When It Doesn't Share Evenly

Fourteen children are going on a school trip by car. Each car can take 4 children. How many cars are needed? 14 ÷ 4 doesn't come out evenly: there is no number that makes 4 × ? = 14. Does that mean the question has no answer?

Something left over

Let's do it as in the Sharing Fairly lesson: fill one car with 4 children, then another, then another.

• After 3 cars, 12 children are seated (3 × 4 = 12).
• 2 children are still standing on the pavement.
• They are not enough to fill another car.

So 14 ÷ 4 is 3, with 2 left over. What is left over is called the remainder. We write it:

• 14 ÷ 4 = 3 remainder 2.

You can check it: 3 cars of 4 is 12, and 12 + 2 = 14. Every child is counted.

The remainder is always small

The remainder is always less than the size of the group. If 4 or more children were left over, they could fill another car, and we would not have finished. So when you divide by 4, the remainder can only be 0, 1, 2 or 3.

A remainder of 0 means the number shares evenly, like 12 ÷ 4 = 3.

What to do with the remainder

The sum is the same in each of these questions, 14 ÷ 4 = 3 remainder 2. But the answer to the question is not always the same:

• How many cars are needed? The 2 children left over still need a car, so the answer is 4 cars - one more than 3.
• How many full boxes of 4 eggs can you pack from 14 eggs? Only full boxes count, so the answer is 3 boxes (and 2 eggs stay out).
• Share 14 apples fairly between 4 friends. Each gets 3, and 2 are left. Or you could cut the 2 left over into pieces - but that needs numbers smaller than one, which come in the next module.

So always ask: what does the remainder mean here? That decides the answer, not the sum alone.

Try it at home

1. Deal 17 coins into piles of 5. How many full piles, and how many left over?
2. A bus holds 30 people. How many buses are needed for 70 people? Answers below.

Answers: 3 piles, remainder 2; 70 ÷ 30 is 2 remainder 10, so 3 buses.

Words to know

• remainder - what is left over when a number doesn't share evenly; it is always less than the size of the group

Big idea

When a number doesn't share evenly, something is left over: 14 ÷ 4 is 3 remainder 2. The remainder is always smaller than the group. What you do with it - another car, or leave it out - depends on the question.