Division Facts

Grade 3 · Math · Study Guide

Understand division as sharing equally or grouping, and use multiplication facts to divide.

Division is the process of splitting a number into equal groups. There are two ways to think about division.

Sharing equally: If you have 20 cookies and share them equally among 4 friends, each friend gets 20 ÷ 4 = 5 cookies. You are splitting a total into equal shares.

Grouping: If you have 20 cookies and put them in groups of 4, how many groups do you get? 20 ÷ 4 = 5 groups. You are counting how many groups fit.

Division and multiplication are related — they are inverse operations. If you know 5 × 4 = 20, then you also know 20 ÷ 4 = 5 and 20 ÷ 5 = 4. A fact family connects these number sentences.

In a division equation, the dividend is the number being divided, the divisor is the number you divide by, and the quotient is the answer. For example, in 18 ÷ 3 = 6: 18 is the dividend, 3 is the divisor, and 6 is the quotient.

When you cannot divide a number evenly, there is a remainder — the amount left over. For example, 17 ÷ 5 = 3 remainder 2.

Key terms

Division
Splitting a number into equal groups or finding how many groups can be made.
Dividend
The number being divided in a division problem.
Divisor
The number you divide by.
Quotient
The answer to a division problem.
Remainder
The amount left over when a number cannot be divided evenly.
Fact family
A group of related multiplication and division equations using the same three numbers.

Flashcards

Fact family: 3, 7, 21
3 × 7 = 21, 7 × 3 = 21, 21 ÷ 3 = 7, 21 ÷ 7 = 3
Fact family: 4, 8, 32
4 × 8 = 32, 8 × 4 = 32, 32 ÷ 4 = 8, 32 ÷ 8 = 4
Dividing by 1
Any number ÷ 1 = that number. Example: 9 ÷ 1 = 9.
Dividing by itself
Any number ÷ itself = 1. Example: 9 ÷ 9 = 1.
0 ÷ any number
0 ÷ any non-zero number = 0. Example: 0 ÷ 5 = 0.
48 ÷ 6
8. Think: 6 × ? = 48. 6 × 8 = 48, so 48 ÷ 6 = 8.
63 ÷ 9
7. Think: 9 × ? = 63. 9 × 7 = 63, so 63 ÷ 9 = 7.
Remainder
What is left over when dividing. 19 ÷ 4 = 4 remainder 3, because 4 × 4 = 16, and 19 - 16 = 3.

Questions

  1. What is 36 ÷ 4?

    1. 7
    2. 8
    3. 9
    4. 10
    Show answer

    Answer: 9

    36 ÷ 4 = 9. Think: 4 × 9 = 36.

  2. Multiplication and division are inverse operations.

    Show answer

    Answer: True

    Division undoes multiplication and vice versa. If 5 × 6 = 30, then 30 ÷ 6 = 5.

  3. In 42 ÷ 6 = 7, what is the divisor?

    1. 42
    2. 6
    3. 7
    4. 1
    Show answer

    Answer: 6

    In 42 ÷ 6 = 7, the divisor is 6 — the number you are dividing by.

  4. If 8 × 7 = 56, then 56 ÷ 8 = ___.

    Show answer

    Answer: 7

    Since 8 × 7 = 56, the inverse relationship gives 56 ÷ 8 = 7.

  5. 24 apples are shared equally among 6 children. How many does each child get?

    1. 3
    2. 4
    3. 5
    4. 6
    Show answer

    Answer: 4

    24 ÷ 6 = 4. Each child gets 4 apples. Check: 6 × 4 = 24.

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