Question

Find the multiplication of \[2\dfrac{1}{2} \times 1\dfrac{3}{8}\].

Answer 1

Hint: In case of a whole number we simply multiply the denominator of the fractional number by the whole number. In such fraction cases the denominator always remains the same. These fractions are called mixed fractions. When both the fractions are mixed fractions then the mixed numbers are changed into improper fractions and then they are multiplied as usual. The fractional part must be simplified by dividing both the numerator and denominator by the common factor and hence result is
obtained.

Complete step by step solution:
Converting the mixed number into improper fractions we have,
\[
2\dfrac{1}{2} = \dfrac{{2 \times 2 + 1}}{2} \\
\Rightarrow \dfrac{5}{2} \\
\]
And
\[
1\dfrac{3}{8} = \dfrac{{8 \times 1 + 3}}{8} \\
\Rightarrow \dfrac{{11}}{8} \\
\]
The fractions are obtained by multiplying the denominator with the whole number and adding it with the numerator. The denominator remains the same always.
Now, multiplying the two fractions which are obtained by solving the mixed fractions we have,
\[
\dfrac{5}{2} \times \dfrac{{11}}{8} = \dfrac{{5 \times 11}}{{2 \times 8}} \\
\Rightarrow \dfrac{{55}}{{16}} \\
\]
Hence, numerators are multiplied together and similarly the denominators are multiplied.
After multiplying the given two mixed fractions we have \[\dfrac{{55}}{{16}}\] as the product.

Note: First conversion of mixed fractions into improper fractions is important and after that if there is possibility of simplification then the fraction should be simplified. The numerators should be multiplied with numerators only and the denominators should be multiplied with the denominators only. There should not be any cross multiplication in case of finding a product of two fractions. The product obtained should also be put in lowest forms that are the fractional part must be simplified by dividing both the numerator and denominator by the common factor.