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Stage 18 of 20

Division Basics

Learn exact division and remainders through equal sharing, inverse multiplication, fact families, decomposition, and meaningful answer checks.

Start the interactive drill 18 checkable exercises

What You'll Learn

  • Interpret division as both equal sharing and counting equal groups
  • Use multiplication facts from Stages 15–17 to solve exact quotients
  • Represent a remainder correctly and explain what it means in context
  • Decompose larger dividends using the distributive property

The Reasoning Behind Division Basics

Division asks about sharing or grouping. In 56 ÷ 7, sharing asks how many each of seven groups receives; grouping asks how many sevens fit into 56. Both give 8. The equation divisor × quotient = dividend links directly to Stage 17.

Because 7 × 8 = 56, the same fact family contains 56 ÷ 7 = 8 and 56 ÷ 8 = 7. For exact division, ask which number multiplied by the divisor produces the dividend, then multiply back.

Partition larger dividends into divisible parts. For 96 ÷ 8, use 96 = 80 + 16. The distributive property gives (80 + 16) ÷ 8 = 10 + 2 = 12. Choose parts that divide cleanly.

For 50 ÷ 7, seven groups use 49 and leave 1, written 7 R1. A valid remainder satisfies 0 ≤ remainder < divisor. A remainder of 8 after division by 7 means one more group was missed.

Context controls leftovers. Fifty people in seven-seat cars require 8 cars, but fifty biscuits packed seven per bag make 7 full bags with 1 loose. Decide whether to keep the remainder, round, or use a fraction.

Why This Skill Matters

Division drives unit prices, rates, averages, recipes, schedules, and fair sharing. Thinking through multiplication links the operations and prepares for Stage 19, where division and multiplication share priority.

Where You Will Use Division Basics

Suppose 96 metres of cable is cut into 8 equal lengths. Since 96 ÷ 8 = 12, every length is 12 metres. Multiplying 12 × 8 checks that no cable has vanished or been added.

See the Strategy in Action

Read the strategy, then prove you can use it: every example ends with a matching problem on new numbers that you answer and check right here. Answer it and press New numbers for as many fresh problems as you like.

Recover a quotient from a fact

72 ÷ 8

  1. 1 Ask which multiplication fact has 8 as a factor and 72 as the product.
  2. 2 Recall 8 × 9 = 72 from Stage 17.
  3. 3 Multiply back: 9 × 8 = 72, so the quotient is confirmed.

72 ÷ 8 = 9

Your turn — try it on new numbers

20 ÷ 2 = ?

Split into divisible parts

84 ÷ 4

  1. 1 Partition 84 as 80 + 4; both parts are divisible by 4.
  2. 2 Calculate 80 ÷ 4 = 20 and 4 ÷ 4 = 1.
  3. 3 Add the partial quotients: 20 + 1 = 21.

84 ÷ 4 = 21

Your turn — try it on new numbers

54 ÷ 9 = ?

Find and check a remainder

65 ÷ 9

  1. 1 Locate the greatest multiple of 9 not exceeding 65: 9 × 7 = 63.
  2. 2 Subtract to find the leftover: 65 − 63 = 2.
  3. 3 Check 9 × 7 + 2 = 65 and note that 2 is less than 9.

65 ÷ 9 = 7 R2

Your turn — try it on new numbers

36 ÷ 4 = ?

Interpret rounding in context

How many 6-seat vans are needed for 38 passengers?

  1. 1 Six full vans seat 6 × 6 = 36 passengers.
  2. 2 Two passengers remain, so a seventh van is still necessary.

7 vans are needed

Your turn — try it on new numbers

108 ÷ 9 = ?

Self-Check: Errors to Avoid

Reversing dividend and divisor

In 56 ÷ 7, 56 is divided. Read “56 in groups of 7,” then multiply back.

Allowing a remainder as large as the divisor

A remainder of 8 after dividing by 7 contains another group. Regroup it so the remainder is smaller than 7.

Automatically rounding every remainder down

Packing may use full boxes, while transport needs another vehicle. Interpret the leftover before rounding.

Pro Tips

  • • Translate division into a missing-factor multiplication.
  • • Split dividends into obvious multiples of the divisor.
  • • Check divisor × quotient + remainder = dividend.
  • • Use context to decide how to report leftovers.

Practice Exercises

Work each problem mentally, then type the answer and check it. Nothing is marked correct until you enter a value that actually equals the result, and every problem keeps its mental-steps note in reach if you get stuck.

  1. 1. 56 ÷ 7 = ?
  2. 2. 72 ÷ 9 = ?
  3. 3. 96 ÷ 8 = ?
  4. 4. 63 ÷ 7 = ?
  5. 5. 84 ÷ 4 = ?
  6. 6. 54 ÷ 6 = ?
  7. 7. 88 ÷ 8 = ?
  8. 8. 81 ÷ 9 = ?
  9. 9. 42 ÷ 7 = ?
  10. 10. 65 ÷ 9 = ?
  11. 11. 50 ÷ 7 = ?
  12. 12. 38 ÷ 6 = ?
  13. 13. 144 ÷ 12 = ?
  14. 14. 100 ÷ 8 = ?
  15. 15. How many groups of 9 are in 108?
  16. 16. 73 stickers are shared equally among 8 people. How many each, and how many remain?
  17. 17. How many 5-seat cars are needed for 42 people?
  18. 18. Complete: 7 × ? + 3 = 52

Drill Stage 18 with unlimited problems

Type your answer and press Enter. Every problem is generated on the spot and uses division facts checked against the multiplication tables. Get it wrong and the steps below show how that exact problem is solved mentally.

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Problem 1

80 ÷ 8 = ?

Stage 18 Questions

Why can division produce two different-looking interpretations?

Sharing fixes the number of groups; grouping fixes each group’s size. Both represent the same multiplication relationship.

Can zero be divided by a nonzero number?

Yes: 0 ÷ 7 = 0 because each group receives zero. Division by zero is undefined.

When should a remainder become a decimal or fraction?

Discrete objects may require R notation or rounding; measured quantities can use fractions or decimals.