Jackson cuts one and a half melons into portions, each of which is three-eighths of a whole melon. How many portions does he get?
In order to calculate the number of portions, we need to divide the total amount of melon, one and a half, by the size of each portion, in this case three-eighths. In order to divide a mixed number by a fraction, we firstly need to convert the mixed number into a top-heavy or improper fraction. We are told that Jackson has one and a half melons. This is the same as three-halves or three over two. We need to divide three-halves by three-eighths. When dividing two fractions, we simply multiply the first fraction by the reciprocal of the second fraction. This is often known as KCF. We keep the first fraction the same, we change the division to a multiplication, and we flip the second fraction.
Three-halves divided by three-eighths is therefore equal to three-halves multiplied by eight-thirds. When multiplying two fractions, we usually just multiply the numerators and then multiply the denominators. However, it is always worth checking whether we can cross cancel or cross simplify first. There is a three on the numerator and denominator. Therefore, these will cancel. Two and eight are both divisible by two, as eight divided by two is four and two divided by two is equal to one.
We can now multiply the numerators. One multiplied by four is four. Multiplying the denominators gives us one. Four divided by one or four over one is equal to four. This means that Jackson gets four portions of melon. Had we not recognized that we could cross cancel, we could’ve multiplied the numerators and denominators separately. Three multiplied by eight is 24, and two multiplied by three is six. 24 divided by six or 24 over six is also equal to four. This confirms that our answer was correct.