Evaluate 0.4 x 0.75 divided by 0.5.

Step-by-step solution

1. 1

   Settle the order of operations first. Multiplication and division share the same precedence level, so the expression is evaluated strictly left to right:

   $\left(0.4\times 0.75\right)\div 0.5$

   Doing the division first would compute $0.4\times 1.5=0.6$ — the same answer here by coincidence, but that habit is unreliable in general.

2. 2

   Multiply the first two numbers.

   $0.4\times 0.75=0.3$

   As fractions: $\tfrac25\times\tfrac34=\tfrac{6}{20}=\tfrac{3}{10}$.

3. 3

   Divide by 0.5. Dividing by $\tfrac12$ is the same as doubling:

   $0.3\div 0.5=0.3\times 2=0.6$

4. 4

   Give the exact fraction alongside the decimal.

   $\frac{3}{10}\div\frac12=\frac{3}{10}\times 2=\frac{3}{5}=0.6$

5. 5

   Check by reversing the operations. Multiplying back: $0.6\times 0.5=0.3$, and $0.3\div 0.75=0.4\;\checkmark$. Note the result is larger than the number being divided — dividing by a value below $1$ always increases the quantity, a useful reality check on decimal division.