If Noah’s son is 6.75 years old, express his age as a mixed number in the simplest form.
We’re given the age of Noah’s son as a decimal. We’re told that he’s 6.75 years old. We know the decimals have a whole number part and a part that’s worth less than one. In 6.75, the whole number part is six, six ones. This is the number of whole years in our son’s age. And as we said there’s a part that’s worth less than zero. In this decimal, it’s 0.75 or 75 hundredths. We’re asked to express Noah’s son’s age, not as a decimal, but as a mixed number. If we remind ourselves, a mixed number is a number that’s made up of a whole number and a fraction. So something like two and a half is a mixed number. The whole number part is the number two. And then there’s a fraction on the end; in this case, it’s one half.
This part is less than one. So we need to convert 6.75 into a mixed number. We already know the whole number part of our mixed number is going to be six. But how can we write 0.75, which is the part that’s worth less than one, as a fraction? 0.75 is the same as 75 hundredths. So we could write Noah’s son’s age as six and 75 hundredths. But we are asked to express the mixed number in the simplest form. Can we make the fraction any simpler than it already is? What can we divide both 75 and 100 by?
Both numbers are divisible by 25. There are three 25s in 75, and there are four 25s in 100. So 75 hundredths or 0.75 is the same as three-quarters. You may have known that already. Noah’s son’s age as a decimal is 6.75 years old. And we decided that we could write this as a mixed number as six and 75 hundredths. By dividing both the numerator and denominator by 25, we were able to simplify the fraction part of the mixed number. In its simplest form, Noah’s son’s age is six and three-quarters.