Question

Simplify $(\frac{2}{3} \times \frac{6}{5}) + (\frac{12}{25} \times \frac{20}{3})$.

• A. 12/5
• B. 3
• C. 4
• D. 3/5

Answer 1

Answer:

C. 4

The simplified value of the expression is $4$.

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Following the BODMAS / PEMDAS rule, we solve each multiplication bracket first, then add the results.

1: Simplify the first bracket

$\frac{2}{3} \times \frac{6}{5}$
Cross-cancel 6 in the numerator and 3 in the denominator ($6 \div 3 = 2$):
$2 \times \frac{2}{5} = \frac{4}{5}$

2: Simplify the second bracket

$\frac{12}{25} \times \frac{20}{3}$

• Cross-cancel 12 and 3 ($12 \div 3 = 4$)

• Cross-cancel 20 and 25 by dividing both by 5 ($20 \div 5 = 4$ and $25 \div 5 = 5$)

Now multiply the remaining numbers:
$\frac{4 \times 4}{5} = \frac{16}{5}$

3: Add the two results together

Since both fractions have the same denominator (5), simply add their numerators:
$\frac{4}{5} + \frac{16}{5} = \frac{4 + 16}{5} = \frac{20}{5} = 4$