Mathematics 10 — Exercise 11.2 · Q1 (ii)

Full question

Find the range. Data: ['43.5', '13.6', '18.9', '38.4', '61.4', '29.4']

Step-by-step solution

1. Identify the highest and lowest values.

   $$(61.4,13.6)$$

2. For multiplication of fractions, multiply the numerators together and the denominators together.

   $$\frac{\left(-1\right)\times 68}{1\times 5}$$

3. Calculate these two products separately.

   $$-\frac{68}{5}$$

4. Calculate this operation before combining the remaining terms.

   $$\left(-1\right)\times \frac{68}{5}=-\frac{68}{5}$$

5. To add these fractions, first use a common denominator: the least common multiple of their denominators.

   $$\mathrm{LCD}=5$$

6. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

   $$\frac{307}{5}=\frac{307\times 1}{5\times 1}$$

7. Calculate the converted numerator; the denominator is now common.

   $$\frac{307}{5}$$

8. Multiply this numerator AND denominator by the same factor. Its value stays unchanged.

   $$-\frac{68}{5}=\frac{\left(-68\right)\times 1}{5\times 1}$$

9. Keep the common denominator and add the signed numerators.

   $$\frac{307-68}{5}=\frac{239}{5}$$

10. Calculate this operation before combining the remaining terms.

    $$\frac{307}{5}-\frac{68}{5}=\frac{239}{5}$$

11. Subtract minimum from maximum.

    $$61.4-13.6$$

12. Calculate this operation before combining the remaining terms.

    $$61.4-13.6=47.8$$

Answer

The final answer is shown below.