Simplify (correct to 2 decimal places):
\(\displaystyle\frac{(3.2)^2+(2.8)^2}{(3.2)\times (2.8)}\)
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 2.02
The squares and the product are worked out first, then divided, and the result is rounded to two decimal places.
Sum of the squares: \((3.2)^2+(2.8)^2=10.24+7.84=18.08\)
Product: \(3.2\times2.8=8.96\)
Dividing and rounding: \(\displaystyle \frac{18.08}{8.96}=2.0178\ldots\approx2.02\)
Shortcut: \(\displaystyle \frac{a^2+b^2}{ab}=\frac{a}{b}+\frac{b}{a}\), which avoids the decimals.
The two fractions in lowest terms: \(\displaystyle \frac{3.2}{2.8}=\frac{8}{7}\) and \(\displaystyle \frac{2.8}{3.2}=\frac{7}{8}\)
Their sum: \(\displaystyle \frac{8}{7}+\frac{7}{8}=\frac{64+49}{56}=\frac{113}{56}\approx2.02\)