Question - Mathematical Expressions Simplification
mathsimplify fractionsmultiplying fractionsdividing fractionsmathematical expressions simplification
Solution:
The image shows three mathematical expressions labeled a, b, and c, which are as follows:a) $$ \frac{3}{4} \div \frac{2}{3} $$b) $$ \frac{3}{5} \times 2 $$c) $$ \frac{2}{5} - \frac{5}{2} $$Let's solve each one:a) To divide fractions, you multiply the first fraction by the reciprocal of the second fraction. Therefore,$$ \frac{3}{4} \div \frac{2}{3} = \frac{3}{4} \times \frac{3}{2} = \frac{3 \times 3}{4 \times 2} = \frac{9}{8} $$Since $$ \frac{9}{8} $$ is an improper fraction, it can be simplified to $$ 1 \frac{1}{8} $$ or kept as $$ \frac{9}{8} $$.b) For this one, you can convert the whole number into a fraction by putting it over 1 and then multiply straight across:$$ \frac{3}{5} \times 2 = \frac{3}{5} \times \frac{2}{1} = \frac{3 \times 2}{5 \times 1} = \frac{6}{5} $$This can be simplified to $$ 1 \frac{1}{5} $$ or left as $$ \frac{6}{5} $$.c) To subtract these fractions, they need to have a common denominator. The least common denominator for 5 and 2 is 10:$$ \frac{2}{5} - \frac{5}{2} = \frac{2 \times 2}{5 \times 2} - \frac{5 \times 5}{2 \times 5} = \frac{4}{10} - \frac{25}{10} = -\frac{21}{10} $$This can be simplified to $$ -2 \frac{1}{10} $$.So the simplified results for each expression are:a) $$ 1 \frac{1}{8} $$ or $$ \frac{9}{8} $$b) $$ 1 \frac{1}{5} $$ or $$ \frac{6}{5} $$c) $$ -2 \frac{1}{10} $$ or $$ -\frac{21}{10} $$
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