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Mathematics and English Tuition

Help Pages for Tutors and Parents

Unequal Sharing

Age 10.2 +

EXAMPLE 1:

Together, Joe and Del have 20 stickers, but Joe has 4 more than Del. How many do they each have?

Step 1. ‘Give’ Joe his 4 extra stickers, and then share the rest equally between them. That's 8 stickers each.

Step 2. Joe has 12 stickers and Del has 8.

 Joe Del 4 8 8

Age 11.0 +

EXAMPLE 2:

Kate, Lynn and Sam received a total of £85 for their hard work. Kate received £8 more than Sam but £6 less than Lynn. How much did they each receive?

Step 1. Since there is no ‘three times as many’ or ‘half as much’ in this question (no x or ÷) we can solve this by simply giving those of who have more money their extra bit; and then sharing the rest equally among them.

Step 2. So, ‘give’ Kate her £8 more than Sam. Now, since this very same Kate has £6 less than Lynn, then Lynn must be given £14.

Step 3. That’s (8+14=) £22 given out so far. This leaves (85-22=) £63 still to be given out. Shared equally, this gives each of the girls another £21.

Step 4. So, Kate has £29, Lynn has £35 and Sam has £21.

 K L S 8 14 21 21 21

Age 11.3 +

EXAMPLE 3:

Tom, Dick and Harry share out a bag of 59 sweets so that Dick ends up with twice as much as Harry but 4 less than Tom. How many sweets do they each end up with?

Step 1. Make a table and ‘give’ one of the boys (preferably one who receives little) a small number of sweets. Let’s give Harry 5 sweets and write this in the table. If Harry has 5 sweets then Dick has 10, and Tom has 14. This makes a total of 29 sweets. Too little. They had 59!

Step 2. So, let’s try giving Harry 8 sweets. This gives 16 sweets for Dick and 20 for Tom. A total of 44 sweets. Getting closer to the 59, but not quite there. So try again. (Of course, questions like this can be solved using simple algebra, but pupils of this age usually do not have the expertise to do this.)

 T D H Tot 14 10 5 29 20 16 8 44

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