Four-sixths multiplied by three-fifths equals what?
How do we multiply two fractions together? Well, unlike addition and subtraction where we have to have the same denominator, we
can multiply fractions with different denominators. So we multiply the denominators together, multiply the numerators together. So we could write our answer like this: four multiplied by three over six multiplied
by five. Let’s work out the answer.
First, we can multiply the numerators: four times three, four three to 12. So the numerator in our answer is 12. Now, we multiply the denominators: what six times five? We know that six fives are 30. So the denominator in our answer is 30. This gives us an answer of twelve thirtieths.
We can draw a quick diagram to show that this is correct. Draw a shape, split it into six, and then shade four of those six. So we’ve shown four-sixths. We’re multiplying by three-fifths. So let’s divide the shape in the opposite direction into fifths. We can see that we’ve divided the shape into five columns as well as the six rows
We’re multiplying by three-fifths. So let’s shade in three of those columns. And the part of our diagram that has been shaded twice should give us our answer. There are 12 shaded parts out of a total possible 30, twelve thirtieths.
Now, we could write the answers as twelve thirtieths. It’s completely correct way to answer the question. But we could also simplify the fraction. What can we divide 12 and 30 by to help simplify the fraction? The factors of 12 are one, two, three, four, six, and 12. And the factors of 30 are one, two, three, five, six, 10, 15, and 30.
We can see that the factors we have in common are one, two, three, and six. Let’s divide by six so that we make the fraction as small and as simple as
possible. 12 divided by six equals two and 30 divided by six equals five.
So first, we multiplied the numerators. Then, we multiplied the denominators. This gave us an answer of twelve thirtieths, which is completely correct. But we decided to simplify it. So we divided the numerator and the denominator by the same number. We divided them both by six to get the answer two-fifths.
Four-sixths multiplied by three-fifths equals two-fifths.