Mathematics (Syllabus D) 4024/12 — May/June 2017

Approach

To subtract fractions with different denominators, we must first find a common denominator. The least common multiple (LCM) of 5 and 3 is 15. We convert each fraction to an equivalent fraction with a denominator of 15.

Working

$$\frac{4}{5} - \frac{1}{3}$$

Convert $\frac{4}{5}$ to a fraction with denominator 15:

$$\frac{4 \times 3}{5 \times 3} = \frac{12}{15}$$

Convert $\frac{1}{3}$ to a fraction with denominator 15:

$$\frac{1 \times 5}{3 \times 5} = \frac{5}{15}$$

Subtract the second numerator from the first:

$$\frac{12}{15} - \frac{5}{15} = \frac{12 - 5}{15} = \frac{7}{15}$$

The fraction $\frac{7}{15}$ cannot be simplified further as 7 and 15 share no common factors other than 1.

Answer

$$\frac{7}{15}$$

Approach

To evaluate the product of two decimals, ignore the decimal points initially and multiply the numbers as integers. Then, count the total number of decimal places in the original factors to place the decimal point in the answer correctly.

Working

$$0.2 \times 0.006$$

Ignore the decimal points and multiply $2$ by $6$:

$$2 \times 6 = 12$$

Count the decimal places in the original numbers:

• $0.2$ has 1 decimal place.
• $0.006$ has 3 decimal places.
• Total decimal places required in the answer = $1 + 3 = 4$.

Place the decimal point in the result $12$ so that it has 4 decimal places. Since $12$ only has two digits, we add leading zeros:

$$0.0012$$

Answer

$$0.0012$$