Question

How do you multiply \[\dfrac{{14}}{3} \times \dfrac{5}{7}\] ?

Answer 1

Hint:Here for solving the given question we need to multiply a fractional number with another fractional number so we will rewrite the equation and then simple calculation is required. So, if we need to multiply \[\dfrac{a}{b} \times \dfrac{c}{d}\]then firstly we will multiply the numerators and then we will multiply the denominators. Later on we will simplify the fraction in the simplest form to get the desired result.

Formula used:
The formula that we will use for multiplication of fraction in the above question is
Product of fraction \[ = \] Product of numerator \[ \div \]Product of denominator
\[\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{{a \times c}}{{b \times d}}\]

Complete step by step answer:
As we need to multiply \[\dfrac{{14}}{3} \times \dfrac{5}{7}\]
Here we will multiply the numerators and the denominators separately so we will get
\[\Rightarrow \dfrac{{14}}{3} \times \dfrac{5}{7} = \dfrac{{14 \times 5}}{{3 \times 7}} \\
\Rightarrow \dfrac{{70}}{{21}} \\ \]
Lastly we will reduce the fraction into the simplest form so we will get \[\dfrac{{10}}{3}\]. In the mixed form \[\dfrac{{10}}{3}\] will be \[3\dfrac{1}{3}\] and in decimal form \[3.33\]

Hence \[\dfrac{{10}}{3}\] is the product of \[\dfrac{{14}}{3} \times \dfrac{5}{7}\] after simplification by reduction.

Note:While solving the above problem, always simply or reduce the obtained result into its simpler form by cancelling out the common factors from the numerator and denominator. Otherwise we will not obtain the desired results. Remember that multiplication of fractions will result in fractions. Simplify the obtained results carefully as there is possibility of committing calculation mistakes while simplifying the answer obtained in fractions into simpler form.