Multiplication with fractions

You are baking a chocolate cake. The recipe calls for three-quarters of a deciliter of cocoa. How much cocoa do you need for three chocolate cakes? You need three-quarters, plus three-quarters, plus three-quarters, or three times three quarters. Look at the top of the screen and you'll see that three times three-quarters is nine-quarters, or two-and-one-quarter as a mixed fraction.

So, you need two-and-one-quarter of a deciliter of cocoa for three chocolate cakes. Now you cut a cake in half and eat one-third of one-half. What fraction of the cake have you eaten? As you see, one-third of one-half is equal to one-sixth of the whole cake. So you ate one-sixth of the cake.

Two fractions can always be multiplied by multiplying the numerators and the denominators separately. We write on the same fraction bar and multiply the numerators first. One times one is one. Then multiply the denominators. Three times two is six.

Indeed, the product is one-sixth. Sometimes it's easier to simplify the fractions before multiplying them. When multiplying fractions, you can use cross-simplification which means that you divide the denominator of one fraction and the numerator of the other one by the same number. Let's look at an example, five-sevenths times three-tenths. We can divide the numerator of the first fraction and the denominator of the second fraction by the same number.

In this case, by five. For the numerator, we have five divided by five equals one. And one times three equals three. For the denominator, we have ten divided by five, equals two, and seven times two, equals fourteen. So the product equals three-fourteenth.

Remember to multiply a fraction by a fraction, you multiply the numerators and the denominators separately. Sometimes it can be easier to simplify the fractions before you multiply them. When multiplying fractions, you can use cross-simplification which means that you can divide the numerator of one fraction, and the denominator of another fraction, by the same number.