Question Video: Evaluating the Product of Rational Numbers Given in Different Forms | Nagwa Question Video: Evaluating the Product of Rational Numbers Given in Different Forms | Nagwa

# Question Video: Evaluating the Product of Rational Numbers Given in Different Forms Mathematics • First Year of Preparatory School

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Find the value of the product of −1(1/3) and −0.4 in its simplest fraction form.

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### Video Transcript

Find the value of the product of negative one and one-third and negative 0.4 in its simplest fraction form.

In this question, we are asked to find the product of two rational numbers given in different forms. We need to give our answer as a fraction in its simplest form.

To answer this question, we can note that we can multiply rational numbers together in many ways. However, it is usually easiest to multiply rational numbers written as fractions. Therefore, we will start by converting both rational numbers into fractions.

First, we can convert the mixed number negative one and one-third into the fraction negative four-thirds. Next, we can recall that 0.2 is one-fifth. So negative 0.4 will be negative two times one-fifth, which is negative two-fifths. We can now use these fractions to rewrite the product of negative one and one-third and negative 0.4 as negative four-thirds multiplied by negative two-fifths. We can now multiply the two fractions together by recalling that the product of two negatives is a positive and that we can multiply fractions by multiplying their numerators and denominators separately. In general, we have that 𝑎 over 𝑏 times 𝑐 over 𝑑 is equal to 𝑎𝑐 over 𝑏𝑑.

Therefore, since a negative times a negative is a positive, we can multiply the numerators and denominators separately to obtain four times two over three times five. We can then evaluate the products in the numerator and denominator to get eight over 15. We note that the greatest common factor of these values is one. So we cannot simplify any further. Hence, we leave our answer as eight over 15.

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