Video: Finding as a Fraction the Result of Multiplying Decimal Numbers by Fractions

Find the product of 1.6 and 1/2. Give your answer as a fraction in its simplest form.

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Video Transcript

Find the product of 1.6 and one-half. Give your answer as a fraction in its simplest form.

The word product means multiply or times. Therefore, we need to multiply 1.6 and one-half. Multiplying 1.6 by one-half is the same as halving 1.6. We can halve a number by dividing it by two. 16 divided by two is equal to eight. This means that 1.6 divided by two is equal to 0.8. The product of 1.6 and one-half is 0.8.

We were asked to give our answer as a fraction. And, we know that 0.8 is the same as eight-tenths. This is because eight divided by 10 is equal to 0.8. In order to write this fraction in its simplest form, we need to divide the numerator and denominator by the highest common factor. The highest integer that divides exactly into eight and 10 is two. Therefore, we need to divide the numerator and denominator by two. Eight divided by two is equal to four. And, 10 divided by two is equal to five. The fraction eight-tenths in its simplest form is four-fifths. We can therefore say that the product of 1.6 and one-half, written as a fraction in its simplest form, is four-fifths.

An alternative method would have been to have written the decimal, 1.6, as a fraction to begin with. 1.6 is the same as 16 over 10 or 16 divided by 10. We need to multiply this by one-half. 16 over 10 could be simplified to eight over five or eight-fifths. Multiplying this by one-half, once again, gives us eight-tenths which we know is the same as our final answer of four-fifths.

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