Question Video: Subtracting the Result of Multiplying Fractions by Whole Numbers in Word Problems

Video Transcript

There are 110 boys and 70 girls in a certain school grade. If three-fifths of the boys and five-sevenths of the girls participated in a charity event. How many more boys than girls participated in the event?

We’re told that there are 110 boys and that three-fifths of them participated in the event. This means that we need to calculate three-fifths of 110. This will be the number of boys that participated in the charity event. There were 70 girls in the school grade. And five-sevenths of them participated in the event. To calculate the number of girls, we need to work out five-sevenths of 70. In order to calculate the fraction of any amount, we firstly divide the amount by the denominator or bottom number. We then multiply this answer by the numerator or top number.

For the boys, our first step is to divide 110 by five. We can do this using the bus stop method. Five does not divide into one. Therefore, we can carry the one to the tens column. 11 divided by five is equal to two remainder one as two multiplied by five equals 10. Finally, 10 divided by five is equal to two. This means that 110 divided by five is equal to 22. We could check this by multiplying 22 by five. Two multiplied by five is equal to 10. And 20 multiplied by five is equal to 100. Adding these gives us 110.

We have divided by the denominator. And now we need to multiply this answer by the numerator. We need to multiply 22 by three. We could do this using column multiplication. Three multiplied by two is equal to six. Multiplying the three by the two in the tens column also gives us six. This means that 22 multiplied by three is equal to 66. We can therefore say that three-fifths of 110 is equal to 66. And 66 boys participated in the charity event.

We now need to repeat this process for the girls. We need to calculate five-sevenths of 70. We begin by dividing 70 by the denominator. 70 divided by seven is equal to 10 as 10 multiplied by seven is 70. We then multiply this answer by the numerator. And 10 multiplied by five is equal to 50. Five-sevenths of 70 is equal to 50. And therefore, there were 50 girls who participated in the charity event. We were asked to calculate how many more boys than girls participated in the event. There were 66 boys. And there were 50 girls. Therefore, we need to subtract 50 from 66. This is equal to 16.

Therefore, there were 16 more boys than girls that participated in the charity event.