Q1.
What happens in cases like u/15 = 6?
Answer
The 15 is a divisor, so it is removed by multiplying both sides by 15.
u ÷ 15 = 6
(u ÷ 15) × 15 = 6 × 15
u = 90
(u ÷ 15) × 15 = 6 × 15
u = 90
This gives the third of the chapter's three observations. Put together, they are:
| What sits with the unknown | How to remove it | Example | Becomes |
|---|---|---|---|
| A term added or subtracted | Its additive inverse appears on the other side | 2y + 7 = 21 | 2y = 21 − 7 |
| A factor | Divide the other side by it | 2y = 14 | y = 14 ÷ 2 |
| A divisor | Multiply the other side by it | u/15 = 6 | u = 6 × 15 |
Why it happens: each row is one pair of inverse operations. Addition is undone by subtraction, multiplication by division, division by multiplication. In every case you are still doing the same thing to both sides — the table is just a short way of writing that down.
Check it yourself: 90 ÷ 15 = 6. ✓