Solve 1600 = x times 1.5.

Step-by-step solution

1. 1

   Isolate x with one inverse operation. Only a multiplication by $1.5$ stands between $x$ and the constant, so divide both sides by $1.5$: $x = \dfrac{1600}{1.5}$.

2. 2

   Replace the decimal by a fraction. $1.5 = \tfrac32$, so $x = 1600 \div \frac32 = 1600 \cdot \frac23.$ Multiplying by the reciprocal keeps everything in integers.

3. 3

   Carry out the multiplication. $x = \frac{1600 \cdot 2}{3} = \frac{3200}{3}.$ As $3$ does not divide $3{,}200$ (its digit sum is $5$), the fraction is already reduced.

4. 4

   Write the decimal form. $\frac{3200}{3} = 1066.\overline{6} \approx 1066.67.$

5. 5

   Check exactly. $\tfrac{3200}{3} \cdot \tfrac32 = \tfrac{3200}{2} = 1600$, which is the given left-hand side. Substituting the rounded $1066.67$ would give $1600.005$ instead, showing why the fraction is preferred.

6. 6

   Relate to the 2560 version. The equations differ only in the constant, and the answers scale in the same ratio: $\tfrac{2560}{1600} = 1.6$ and $\tfrac{5120/3}{3200/3} = 1.6$ - a useful check whenever several one-step equations share the same coefficient.