Video: Solving Word Problems Involving the Subtraction of Mixed Numbers

Last month, Anthony trained for 53 1/2 hours at the gym. This month, he trained 46 4/9 hours. How many more hours did he train last month?

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Video Transcript

Last month, Anthony trained for 53 and one-half hours at the gym. This month, he trained for 46 and four-ninth hours. How many more hours did he train last month?

Anthony does a lot of training, last month 53 and one-half hours and this month 46 and four-ninth hours, so we wanna know how much less did he train this month than last month or how many more hours did he train last month.

We’ll have to use subtraction. We can’t subtract four-ninths from one-half because they do not have a common denominator. We need to find a common multiple of two and nine that we can use for a new denominator for one-half and four-ninths.

What is the multiples of nine? Nine times one is nine; nine times two is 18. We can stop there because 18 is an even number, which means that 18 will also be a multiple of two. We can use 18 as the least common multiple for two and nine, which means we’ll rewrite each of these fractions with a denominator of 18.

To go from two to 18, we multiply two times nine, but if we multiply the denominator by nine, we’ll have to multiply the numerator by nine. One-half written with the denominator of 18 is nine eighteenths; we haven’t changed our 53; it’s just a whole number, so we go ahead and bring that down.

Now we have 53 and nine eighteenths. From there, we need to work on our four-ninths. How did we go from a denominator of nine to a denominator of 18? We multiplied by two. And if we multiply by two in the denominator, we must multiply by two in the numerator. Four times two equals eight. Four-ninths is an equivalent fraction for eight eighteenths.

Again, we haven’t changed our whole number, so we bring that 46 down. We also bring down that subtraction symbol. Now we have 53 and nine eighteenths minus 46 and eight eighteenths. If we have nine eighteenths and we take away eight eighteenths, we’re left with one eighteenths. From there, we take 46 from 53, or we say 53 minus 46 equals seven. Anthony trained seven and one eighteenth hour at the gym more last month than he did this month.

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