Removing a divisor from one side

The idea

If one side of an equation is a quotient of two numbers or expressions and the divisor is removed, the other side must be multiplied by that divisor for the equality to hold.

u ÷ 15 = 6

If u = 90, then u ÷ 15 = 6. Now we remove the divisor 15 from the left side. The left side becomes just u, which is 90.

What must the right side, 6, become so that the sides still agree?

• 6 × 15
• 6 ÷ 15
• 6 − 15

Remove the divisor, then repair

Tap the highlighted divisor to remove it. Then choose what the other side must become and test it with the numbers.

Division is undone by multiplication

u ÷ 15 means u cut into 15 equal parts, and one part is 6. To get the whole *u* back, take 15 parts of 6: 6 × 15. So the other side must be multiplied by the divisor.

This is the same as multiplying both sides by 15: u ÷ 15 × 15 = 6 × 15.

If one side of an equation is a quotient and the divisor is removed, the other side must be multiplied by that divisor: u ÷ 15 = 6 becomes u = 6 × 15.

• Equation | After removing the divisor
• u ÷ 15 = 6 | u = 6 × 15
• m ÷ 4 = 9 | m = 9 × 4
• 8 = w ÷ 5 | 8 × 5 = w
• p ÷ 7 = −3 | p = −3 × 7

Notes

A divisor removed from one side means the other side is multiplied by that divisor: u ÷ 15 = 6 becomes u = 6 × 15.

Check yourself

In k ÷ 6 = 5, the divisor 6 is removed from the left. What does the right side become?

Solve z ÷ 8 = 7.

Answer: 56

z = 7 × 8 = 56. Check: 56 ÷ 8 = 7.

Solve n ÷ 3 = −4.

Answer: -12

n = −4 × 3 = −12. Check: −12 ÷ 3 = −4.

Solve k ÷ 4 − 3 = 2.

Answer: 20

k ÷ 4 − 3 + 3 = 2 + 3 gives k ÷ 4 = 5. Then k = 5 × 4 = 20. Check: 20 ÷ 4 − 3 = 2.

• 5 × 6 — correct. Yes! Division is undone by multiplication.
• 5 ÷ 6. That makes the right side smaller. Removing a divisor makes the left side bigger, so multiply.
• 5 − 6. A divisor is removed, so the right side is multiplied by it, not reduced by it.