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

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

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### Video Transcript

In this question, we are asked to find the product of two rational numbers and give our answer as a decimal. There are many ways that we can answer this question. For instance, we could convert both numbers into decimals and then evaluate the multiplication. And while this would work, it is usually easiest to multiply rational numbers given as fractions. So, we will convert 0.4 into a fraction. We know that one-fifth is 0.2. So we can double this to see that two-fifths is 0.4. This allows us to rewrite the product as two-fifths multiplied by five-quarters.

We can now recall that we can multiply fractions together by multiplying their numerators and denominators separately. In general, we have that 𝑎 over 𝑏 times 𝑐 over 𝑑 is equal to 𝑎 times 𝑐 over 𝑏 times 𝑑. Applying this result to our product yields two times five divided by five times four.

We could now evaluate the expressions in the numerator and denominator. However, we can note that there is a shared factor of five in the numerator and denominator that we can cancel. Similarly, we can note that there is a shared factor of two in the numerator and denominator. Canceling the shared factors leaves us with one over two.

Finally, we need to give our answer as a decimal. We can do this by recalling that one-half is equal to 0.5.

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