Video: AQA GCSE Mathematics Higher Tier Pack 1 • Paper 2 • Question 15

AQA GCSE Mathematics Higher Tier Pack 1 • Paper 2 • Question 15

02:47

Video Transcript

In a gymnastics club, 70 percent of the gymnasts are girls. Three-fifths of the girls can perform a front flip. One-fourth of the boys can perform a front flip. What percentage of the gymnastics club can perform a front flip?

Starting with the 70 percent, as a fraction it can be written as seven-tenths, seven over 10. Seven-tenths of the gymnasts are girls. And one whole minus seven-tenths equals three-tenths, which means three-tenths of the gymnasts in the club are boys.

The fraction of gymnasts who are girls and can do a front flip would be equal to seven-tenths times three-fifths because we know that three-fifths of the girls can perform a front flip.

When multiplying fractions, we multiply their numerators, seven times three equals 21, and then multiply the denominators, 10 times five equals 50.

Now, we need the fraction of gymnasts who are boys and can do a front flip which would be equal to the fraction of boys multiplied by the fraction of boys who can perform a front flip. Three-tenths times one-fourth equals three fortieths.

The fraction of gymnasts who can do a front flip is equal to the girls who can do a front flip plus the boys who can do a front flip. In order to add fractions, we need a common denominator. If we multiply 50 times four, we get 200. And if we multiply 40 times five, we get 200.

But remember we need to keep our fractions equivalent. And that means we need to multiply the numerator of 50 by four as well. 21 times four equals 84. And we multiply the numerator of 40 by five as well. Three times five equals 15.

Once we have a common denominator, we add the numerators 84 plus 15 equals 99. And the denominator doesn’t change.

The fraction of gymnasts who can do a front flip is 99 out of 200. And we need to write 99 out of 200 as a percent. We can multiply 99 over 200 by 100 to write it as a percent. We can reduce this multiplication to say 99 over two. 99 divided by two equals 49.5, which is our percent.

49.5 percent of the gymnast can do a front flip.

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