Solution assignment 10 The basics

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Assignment 10

Calculate without the aid of a calculator:

\displaystyle\frac{13}{7}.\frac{12}{5}.\frac{4}{9}.\frac{21}{26}.\frac{10}{36}.

Solution

Use the fact that the value of a fraction does not change when numerator and denominator are divided by the same nonnegative number. We apply this rule and subsequently divide by 13, 7, 12 and 5, resulting in:

\displaystyle\frac{1}{1}.\displaystyle\frac{1}{1}.\displaystyle\frac{4}{9}.\displaystyle\frac{1}{1}.\displaystyle\frac{1}{1}=\displaystyle\frac{4}{9}

As an example, the numerator contains 21 (that is 3*7) and the denominator contains 7 (that is 1*7). If we divide both numerator and denominator by 7 the result will be 3 in the numerator and 1 in the denominator.

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