Evaluate 0.4 x 0.75 + 0.5.

Step-by-step solution

1. 1

   Decide the order before computing anything. There are no brackets and no exponents, so the rule is multiplication before addition. Working strictly left to right would give $0.4\times 0.75=0.3$ then $+0.5$ - which happens to be the same here - but reading it as $0.4\times(0.75+0.5)=0.5$ would be wrong, and that is the trap this expression sets.

2. 2

   Multiply the two decimals. Ignore the points, multiply the digits, then restore them: $4\times 75=300$, and there is one decimal place in $0.4$ plus two in $0.75$, so three in total: $0.4\times 0.75=0.300=0.3.$

3. 3

   Cross-check the product with fractions. $0.4=\tfrac{2}{5}$ and $0.75=\tfrac{3}{4}$, so $\frac{2}{5}\times\frac{3}{4}=\frac{6}{20}=\frac{3}{10}=0.3,$ confirming the decimal-place count.

4. 4

   Add the remaining term. Line up the decimal points: $0.30+0.50=0.80=0.8.$ In fractions, $\tfrac{3}{10}+\tfrac{1}{2}=\tfrac{3}{10}+\tfrac{5}{10}=\tfrac{8}{10}=\tfrac45$, the same value.

5. 5

   Check the size of the answer. $0.4\times 0.75$ must be smaller than $0.4$, because multiplying by a number below $1$ shrinks it; adding $0.5$ then lands between $0.5$ and $0.9$. The result $0.8=\tfrac45$ sits in that window, so the answer is plausible as well as correct.