Video: AQA GCSE Mathematics Foundation Tier Pack 2 • Paper 1 • Question 6

(a) Calculate 7848 ÷ 12. (b) Calculate (9/4) − (3/11). Give your answer as a mixed number.

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Video Transcript

Part a) Calculate 7848 divided by 12. There is a second part of this question that we will look at later.

One way of working out this division calculation is using the bus stop method. In order to do this, we need to know our 12 times table. We cannot divide seven by 12. Therefore, we need to carry the seven to the hundreds column. 78 divided by 12 is equal to six remainder six. This is because six multiplied by 12 is equal to 72. And the difference between 72 and 78 is six. We put a six on the answer line. And we carry the remainder.

64 divided by 12 is equal to five remainder four. This is because five multiplied by 12 is equal to 60. And the difference between 60 and 64 is four. We put a five on the answer line and once again carry the remainder, in this case four. 48 divided by 12 is equal to four as four multiplied by 12 equals 48. This means that our final answer is 654. 7848 divided by 12 equals 654.

We can check this answer by multiplying 654 by 12 as multiplication is the inverse or opposite of division. In order to do this, it is worth splitting 654 into three parts. We will multiply 600 by 12, 50 by 12, and four by 12. As six multiplied by 12 is equal to 72, 600 multiplied by 12 is equal to 7200. We add the two zeros. Five multiplied by 12 is equal to 60. Therefore, 50 multiplied by 12 equals 600.

Finally, four multiplied by 12 equals 48. Adding the units column gives us eight. Adding the tens column gives us four. Adding the hundreds columns, two plus six, gives us eight. And the only number in the thousands column is seven. Therefore, 654 multiplied by 12 is 7848. This means that our answer was correct.

The second part of the question said the following. b) Calculate nine-quarters minus three elevenths. Give your answer as a mixed number.

In order to add or subtract any two fractions, we need to find a common denominator. One way of doing this is to find the lowest common multiple of the two denominators, in this case four and 11. The lowest common multiple of four and 11 is 44 as this is the lowest number in both of four and 11 times tables. To get 44, we need to multiply the first denominator by 11. We need to multiply the denominator of the second fraction by four.

Remember with fractions, whatever we do to the bottom, we must do to the top. If we’re multiplying the denominator by 11, we have to multiply the numerator by 11. Four multiplied by 11 is 44. And nine multiplied by 11 is equal to 99. With our second fraction, 11 multiplied by four is equal to 44. On the top, three multiplied by four is equal to 12. Once the denominators are the same, we just need to subtract the two numerators. The denominator stays as 44.

99 minus 12 is equal to 87. We could do this using column subtraction if needed. Nine minus two is equal to seven. And nine minus one is equal to eight. Therefore, 99 minus 12 equals 87. We have therefore calculated that nine-quarters minus three elevenths is equal to eighty-seven forty-fourths or 87 over 44.

This is not the end of the question though as we were asked to give our answer as a mixed number. In order to do this, we need to work out how many 44s go into 87. Well, two multiplied by 44 is equal to 88, which is too big. This means that we we’ll have one whole one as only one 44 goes into 87. We have a remainder of 43 as 87 minus 44 is equal to 43. This means that the answer to nine-quarters minus three elevenths as a mixed number is one and 43 over 44.

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