Video: AQA GCSE Mathematics Foundation Tier Pack 1 • Paper 1 • Question 7

Some numbers are shown in a grid. Write the numbers in pairs such that the sum of each pair has the same value.

03:20

Video Transcript

Some numbers are shown in a grid. They are 3.7, 10.3, 19.3, 7.7, 16.7, and 23.3. Write the numbers in pairs such that the sum of each pair has the same value.

There are six numbers in the grid. And the word “sum” means “add.” We’re therefore looking for three pairs of numbers that add to the same value. We can see that, of the six numbers, three of them have a tenths value of seven. And the other three have a tenths value of three. As three plus seven is equal to 10, we will need to group one of the numbers with a tenths value of seven and one of the numbers with a tenths value of three.

In order to make finding the pairs easier, we can write the numbers in ascending order. This means from smallest to largest. The smallest number is 3.7. The next smallest is 7.7. Continuing in ascending order gives us 10.3, 16.7, 19.3, and 23.3.

As each pair has to add up to the same value, we’ll have to add the highest number to the lowest number. We will need to add 23.3 and 3.7. We will also have to add the next highest and next lowest numbers: 19.3 and 7.7. Finally, we will need to add 16.7 and 10.3.

When adding these pairs of decimals, we must ensure that our decimal point stays in the same position. We will start by adding 23.3 and 3.7. Adding the numbers in the tenths column, three plus seven gives us 10. We put a zero in the answer and carry the one. Next, we add the units. Three plus three is six. Adding the one gives us seven. Finally, we have two in the tens column. This means that 23.3 plus 3.7 is equal to 27 or 27.0.

Repeating this method with 19.3 and 7.7 gives us 10 once again in the tens column. Nine plus seven is equal to 16. Adding the one gives us 17. Finally, adding the two ones gives us two. Therefore, 19.3 plus 7.7 is also 27.

Our final pair of numbers, 16.7 and 10.3, also add to 27. This means that the three pairs of values that sum to the same value are 23.3 and 3.7, 19.3 and 7.7, and 16.7 and 10.3.

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