Video: Evaluating Numerical Expression by Multiplying and Dividing Rational Numbers

Evaluate ((3/4) × (−2/3)) ÷ 1/5 giving the answer in its simplest form.

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Video Transcript

Evaluate three-quarters multiplied by negative two-thirds divided by one-fifth giving the answer in its simplest form.

Our first step is to multiply the two fractions in the bracket, three-quarters multiplied by negative two-thirds. In order to multiply two fractions, we multiply the numerators and then separately multiply the denominators. In this case, we can multiply three by negative two and four by three. In some cases, like in this question, we can cross cancel or cross simplify first.

The three on the top and the three on the bottom are both divisible by three. And three divided by three is equal to one. The negative two and four are both divisible by two. Four divided by two is equal to two. And negative two divided by two is equal to negative one. We can now multiply the new denominators and the new numerators. One multiplied by negative one is equal to negative one as multiplying a positive by a negative gives a negative answer. On the bottom of the fraction, two multiplied by one is equal to two. This means that three-quarters multiplied by negative two-thirds is equal to negative one-half.

Our final step is to divide negative one-half by one-fifth. Dividing by a fraction is the same as multiplying by the reciprocal of this fraction. This means that dividing by one-fifth is the same as multiplying by five over one or five. We need to multiply negative one-half by five over one. Dividing by a fraction is sometimes taught using the acronym KCF. We keep the first fraction the same. We change the sign. And we flip the second fraction. We now need to multiply the two numerators and then multiply the denominators. Negative one multiplied by five is equal to negative five. Two multiplied by one is equal to two. Therefore, negative a half multiplied by five over one is negative five over two or negative five-halves.

The answer to the calculation three-quarters multiplied by negative two-thirds divided by one-fifth in its simplest form is negative five over two. This could also be written as a mixed fraction or mixed number. Five divided by two is equal to two and a half. Therefore, negative five over two is the same as negative two and a half. We could also write this as a decimal, negative 2.5.

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