Division as a multiplication problem

The idea

A division can be restated as a multiplication problem: dividend ÷ divisor asks which number, multiplied by the divisor, gives the dividend.

A division is a question

12 ÷ 4 = 3 because 4 × 3 = 12. Every division can be asked as a multiplication with a missing number: 4 × ? = 12.

What is the missing number in 5 × ? = 30? That is 30 ÷ 5.

• 6
• 25
• 150

Find the missing number

The top bar is the dividend. Below it, rods of the divisor are laid end to end, ? of them. Set ? with the buttons until the rods end exactly where the bar ends.

Divide = what do I multiply by?

Dividend ÷ divisor asks: which number, multiplied by the divisor, gives the dividend? That number is the quotient. It works for fractions too.

Check each answer by multiplying it back: 2/3 × 3/2 = 1 and 1/2 × 2/5 = 1/5.

Dividing asks: what do I multiply the divisor by to get the dividend? 3 ÷ 2/3 = 9/2 because 2/3 × 9/2 = 3 2/3 ÷ 3/5 = 10/9 because 3/5 × 10/9 = 2/3

• Division | Asks | Answer
• 12 ÷ 4 | 4 × ? = 12 | 3
• 1 ÷ 2/3 | 2/3 × ? = 1 | 3/2
• 1/5 ÷ 1/2 | 1/2 × ? = 1/5 | 2/5

Notes

Dividing asks: what do I multiply the divisor by to get the dividend? 3 ÷ 2/3 = 9/2 because 2/3 × 9/2 = 3 2/3 ÷ 3/5 = 10/9 because 3/5 × 10/9 = 2/3

Check yourself

3/4 ÷ 1/8 asks: 1/8 × ? = 3/4. What is the missing number?

Answer: 6

1/8 × 6 = 6/8 = 3/4, so 3/4 ÷ 1/8 = 6.

Which multiplication is the same question as 2/3 ÷ 3/5?

4/5 ÷ 2 asks: 2 × ? = 4/5. What is the missing number? Type a fraction like 3/7.

Answer: 2/5

2 × 2/5 = 4/5, so 4/5 ÷ 2 = 2/5.

5/6 ÷ 5/12 asks: 5/12 × ? = 5/6. What is the missing number?

Answer: 2

5/12 × 2 = 10/12 = 5/6, so 5/6 ÷ 5/12 = 2.

• 3/5 × ? = 2/3 — correct. Yes! The divisor 3/5 is multiplied by the missing number to give the dividend 2/3.
• 2/3 × ? = 3/5. The numbers are the wrong way round. The divisor times the missing number must equal the dividend.
• 2/3 + ? = 3/5. Division is a multiplication question, not an addition one.