Solving Combined Products With Sums & Differences

Worked Example 3.3.1:

Subtract the product of 9 and 40 from 450 

Solution

You solve them in stages/steps:

Step 1: Product of 9 and 40 ⇒ 9 × 40 = 360

Step 2: Subtract the product from 450 ⇒ 450 – 360 = 90

Worked Example 3.3.2:

Add the negative difference between 27.9 and 35.7 to the product of 27.9 and 35.7

Solution

Step 1: Negative difference ⇒ 27.9 – 35.7 = -7.8

Step 2: Product ⇒ 27.9 × 35.7 = 996.03

Full Equation: (27.9 × 35.7)  +  (27.9 – 35.7)

= 996.03 + (- 7.8)

⇒ (+ × – = -)

=   996.03 – 7.8

Ans = 988.23

Worked Example 3.3.3:

Find the difference between the product of \(\scriptsize 1 \frac{5}{8} \; and \; \frac{4}{5}\) and the difference between \(\scriptsize 1 \frac{5}{8} \; and \; \frac{4}{5}\)

Solution

\(\left [ \scriptsize 1 \frac{5}{8} \: \times \; \frac{4}{5} \right] \: – \: \left[ \scriptsize 1 \frac{5}{8} \: – \: \frac{4}{5} \right] \\ \left [ \frac{13}{8} \: \times \: \frac{4}{5} \right] \: – \: \left[\frac{13}{8} \: – \: \frac{4}{5} \right] \)

\( \frac{13}{10} \: – \: \frac {65 \: – \: 32}{40} \\ = \frac{13}{10} \: – \: \frac{33}{40} \\ = \frac{ 52 \: – \: 33}{40}\\ = \frac{19}{40} \)