Chapter 2

Simplify \(\frac{1}{3}+\frac{2}{7}\)

Find the value of \(3 \frac{2}{3}-2 \frac{1}{6}\)

Evaluate \(7 \frac{1}{8}-5 \frac{3}{7}\)

Determine the value of \(4 \frac{5}{8}-3 \frac{1}{4}+1 \frac{2}{5}\)

Find the value of \(\frac{3}{7} \times \frac{14}{15}\)

Evaluate \(1 \frac{3}{5} \times 2 \frac{1}{3} \times 3 \frac{3}{7}\)

Simplify \(\frac{3}{7} \div \frac{12}{21}\)

Find the value of \(5 \frac{3}{5} \div 7 \frac{1}{3}\)

Simplify \(\frac{1}{3}-\left(\frac{2}{5}+\frac{1}{4}\right) \div\left(\frac{3}{8} \times \frac{1}{3}\right)\)

Determine the value of $$ \frac{7}{6} \text { of }\left(3 \frac{1}{2}-2 \frac{1}{4}\right)+5 \frac{1}{8} \div \frac{3}{16}-\frac{1}{2} $$

Divide 126 in the ratio of 5 to 13 .

A piece of timber \(273 \mathrm{~cm}\) long is cut into three pieces in the ratio of 3 to 7 to 11 . Determine the lengths of the three pieces.

Prob A gear wheel having 80 teeth is in mesh with a 25 tooth gear. What is the gear ratio?

Express \(25 \mathrm{p}\) as a ratio of \(£ 4.251\)

An alloy is made up of metals A and B in the ratio \(2.5: 1\) by mass. How much of \(\mathrm{A}\) has to be added to \(6 \mathrm{~kg}\). of \(\mathrm{B}\) to make the alloy?

If 3 people can complete a task in 4 hours, find how long it will take 5 people to complete the same task, assuming the rate of work remains constant.

Evaluate \(42.7+3.04+8.7+0.06\)

Evaluate \(42.7+3.04+8.7+0.06\)

Find the value of $$ 23.4-17.83-57.6+32.68 $$

Determine the value of \(74.3 \times 3.8\)

Evaluate \(37.81 \div 1.7\), correct to (i) 4 significant figures and (ii) 4 decimal places.

Convert (a) \(0.4375\) to a proper fraction and (b) \(4.285\) to a mixed number.

Express as decimal fractions: (a) \(\frac{9}{16}\) and (b) \(5 \frac{7}{8}\)

Express as percentages: (a) \(1.875\) and (b) \(0.0125\)

Express as percentages: (a) \(\frac{5}{16}\) and (b) \(1 \frac{2}{5}\)

It takes 50 minutes to machine a certain part. Using a new type of tool, the time can be reduced by \(15 \%\). Calculate the new time taken.

\text { Find } 12.5 \% \text { of } £ 378

Express 25 minutes as a percentage of 2 hours, correct to the nearest \(1 \%\).

A German silver alloy consists of \(60 \%\) copper, \(25 \%\) zinc and \(15 \%\) nickel. Determine the masses of the copper, zinc and nickel in a \(3.74\) kilogram block of the alloy.