarter is ten, and the whole is forty apples!

Let's try one together. One third of a number is seven. What's the number? Say it out loud!

One part is seven, and there are three parts. Three times seven is twenty-one!

Here's a question that catches lots of people. Two sevenths of a number is twelve. Some people work out two sevenths of twelve instead. But twelve is only a part of the number, so the whole must be bigger than twelve! The whole is forty-two.

Your turn! Three fifths of a number is twenty-four. What's the number? Pick the right card. You've got twenty seconds, or pause the video. Go!

Time's up! Three parts are twenty-four, so one part is eight. Five parts are five times eight: forty!

Quick review. Draw a bar cut into equal parts. Divide by the top to find one part. Multiply by the bottom to find the whole. And check: the whole must be bigger than the part you were given. See you next time!