Question

Find the product of the following.
\[\dfrac{9}{2}\times \left( \dfrac{-7}{4} \right)\]

Answer 1

Hint: We are asked to find the product of fractions \[\dfrac{9}{2}\] and \[\dfrac{-7}{4},\] we will first learn how to simplify the fractions and then we will solve \[\dfrac{9}{2}\] and \[\dfrac{-7}{4}\] as those fractions, numerator, and denominator have nothing in common, so the product will be simple, multiplying the numerator to numerator and denominator to the denominator.

Complete step by step answer:
We are given two fractions and we are asked to find the product of these fractions. The first one is \[\dfrac{9}{2}\] and another one is \[\left( \dfrac{-7}{4} \right).\] We have to calculate the product of these two. Before we move forward we will learn about multiplying two fractions. Whenever we have a number in the form of a fraction, firstly convert each type of fraction into a simple fraction and then we do the product. For example, if we have \[3\dfrac{1}{2}\] and \[4\dfrac{1}{3}\] so first we will convert a mixed fraction into an improper fraction, so it will be \[3\dfrac{1}{2}=\dfrac{7}{2}\] and \[4\dfrac{1}{3}=\dfrac{13}{3}.\]
Once we get the fraction into an improper fraction, we will then go for the product. While computing the product, we will follow these steps.
1. We will cancel the terms in the numerator and denominator if there are some common multiples.
2. Once we cancel all the common terms, we will then do the product, we will multiply the numerator by numerator and denominator by denominator.
Now we are given fractions as \[\dfrac{9}{2}\] and \[\dfrac{-7}{4}\] as we can see clearly that both fractions are already in simple fraction form so we can move forward.
Now, \[\dfrac{9}{2}\times \dfrac{-7}{4},\] we will check the numerator and denominator if there is any common factor. As we observe that the numerator has 9 and – 7, while the denominator has 2 and 4, so there is nothing in common. So, we now just need to multiply the terms numerator will be multiplied by numerator and denominator by denominator. So, we get,
\[\dfrac{9}{2}\times \dfrac{-7}{4}=\dfrac{9\times -7}{2\times 4}\]
\[2\times 4=8\] and \[9\times -7=-63\]
Simplifying, we get,
\[\dfrac{9}{2}\times \dfrac{-7}{4}=\dfrac{-63}{8}\]
Hence, the answer is \[\dfrac{-63}{8}.\]

Note:
 Students need to remember that the common multiple can be canceled from the numerator and denominator. So, do not get confused and cancel both the denominators like \[\dfrac{9}{2}\times \dfrac{-7}{4}\ne \dfrac{9}{1}\times \dfrac{7}{2}.\] Cancelling the denominator and denominator is incorrect. Also, the product of positive and negative is a negative term.