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Chapter 2: Problem 10

Calculate (a) \(\frac{1}{4}\) of 60 (b) \(\frac{2}{3}\) of 75 (c) \(\frac{3}{8}\) of 64 (d) \(\frac{2}{5}\) of \(\frac{15}{16}\) (e) \(\frac{3}{4}\) of \(\frac{20}{21}\) expressing each answer as a fraction in its simplest form.

Short Answer

Expert verified
Answer: a) 15 b) 50 c) 24 d) 3/8 e) 5/7

Step by step solution

01

Part (a): Find \(\frac{1}{4}\) of 60

To find \(\frac{1}{4}\) of 60, multiply the fraction by 60. $$\frac{1}{4} \times 60 = \frac{1 \times 60}{4}$$ Simplify the fraction to get the answer. $$\frac{60}{4} = \frac{60 \div 4}{ 4 \div 4} = \frac{15}{1} = 15$$
02

Part (b): Find \(\frac{2}{3}\) of 75

To find \(\frac{2}{3}\) of 75, multiply the fraction by 75. $$\frac{2}{3} \times 75 = \frac{2 \times 75}{3}$$ Simplify the fraction to get the answer. $$\frac{150}{3} = \frac{150 \div 3}{ 3 \div 3} = \frac{50}{1} = 50$$
03

Part (c): Find \(\frac{3}{8}\) of 64

To find \(\frac{3}{8}\) of 64, multiply the fraction by 64. $$\frac{3}{8} \times 64 = \frac{3 \times 64}{8}$$ Simplify the fraction to get the answer. $$\frac{192}{8} = \frac{192 \div 8}{ 8 \div 8} = \frac{24}{1} = 24$$
04

Part (d): Find \(\frac{2}{5}\) of \(\frac{15}{16}\)

To find \(\frac{2}{5}\) of \(\frac{15}{16}\), multiply the fractions together. $$\frac{2}{5} \times \frac{15}{16} = \frac{2 \times 15}{5 \times 16}$$ Simplify the fraction to get the answer. $$\frac{30}{80} = \frac{30 \div 10}{80 \div 10} = \frac{3}{8}$$
05

Part (e): Find \(\frac{3}{4}\) of \(\frac{20}{21}\)

To find \(\frac{3}{4}\) of \(\frac{20}{21}\), multiply the fractions together. $$\frac{3}{4} \times \frac{20}{21} = \frac{3 \times 20}{4 \times 21}$$ Simplify the fraction to get the answer. $$\frac{60}{84} = \frac{60 \div 12}{84 \div 12} = \frac{5}{7}$$

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Most popular questions from this chapter

Calculate (a) \(\frac{6}{7} \times \frac{14}{27}\) (b) \(\frac{7}{10} \times \frac{4}{5} \times \frac{30}{49}\) (c) \(\frac{8}{9} \times \frac{18}{25}\) (d) \(\left(-\frac{4}{5}\right) \times\left(-\frac{3}{4}\right)\) (e) \(\frac{16}{21} \times\left(-\frac{3}{4}\right)\)

Dynamics - Pressure in a vessel. The pressure in a vessel is \(30 \mathrm{~N} \mathrm{~cm}^{-2}\). If the pressure is reduced by \(\frac{7}{100}\) of its original value, calculate (a) the decrease in pressure, (b) the resulting pressure in the vessel.

Thermodynamics - Temperature of a metal bar. A metal bar is heated and its temperature is measured every 5 minutes. The table records the temperature readings. \begin{tabular}{lrrrrr} \hline Time (min) & 0 & 5 & 10 & 15 & 20 \\ Temp \(\left({ }^{\circ} \mathrm{C}\right)\) & 21 & 27 & 31 & 33 & 35 \\ \hline \end{tabular} Calculate the rate of increase of temperature in units of \({ }^{\circ} \mathrm{C}\) per minute (a) in the first 5 minutes (b) in the first 10 minutes (c) in the first 15 minutes (d) in the first 20 minutes (e) in the last 5 minutes (f) in the last 10 minutes In each case express your answer as a fraction in its simplest form.

Evaluate (a) \(6 \frac{2}{3} \div 4\) (b) \(10 \div 2 \frac{1}{3}\) (c) \(\left(\frac{1}{2}+\frac{1}{3}\right) \div\left(\frac{2}{3}+\frac{1}{5}\right)\) (d) \(\left(6-2 \frac{1}{3}\right) \times\left(4 \frac{1}{2}-1 \frac{3}{4}\right)\) (e) \(\frac{2 \frac{1}{2}+1 \frac{1}{3}}{6 \frac{2}{3}-2 \frac{1}{4}}\)

Calculate (a) \(\frac{7}{9} \div \frac{2}{3}\) (b) \(\frac{8}{15} \div \frac{4}{5}\) (c) \(\frac{9}{10} \div \frac{9}{20}\) (d) \(\frac{6}{11} \div \frac{7}{12}\) (e) \(\frac{12}{13} \div \frac{6}{7}\)
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