Finding the unknown number
An equation is like a balance with two equal sides. To find the unknown we undo what was done to it, using the opposite operation on both sides. If x + 12.5 = 20, then x is 20 take away 12.5, so x = 7.5. If n − 3.4 = 6.25, undo the subtraction by adding: n = 6.25 + 3.4 = 9.65. If 4 × p = 18.4, undo the multiplication by dividing: p = 18.4 ÷ 4 = 4.6. If y ÷ 5 = 0.35, undo the division by multiplying: y = 0.35 × 5 = 1.75. Always check by replacing the letter in the original equation. The same steps work for decimals up to thousandths: if 0.875 + a = 1.5, then a = 1.5 − 0.875 = 0.625.
| Equation | Opposite operation | Unknown |
|---|---|---|
| x + 12.5 = 20 | 20 − 12.5 | x = 7.5 |
| n − 3.4 = 6.25 | 6.25 + 3.4 | n = 9.65 |
| 4 × p = 18.4 | 18.4 ÷ 4 | p = 4.6 |
| y ÷ 5 = 0.35 | 0.35 × 5 | y = 1.75 |
Mystery number. One person thinks of a decimal, such as 2.4. They tell the other the result of one step: “I added 3.75 and got 6.15”. The other writes an equation, x + 3.75 = 6.15, and solves it by using the opposite operation. Then swap and use multiplication or division in the clue.