What division means

Sharing a pile equally

Division is the arithmetic of fair shares. You have a pile of something and a number of people or places to share it among. Division tells you how much each share gets. Twelve grapes shared among three children gives four grapes each. We write that as 12 ÷ 3 = 4.

The division sign asks a question: if the pile is split into that many equal groups, how big is one group? The key word is equal. Every share must be the same size, exactly as the groups in a multiplication must be the same size.

Making equal groups

There is a second way to read the same division. Instead of counting out shares, you can ask how many groups of a given size fit into the pile. Twelve grapes make three groups of four. The picture is the same; the question is different.

This second reading is useful for problems about packing. If 54 pencils are packed with 6 in each box, you are asking how many boxes of 6 fit into 54. The division 54 ÷ 6 = 9 answers it directly. Children who can move between the two pictures find division word problems much easier.

The names of the parts

Division has its own three names. The number being divided is the dividend. The number you divide by is the divisor. The answer is the quotient. In 12 ÷ 3 = 4, the dividend is 12, the divisor is 3 and the quotient is 4.

Notice how the three numbers line up with a multiplication fact: 12 ÷ 3 = 4 and 3 × 4 = 12. Division undoes multiplication, and multiplication undoes division. This back-and-forth relationship is the theme of the last lessons in this course.