Division facts: learn and practice

Who this lesson is for

This division lesson is for grade 3. Students share a number into equal groups when nothing is left over. Long division with a remainder is a different lesson, on its own page, for grade 4. The practice link opens exact division. Only the grade 3 hub links here.

Division undoes multiplication

24 ÷ 6 asks how many groups of 6 sit inside 24, or how many each group gets if there are 6 groups. The answer is 4, because 6 × 4 = 24. The number you divide is the dividend. The number you divide by is the divisor. The answer is the quotient. On this page the quotient is a whole number, so the remainder is 0.

The multiply-back check

After you name a quotient, multiply it by the divisor. The product has to be the dividend. If 35 ÷ 5 = 7, then 5 × 7 must be 35. If the product is 30 or 40, the quotient is off by one group. That check is the whole method. You are not guessing a division fact you have never seen. You are looking for the multiplication fact you already know.

Worked example 1: 24 divided by 6

Find 24 ÷ 6. Ask which fact ends at 24 and uses 6. 6 × 4 = 24, so the quotient is 4. As a picture, 24 counters in groups of 6 make 4 groups, and nothing is left outside a group. Check: 6 × 4 = 24. If you had said 3, the check would be 6 × 3 = 18, which is short of 24 by one whole group.

Worked example 2: 35 divided by 5

Find 35 ÷ 5. Count by fives until you reach 35: 5, 10, 15, 20, 25, 30, 35. That is 7 jumps, so the quotient is 7. The matching fact is 5 × 7 = 35. Sharing 35 stickers among 5 children gives 7 stickers each, and the pile is empty at the end. There is no remainder to carry into a later step.

Worked example 3: 18 divided by 3

Find 18 ÷ 3. The fact 3 × 6 = 18 says the quotient is 6. Three groups of 6 use up 18, and six groups of 3 use it up as well. Both readings are the same division. Check: 3 × 6 = 18. A nearby wrong answer is 5, because 3 × 5 = 15 and 3 are left over. Those 3 make another group, so 5 is not the exact quotient this page is practicing.

Checks before you leave the problem

Multiply the quotient by the divisor and match the dividend. If anything is left over, this is not one of the exact facts. Grade 4 long division is the lesson that keeps a remainder on purpose. Then practice exact division on the board.

Common questions about division facts

What is a quotient?

The quotient is the answer to a division. In 24 ÷ 6 = 4, the quotient is 4. It tells how many equal groups, or how many are in each group.

What if the numbers do not divide evenly?

Then there is a remainder, and this grade 3 page is not the lesson for that case. Exact facts are the ones where multiplying back lands on the dividend with nothing left.

How is this different from long division?

These facts are one multiplication lookup. Long division, on the grade 4 page, repeats divide, multiply, subtract, and bring down across more than one digit.