Simplify the following:
\(\displaystyle\frac{(3+7)\times2-4}{(3+7)\times(2-4)}+\frac{3+7\times2-5}{3+7\times(2-5)}\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(-\frac{22}{15}\)
Work out each fraction by BODMAS: brackets first, then multiplication, then addition and subtraction.
The first fraction:
Numerator: \((3+7)\times2-4=20-4=16\)
Denominator: \((3+7)\times(2-4)=10\times(-2)=-20\)
Value: \(\displaystyle\frac{16}{-20}=-\frac{4}{5}\)
The second fraction:
Numerator: \(3+7\times2-5=3+14-5=12\)
Denominator: \(3+7\times(2-5)=3-21=-18\)
Value: \(\displaystyle\frac{12}{-18}=-\frac{2}{3}\)
The sum:
\(\displaystyle-\frac{4}{5}-\frac{2}{3}=-\frac{12}{15}-\frac{10}{15}=-\frac{22}{15}\)
Tip: Without brackets, multiplication comes before addition: \(3+7\times2\) is \(3+14=17\), not \(10\times2=20\). The two fractions differ only in their brackets, which is what the question tests.