What is three-eighths divided by six?
In this problem, we’re being asked to divide a fraction, three-eighths, by a whole number, six. We could write this as three-eighths divided by six or another way of expressing the same thing, three-eighths divided by six over one. This way, both of the numbers are written as fractions. Six over one is an improper fraction. It has a value larger than one. We can see that the numerator — the number on the top — is larger than the denominator — the number on the bottom. But six over one has a value of six. And so, our calculation is still three-eighths divided by six.
This model represents our proper fraction, three-eighths. We’ve divided the rectangle into eight equal parts and three out of the eight parts are shaded. Now, we have to divide these three-eighths by six: one, two, three, four, five, six. We divided three-eighths into six. We can see that each of the six parts we’ve divided three-eighths into contains three smaller rectangles: one, two, three. But what fraction of the whole amount does this represent? Three out of what? The way to find out is to extend each of our lines across the entire shape. And this way, we’re dividing all of the shape into parts of equal size. Once we’ve done that, we can count the number of parts and find out how many there are in one whole.
We can see that there are eight columns and we already know that there are six rows. Eight lots of six equals 48. And so, we know that there are 48 parts. When we divided three-eighths by six, we chose three of these 48 parts. As with a fraction, that is the same as three-eighths divided by six is three 48ths. Now, we can simplify this fraction by dividing both the numerator and the denominator by the same number.
What number can we divide both three and 48 by? Well, we could divide by one. But it would have no effect on the fraction. But we also could divide by three because three is a factor of both three and 48. Three divided by three equals one. And how many threes are in 48? To help us, we could partition 48 into 30 and 18. There are 10 threes in 30. And we know six threes make 18 and 10 plus six equals 16. So 48 divided by three equals 16. So although the answer is three 48ths, we can write this much more simply as one 16th.
We could also calculate the same answer using a written method. Dividing three-eighths by six is the same as multiplying three-eighths by one over six or one-sixth. Look how we’ve turned the second fraction upside down and changed the sign from a division to a multiplication. And watch how if we do this, we still get the same answer. Remember, to multiply two fractions together, we need to multiply the numerators and then the denominators. Three times one equals three and eight multiplied by six — we’ve done this already — is 48. And, of course, we can use the same simplification method to change this to one 16th. There’re two methods and they both find us the same answer.
Three-eighths divided by six equals one 16th.