Video: Solving Word Problems by Multiplying a Whole Number by Two Fractions

A small town has 640 residents. If 7/8 of the residents live in houses, and of those residents, only 5/7 own pets, determine how many of the town’s residents are pet owners.

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Video Transcript

A small town has 640 residents. If seven-eighths of the residents live in houses, and of those residents, only five-sevenths own pets, determine how many of the town’s residents are pet owners.

In this question, we’re given three bits of information. Firstly, the town has 640 residents. Seven-eighths of these live in houses. And of those that live in houses, five-sevenths own pets. Our first step is to calculate the number of residents that live in houses. This is equal to seven-eighths of 640. In order to calculate the fraction of any amount, we firstly divide by the bottom or denominator. We then multiply this answer by the top or numerator of the fraction.

Our first step here is to divide 640 by eight. We can do that by using the short division, bus stop method. Eight doesn’t divide into six, so we need to carry the six to the tens column. 64 divided by eight is equal to eight with no remainder, as eight multiplied by eight is 64. Zero multiplied by eight is equal to zero. This means that 640 divided by eight equals 80.

We now need to multiply this answer by our numerator, which was seven. From our times tables, eight multiplied by seven is equal to 56. This means that 80 multiplied by seven is equal to 560. As seven-eighths of 640 is 560, then there are 560 residents that live in houses.

Our next step is to calculate the number of residents that own pets. We were told that five-sevenths of the residents that live in houses own pets. Therefore, we need to calculate five-sevenths of 560. Once again, we can divide by the denominator and then multiply by the numerator of the fraction.

We could divide 560 by seven using the bus stop method again. However, 56 divided by seven is equal to eight. Therefore 560 divided by seven is equal to 80. We now need to multiply this answer by our numerator of five. Eight multiplied by five is equal to 40. Therefore, 80 multiplied by five is equal to 400. This means that 400 out of the 640 residents in the small town are pet owners.

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