1.3.1 Fractions Revision, PT3 Practice - Mathematics

Question 1:

3 \frac{2}{5} + 1 \frac{5}{6} - \frac{1}{5} =

$3 \frac{2}{5} + 1 \frac{5}{6} - \frac{1}{5} =$

Solution:

\begin{matrix} 3 \frac{2}{5} + 1 \frac{5}{6} - \frac{1}{5} = 3 \frac{12}{30} + 1 \frac{25}{30} - \frac{6}{30} = 4 \frac{37}{30} - \frac{6}{30} = 4 \frac{31}{30} = 5 \frac{1}{30} \end{matrix}

$\begin{array}{l} 3 \frac{2}{5} + 1 \frac{5}{6} - \frac{1}{5} \\ = 3 \frac{12}{30} + 1 \frac{25}{30} - \frac{6}{30} \\ = 4 \frac{37}{30} - \frac{6}{30} \\ = 4 \frac{31}{30} \\ = 5 \frac{1}{30} \end{array}$

Question 2:

6 \frac{1}{12} - 3 \frac{2}{3} - 1 \frac{5}{6} =

$6 \frac{1}{12} - 3 \frac{2}{3} - 1 \frac{5}{6} =$

Solution:

\begin{matrix} 6 \frac{1}{12} - 3 \frac{2}{3} - 1 \frac{5}{6} = 6 \frac{1}{12} - 3 \frac{8}{12} - 1 \frac{10}{12} = (5 \frac{13}{12} - 3 \frac{8}{12}) - 1 \frac{10}{12} = 2 \frac{5}{12} - 1 \frac{10}{12} = 1 \frac{17}{12} - 1 \frac{10}{12} = \frac{7}{12} \end{matrix}

$\begin{array}{l} 6 \frac{1}{12} - 3 \frac{2}{3} - 1 \frac{5}{6} \\ = 6 \frac{1}{12} - 3 \frac{8}{12} - 1 \frac{10}{12} \\ = (5 \frac{13}{12} - 3 \frac{8}{12}) - 1 \frac{10}{12} \\ = 2 \frac{5}{12} - 1 \frac{10}{12} \\ = 1 \frac{17}{12} - 1 \frac{10}{12} \\ = \frac{7}{12} \end{array}$

Question 3:

30 - (\frac{2}{7} \div \frac{2}{21}) =

$30 - (\frac{2}{7} \div \frac{2}{21}) =$

Solution:

\begin{matrix} 30 - (\frac{2}{7} \div \frac{2}{21}) = 30 - (\frac{2}{7} \times \frac{21^{3}}{2}) = 30 - 3 = 27 \end{matrix}

$\begin{array}{l} 30 - (\frac{2}{7} \div \frac{2}{21}) \\ = 30 - (\frac{2}{7} \times \frac{21^{3}}{2}) \\ = 30 - 3 \\ = 27 \end{array}$

Question 4:

(7 \frac{1}{2} - 3 \frac{2}{3}) \times \frac{12}{69} =

$(7 \frac{1}{2} - 3 \frac{2}{3}) \times \frac{12}{69} =$

Solution:

\begin{matrix} (7 \frac{1}{2} - 3 \frac{2}{3}) \times \frac{12}{69} = (7 \frac{3}{6} - 3 \frac{4}{6}) \times \frac{12}{69} = (6 \frac{9}{6} - 3 \frac{4}{6}) \times \frac{12}{69} = 3 \frac{5}{6} \times \frac{12}{69} = \frac{23}{6} \times \frac{12^{2}}{69^{3}} = \frac{2}{3} \end{matrix}

$\begin{array}{l} (7 \frac{1}{2} - 3 \frac{2}{3}) \times \frac{12}{69} \\ = (7 \frac{3}{6} - 3 \frac{4}{6}) \times \frac{12}{69} \\ = (6 \frac{9}{6} - 3 \frac{4}{6}) \times \frac{12}{69} \\ = 3 \frac{5}{6} \times \frac{12}{69} \\ = \frac{23}{6} \times \frac{12^{2}}{69^{3}} \\ = \frac{2}{3} \end{array}$

Question 5:

1 \frac{1}{5} \div (4 - 2 \frac{1}{2}) =

$1 \frac{1}{5} \div (4 - 2 \frac{1}{2}) =$

Solution:

\begin{matrix} 1 \frac{1}{5} \div (4 - 2 \frac{1}{2}) = 1 \frac{1}{5} \div (3 \frac{2}{2} - 2 \frac{1}{2}) = \frac{6}{5} \div (1 \frac{1}{2}) = \frac{6}{5} \div \frac{3}{2} = \frac{6^{2}}{5} \times \frac{2}{3} = \frac{4}{5} \end{matrix}

$\begin{array}{l} 1 \frac{1}{5} \div (4 - 2 \frac{1}{2}) \\ = 1 \frac{1}{5} \div (3 \frac{2}{2} - 2 \frac{1}{2}) \\ = \frac{6}{5} \div (1 \frac{1}{2}) \\ = \frac{6}{5} \div \frac{3}{2} \\ = \frac{6^{2}}{5} \times \frac{2}{3} \\ = \frac{4}{5} \end{array}$

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