Video: Solving Word Problems Involving the Multiplication of Mixed Numbers by Fractions

A man weighs 97 4/5 kg on Earth, and his weight on the Moon is 1/6 of its value on Earth. Find the man’s weight on the Moon.

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Video Transcript

A man weighs 97 and four-fifths of a kilogram on Earth, and his weight on the Moon is one-sixth of its value on Earth. Find the man’s weight on the Moon.

We are given the man’s weight on Earth, and we are told that on the Moon it is one-sixth of this. We therefore need to multiply 97 and four-fifths by one-sixth. Our first step is to convert the mixed number 97 and four-fifths into an improper or top-heavy fraction. We do this firstly by multiplying 97 by five, which gives us 485. We then add the numerator to this, giving us 489. 97 and four-fifths is equal to four hundred and eighty-nine fifths.

When multiplying two fractions, we need to multiply the numerators and separately the denominators. We can cross cancel first, though, as six and 489 are both divisible by three. Six divided by three is two, and 489 divided by three is 163 as shown in the bus stop short division method. Multiplying the numerators gives us 163, and multiplying the denominators gives us 10. We can now convert this improper fraction back into a mixed number by dividing the numerator by the denominator. 163 divided by 10 is equal to 16 remainder three. Therefore, 163 over 10 is the same as 16 and three-tenths. The man’s weight on the Moon is 16 and three-tenths of a kilogram. This could also be written in decimal form as 16.3 kilograms.

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