There is a pile of 27 cards. 15 of the cards are red. The rest of the cards are black. Part a) What fraction of the cards are black?
Wait, to answer this question, we need to first work out the number of black cards in the pile as we haven’t been given this information explicitly in the question. We’re told that there are 27 cards in the pile and 15 of them are red. So to find the number of black cards, we need to subtract 15 from 27. And it gives 12. So this tells us then that 12 out of the 27 cards are black. We can write 12 out of 27 as a fraction. It’s equal to 12 over 27.
So we’ve written down the fraction of black cards. But this fraction can be simplified as both the numerator and denominator can be divided by three. 12 divided by three is four and 27 divided by three is nine. So the fraction simplifies to four over nine or four-ninths. This is an equivalent fraction as we’ve done the same thing, that is divide by three, to both the numerator and denominator. The fraction of black cards in the pile is four-ninths.
Part b) State the ratio of the number of black cards to the number of red cards. You must give your ratio in its simplest form.
When we’re asked for a ratio, we must make sure we give the numbers in the order that they’ve been requested in the question. So this question says black cards to red cards. So we’re writing the number of black cards first and then the number of red cards. The number of black cards in the pile we found was 12. And the number of red cards is 15. So the ratio of black cards to red cards is 12 to 15. So we’ve written down the ratio. But the question tells us that we must give our ratio in its simplest form. Which means we need to cancel down any common factors.
12 and 15 are both in the three times table. Which means we can divide both parts of this ratio by three. 12 divided by three is four and 15 divided by three is five. So the ratio simplifies to four to five. Four and five have no common factors other than one. So the ratio can’t be simplified any further. The ratio of the number of black cards to the number of red cards in the pile, in its simplest form, is four to five.