Video: Evaluating Numerical Expressions by Multiplying Rational Numbers

Calculate (2 3/5) × (−2/7). Give your answer as a fraction in simplest form.

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Video Transcript

Calculate two and three-fifths multiplied by negative two-sevenths. Give your answer as a fraction in simplest form.

In order to multiply these two fractions, we firstly need to convert two and three-fifths into an improper or top-heavy fraction. We do this by multiplying the whole number by the denominator and then adding the numerator. Two multiplied by five is 10, and adding three gives us 13. The denominator of the fraction stays the same, so two and three-fifths is the same as thirteen-fifths.

We now need to multiply thirteen-fifths or 13 over five by negative two-sevenths. We can multiply any two fractions by firstly multiplying the numerators and then separately multiplying the denominators. We recall that multiplying a positive number by a negative number gives a negative answer.

When dealing with fractions, we can consider the whole fraction to be negative or just the numerator or just the denominator. In this case, let’s assume the numerator is negative. So, 13 multiplied by negative two is equal to negative 26. Five multiplied by seven is equal to 35. So, 13 over five multiplied by negative two over seven is negative 26 over 35. This is, therefore, also the answer to two and three-fifths multiplied by negative two-sevenths.

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