# Division with Remainders

- Link: https://thecuriosi.com/lessons/division-with-remainders/
- Published: 2026-10-31T14:56:10+05:30
- Author: MAHENDRA MANCHIKALAPATI

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Sometimes things do not share out perfectly. If you share 13 marbles between 4 friends,
each friend gets 3 marbles, but 1 marble is left over. The amount left over is called
the **remainder**. In this lesson you will learn to find remainders and decide what
to do with them.

## What is a remainder?

A remainder is what is **left over** after you make as many equal groups as possible.
The remainder must always be **smaller than the divisor**. If it is not, you can
make another group.

### Example

Share 13 marbles among 4 friends:

 * Each friend gets 3 marbles, using 4 × 3 = 12 marbles.
 * 13 − 12 = 1 marble is left over.

We write: **13 ÷ 4 = 3 r 1** (read “3 remainder 1”).

If there is nothing left over, the remainder is 0, and we say the number divides**
exactly**. For example, 12 ÷ 4 = 3 with nothing left over.

## How to find a remainder

 1. Find the biggest multiple of the divisor that is **not more than** the total.
 2. That gives you the quotient.
 3. Subtract to find what is left over.

  |  Problem |  Biggest multiple that fits |  Quotient |  Remainder |  Answer |  
   |  17 ÷ 5 |  5 × 3 = 15 |  3 |  17 − 15 = 2 |  3 r 2 |  
 |  26 ÷ 4 |  4 × 6 = 24 |  6 |  26 − 24 = 2 |  6 r 2 |  
 |  50 ÷ 7 |  7 × 7 = 49 |  7 |  50 − 49 = 1 |  7 r 1 |

### Check your answer

Multiply the quotient by the divisor, then add the remainder. You should get the
total. For 17 ÷ 5 = 3 r 2: 3 × 5 = 15, and 15 + 2 = **17**. Correct!

## What does the remainder mean?

In real life, we must think about what to do with the remainder. There are three
common choices.

### Round up

**29 children** are going on a trip. Each car holds **4 children**. 29 ÷ 4 = 7 r
1. Seven cars carry 28 children, but one child still needs a seat! We need **8 cars**.

### Ignore it

You have **20 sweets** and want to make bags of **6**. 20 ÷ 6 = 3 r 2. You can make**
3 full bags**. The 2 extra sweets cannot fill a bag.

### Share it

**3 friends** share **7 pizzas**. 7 ÷ 3 = 2 r 1. Each friend gets 2 pizzas, and 
they can cut the last pizza into 3 equal slices to share. (You will learn about 
these parts, called fractions, later.)

## Key takeaways

 * The remainder is what is left over after making equal groups.
 * The remainder must be smaller than the divisor.
 * Check: quotient × divisor + remainder = total.
 * In word problems, decide whether to round up, ignore or share the remainder.

## Practice

 1. 23 ÷ 5
 2. 38 ÷ 6
 3. 30 people want to ride a boat. Each boat holds 8 people. How many boats are needed?

Answers: 1 is 4 r 3. 2 is 6 r 2. 3 is 30 ÷ 8 = 3 r 6, so 4 boats are needed (round
up).

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