Which of the following division expressions has a quotient of two-thirds? Two-ninths divided by six-sevenths. One-quarter divided by one-seventh. Two-thirds divided by four-sevenths. Four-ninths divided by two-thirds. Or three-quarters divided by one-sixth.
Each of the division expressions in this question involves a fraction being divided by another fraction. Dividing two fractions can be a tricky concept to understand. We’re looking for a division that has a quotient of two-thirds. Remember that, in a division calculation, the quotient is the answer. The amount that we get when we divide one number by another number. Let’s remind ourselves how to divide two fractions. We keep the first fraction the same. But we turn the second fraction upside down. So the denominator becomes the numerator. And the numerator becomes the denominator. The second thing we do is to swap the division symbol for a multiplication. And we multiply the two fractions together.
Remember, when we multiply two fractions, we can simply multiply the numerator and then the denominator. Two times seven equals 14. And nine sixes are 54. The quotient is 14 over 54. This doesn’t say two-thirds. But remember, it may still be worth two-thirds. So we need to simplify it as far as we can. We can divide by the numerator and the denominator by two. So the answer is worth seven twenty-sevenths. Our first calculation does not have a quotient of two-thirds.
Let’s try the second. Swap the second fraction around. And then turn the calculation into a multiplication. One times seven equals seven. And four multiplied by one equals four. This time, the answer is an improper fraction. It’s greater than one. Two-thirds is less than one. So this calculation doesn’t have a quotient of two-thirds either.
Onto the third division. Swap the numerator and the denominator. Change from a division into a multiplication. And then multiply. Two times seven equals 14. And three times four equals 12. Again, our fraction is an improper fraction. The numerator is larger than the denominator. This means it’s greater than one. So even though we could simplify this fraction, we could divide both the numerator and denominator by two. It’s not worth doing because we know that it’s not gonna have a value of two-thirds. Two-thirds is less than one.
Onto our fourth calculation. Step one. Step two. Step three. Four times three is 12. And nine times two equals 18. This time, the numerator is less than the denominator. Could this be worth two-thirds? Let’s simplify the fraction. Both numbers are multiples of six. So let’s divide by six. 12 divided by six equals two. And 18 divided by six equals three. The quotient is worth two-thirds. We found the division expression that has a quotient that’s worth two-thirds.
There was only one more division left. So we might as well just check that our answer is correct and check that this isn’t worth two-thirds. Step one. Step two. And then multiply. Three multiplied by six is 18. And four multiplied by one equals four. It’s another fraction that’s greater than one whole. And so we’ve identified the division expression that has a quotient of two-thirds. We calculated that four-ninths divided by two-thirds had a quotient of twelve eighteenths. And this could be simplified to two-thirds.
So we know the division expression that has a quotient of two-thirds is four-ninths divided by two-thirds.