Fill in the blanks. Eight-tenths equals 16 over what equals what thirtieths.
In this problem, we’re given three fractions. And they’re all worth the same. And the way of saying this is that they’re all equivalent. We know this because of the equal size that is separating them. But we can see that not all of these fractions have been completed. The denominator is missing from the second fraction. And in the final fraction, the numerator is missing.
Our task in this problem is to fill in the blanks, to find out what those missing numbers are. And the way we can do this is to remind ourselves how to find an equivalent fraction. To find an equivalent fraction to another fraction, we either have to multiply or divide the numerator and the denominator. And the really important rule that we need to remember is whatever we do to the top number, we must also do to the bottom.
Now, we know that 16 over something is equivalent to eight-tenths. We may not know what the denominator of the second fraction is. But we do know what the numerator is. And we can see how it’s changed. It was eight in eight-tenths. And now, it’s 16. So what could we have multiplied or divided by to get from eight to 16? Well, 16 is double eight. We must’ve multiplied by two. And to keep our fraction equivalent, we need to obey that rule. Whatever we do to the top number, we must also do to the bottom. So we need to multiply the bottom number or the denominator by two. 10 multiplied by two equals 20. So we can say eight-tenths is equal to sixteen twentieths.
In our final fraction, we’ve got the denominator. But we don’t have the numerator. We can see that the denominator is 30. So we could think to ourselves, how do we get from 20 to 30? Well, one way is to add 10. But we know that finding the equivalent fraction doesn’t work like this. It always has to be to multiply or divide. And we can’t multiply or divide 20 by a whole number to get 30 at all. How are we going to find the answer? Well, remember that all three fractions are equivalent. So we can go all the way back to the first fraction. The denominator in our first fraction is 10.
So how do we get from 10 to 30? The denominator is being multiplied by three. So to find our missing numerator, we need to multiply eight by three too. Eight threes or three lots of eight equals 24. And so twenty-four thirtieths is also the same as eight-tenths and sixteen twentieths. To find our missing numbers, we looked at how the numerator or the denominator changed. And once we worked out what was being multiplied by or divided by, we could then apply this to find our missing numbers. Eight-tenths equals sixteen twentieths equals twenty-four thirtieths.
Our two missing numbers are 20 and 24.