Multiplying fractions

We want to work out one half of one third. Here's a strip of paper to do it on. We'll fold it twice. In maths, the word 'of' means multiply, so one half of one third is one half times one third. Let's fold the strip and see what that comes to. One third means one part out of 3, so we fold the strip into 3 equal parts. One of them is one third, and we'll colour it blue. Now we want one half of that blue one third. Half means 2 parts, so we fold in half the other way. The two folds cross. 3 parts one way and 2 parts the other make 6 equal parts. One half of the blue one third is this one piece. That one piece out of 6 is one sixth. On the expression, 1 times 1 goes on top, and 2 times 3 goes on the bottom. That's one sixth, the very piece we folded. Multiply the tops, and multiply the bottoms. The rule works on any two fractions. Try two thirds times one quarter. Before multiplying, look across the expression: the top 2 and the bottom 4 share a factor of 2. So divide both by it: cross them out, and write 1 above the 2, and 2 below the 4. Now multiply what is left. 1 times 1 goes on top, and 3 times 2 goes on the bottom. One sixth, already in its simplest form. Your turn now. This one has no strip to fold. Work out three quarters times two fifths. Cancel any common factor first, then multiply, and give the answer in its simplest form. Try it first. Pause if you like. Let's finish it. Look across the expression: the bottom 4 and the top 2 share a factor of 2. So divide both by it: cross them out, and write 2 below the 4, and 1 above the 2. 3 times 1 goes on top, and 2 times 5 goes on the bottom. Three quarters times two fifths is three tenths. To multiply fractions, multiply the top numerator, then multiply the bottom denominator. Cancel any common factor, so that the answer is in its simplest form. A fraction of a fraction is a multiplication, every time.