Solving Decimal Equations Directly

Property A decimal equation can also be solved by using inverse operations without multiplying by a power of 10 first.

Examples Solve $0.3m + 0.6 = 1.5$ by first subtracting $0.6$ from both sides to get $0.3m = 0.9$. After simplifying to $0.3m = 0.9$, divide both sides by $0.2$ to find the solution: $\frac{0.3m}{0.3} = \frac{0.9}{0.3}$, so $m=3$. Solve $ 0.04n 1.5 = 1.62$ by adding $1.5$ to both sides, which simplifies to $ 0.04n = 0.12$, so $n=3$.

Explanation If you're comfortable with decimals, you don't have to clear them. You can solve the equation directly using the same inverse operations you already know, like subtracting a decimal from both sides or dividing by a decimal. It’s the same process as with integers; you just need to be extra careful where that decimal point lands in your final answer!