Skill: Choose tools appropriately

Choose a tool by asking: What do I need to find, and what unit or precision do I need?

• Use a ruler to measure length.
• Use a calculator to compute quickly.
• Use a number line or diagram to understand relationships.
• Check the result with an estimate.

Example: A map uses the scale $(1\text{ cm}=2\text{ km})$. The distance from a school to a library is shown by a line on the map. What is the actual distance?

1. Choose a ruler because we need to measure the line’s length. The ruler shows that the line is $(4.6\text{ cm})$ long.

2. Use the scale. Each centimeter represents $(2\text{ km})$, so calculate

$$4.6\times 2.$$

3. Use a calculator to multiply:

$$4.6\times 2=9.2.$$

4. Include the correct unit. The actual distance is about

$$\boxed{9.2\text{ km}}.$$

5. Check the answer. Since $(4.6)$ cm is close to $5$ cm, the distance should be close to $(5\times2=10)$ km. So $(9.2)$ km makes sense.

The ruler gave a measurement, so the answer is an estimate rather than perfectly exact. Always check that the tool fits the task and that the result’s units and size make sense.