Simplification & Approximation — Practice

Question 1

Simplify exactly: $\frac{18 	imes 6}{9 - 3} + 7$.

Accepted Answer

Bracket first: $9-3=6$. Then $18	imes6=108$, $108\div6=18$. Finally $18+7=25$.

Answer: 25.

Question 2

Simplify exactly: $\sqrt{169} + \sqrt[3]{64}$.

Accepted Answer

$\sqrt{169}=13$ and $\sqrt[3]{64}=4$. Sum $=17$.

Answer: 17.

Question 3

Approximate: $60.1\%$ of $799.8$.

Accepted Answer

Round to $60\%$ of $800 = 480$.

Answer: approximately 480.

Question 4

Simplify exactly: $\left(\frac{5}{6} + \frac{1}{4}ight) 	imes 24$.

Accepted Answer

LCM of 6 and 4 is 12: $\frac{10}{12}+\frac{3}{12}=\frac{13}{12}$. Then $\frac{13}{12}	imes24=26$.

Answer: 26.

Question 5

Approximate: $8.98 	imes 30.02$.

Accepted Answer

Round to $9	imes30=270$.

Answer: approximately 270.

Question 6

Simplify exactly: $20\%$ of $350$ + $\frac{1}{5}$ of $200$.

Accepted Answer

$20\%$ of $350=70$. $\frac{1}{5}$ of $200=40$. Sum $=70+40=110$.

Answer: 110.

Question 7

Approximate: $\sqrt{624.5}$.

Accepted Answer

The nearest perfect square to 624.5 is $625=25^2$, so $\sqrt{624.5}\approx25$.

Answer: approximately 25.

Question 8

Approximate: $15.02^2$.

Accepted Answer

Round to $15^2=225$.

Answer: approximately 225.

Practice — Simplification & Approximation