Money Calculations

Adding values ending with 9:

£4.99 + £2.75 =

Round £4.99 to £5 and then add £2.75; answer will be £7.75

As you have added 1p to £4.99 when you rounded it to £5, you have to take away 1p from £7.75. So, final answer is £7.74

£3.29 + £2.20 =

Round £3.29 to £3.30 and then add £2.20; answer will be £5.50

As you have added 1p to £3.29 when you rounded it £3.30, you have to take away 1p from £5.50. So, final answer is £5.49

Now try these problems:

1. £7.49 + £3.50 =

2. £8.69 + £4.20 =

3. £11.29 + £3.26 =

4. £56.49 + £25.20 =

5. £34.79 + £46.20 =

6. £49.25 + £26.89 =

7. £57.28 + £22.19 =

8. £28.35 + £28.39 =

Facts:

0.5 + 0.5 = 1

0.25 + 0.75 = 1

0.75 + 0.5 = 1.25

0.75 + 0.75 = £1.50

So 50p + 50p = £1

     25p + 75p = £1

     75p + 50p = £1.25

     75p + 75p = £1.50

Example: £4.50 + £3.50 =

£4.00 + £3.00 = £7.00

£0.50 + £0.50 = £1.00

So, answer is £7.00 + £1.00 = £8.00

Now try these problems:

1. £3.25 + £4.75 =

2. £9.25 + £3.75 =

3. £14.50 + £3.75 =

4. £12.50 + £2.75 =

5. £16.75 + £3.50 =

6. £18.25 + £13.50 =

7. £36.75 + £24.25 =

8. £49.50 + £29.50 =

9. £27.25 + £19.75 =

10. £39.75 + £49.75 =

Facts:

£1.00 - 50p = 50p = £0.50

£1.00 - 25p = 75p = £0.75

£1.00 - 75p = 25p = £0.25

Example:

£8.00 - £0.25

Split £8 into £7 and £1

Take away 25p from £1 which will be 75p

Now you have £7 and 75p

So, answer is £7.75

Example: £15 - £3.25

Step 1: Split £3.25 into £3 and 25p

Step 2: £15 - £3 = £12

Step 3: £12 - 25p = £11.75

Now try these problems

1. £15 - 50p =

2. £35 - 75p =

3. £45 - £1.25 =

4. £27 - £2.50 =

5.  £19 - £3.75 =

6. £35 - £2.50 =

7. £46 - £3.50 =

8. £65 - £5.50 =

9. £40 - £5.25 =

10. £20 - £4.75 =

Money problems

How to calculate change quickly?

Sam buys 3 lollipops at 39 each. What change does he get if he pays with a £2 coin?

working out

39p x 3 = 87p

Count onwards from 87p to £2 that is 200p

87p + 3p = 90p

90p + 10 = 100p

100p + 100p = 200p

In total, we have added 3p + 10p + 100p = 113p = £1.13

Now try these questions:

1.Sam buys a sandwich for £2.53 and drink for 37p. What change will he get if he pays with a £5 note?

2. Anna buys a book for £4.59 and a pen for £2.19. What change will he get if she pays with £10?

3. Sam buys a video game for £13.99 and a ball for £5.24. What change will he get if he pays with £20?

4. Sam buys a cup cake for £3.25 and ice cream for £2.25. What change will he get if he pays with £10?

5. Anna buys a bag for £11.75 and a teddy for £3.50. What change will she get if he pays with £20?

Multiplication

Mental Multiplication:
Example:  83 x 30

Step 1: 83 x 3 = 249, so 83 x 3 = 2490

Now try these:

1.  49 x 50

2. 152 x 30

3. 462 x 40

4. 562 x 30

5. 98 x 20

Example: 34 x 12

Step 1: keep 34 as it is and partition 12 into 10 and 2.

Step 2: 34 x 10 = 340

            34 x 2    =  68

Step 3:  Add 340 and 68. Answer is 408

Now try these:

1. 78 x 13

2. 35 x 14

3. 48 x 16

4. 94 x 14

5. 84 x 22

6. 49 x 23

7. 76 x 31

8. 71 x 19

9. 72 x 22

10. 63 x 12

Example:

156 x 3

Step 1. Partition 156 into 100, 50 and 6

Step 2. Multiply: 100 x 3 = 300

                              50 x 3 = 150

                                6 x 3 =    18

Step 3: Add them: 300 + 150 + 18 = 468

Now try these:

1. 461 x 7           6. 234 x 5

2. 528 x 4           7. 456 x 3

3. 432 x 6           8. 782 x 2

4. 327 x 8

5. 148 x 9

             

Multiplying and Dividing Whole Numbers and Decimals by 10, 100 and 1000

1.  32 ÷ 10 =

2.  345 ÷ 100 =

3. 18 ÷ 10 =

4. 3.5 x 100 =

5. 42.6 ÷ 10 =

6. 378 ÷ 1000 =

7. 4.05 x 10 =

8. 3.56 x 10 =

9. 12 ÷ 100 =

10. 135 ÷ 1000 =

11. 3.256 x 10 =

12. 4.278 x 100 =

13. 5.45 x 1000 =

14. 5.023 x 1000 =

15. 4.52 x 1000 =

16. 4.52 x 100 =

17. 3 ÷ 1000 =

18. 30 ÷ 1000 =

19. 150 ÷ 1000 =

20. 29 ÷ 100 =

21. 204 ÷ 100 =

22. 204 ÷ 1000 =

23. 785 ÷ 10 =

24. 785 ÷ 100 =

25. 785 ÷ 1000 =

Now answer the following questions:

1. 3.5 km = ----------- m

2. 4.75 km = ----------- m

3. 6.25 kg = ---------- g

4. 7.5 kg = ------------ g

5. 8.4 kg = ----------- g

6. 9.04 L = ----------- ml

7. 3.3 L = ----------- ml

8. 3.25 L =  --------- ml

9. 8.1 kg = ---------- g

10. 4.9 kg =--------- g

nth term formula

Find the nth term formula, 50th term and 100th term for the following sequences:

1.  3, 7, 11, 15.....

2.  -1, 4, 9, 14, 19....

3. 6, 9, 12,15..........

4. 7, 12, 17, 22..........

5. 8, 11, 14, 17.........

6. 11, 17, 23, 29..........

7. 13, 15, 17, 19, 21..........

8. 3, 8, 13, 18..........

9. 4, 13, 22, 31.........

10. 6, 10, 14, 18.........

Algebra - Word problems

1. If length of one side of a square is 4x, what is its perimeter and area?

2. If length of one side of a square is 5x + 3, what is its perimeter?

3. If length of a rectangle is 3x + 8 and its breadth is 5x + 7, find its perimeter?

4. If one side of an equilateral triangle is 3x + 1, what is the total distance around the triangle?

5. If one side of a regular octagon is 7x + 2, what is its perimeter?

6. If length of a rectangle is 7x + 4 and its breadth is 3x + 6, find its perimeter?

  If perimeter of the rectangle is 100, find x.

Algebra

Expand:

1. 3(4x + 3y)
2. 5(3x + 8y)
3. 9(2x - 6y)
4. 5(3x - y)
5. 6(5x + 3y)
6. 7(2x + 1)
7. 3(5x - 2)
8. 5(3x + 4)
9. 8x(7x + 3y)
10. 5x(3x + 7)

Find y,

1. if  3x = 5y/2                  6. if 8x = (3y - 7)/7
2. if  x = 9y/2                    7. if 5y = (2x - 4)/5
3. if 5x = 3y/4                   8. if 4y = (3x - 2)/5
4. if 7x = (3y + 2)/4          9. if 2y = (5x - 8)/3
5. if x = (5x - 3)/7           10. if 6y = (7x - 3)/4

Find x:

1. 7x - 3 = x - 9
2. 9x - 4 = 2x + 10
3. 4x - 3 = 12 - x
4. 7x - 8 = 19 - 2x
5. 5x + 12 = 6x - 3
6. 8x + 3 = 5x - 12
7. 9x + 4 = 8x - 3
8. 12x + 4 = 19 - 3x
9. x  - 5 = 3x - 7
10. 3x - 7 = 3 - 2x

1. If 3x = 4y/5, y =
2. If 2x = 8y/3, y =
3. If 4x = 9y/5, y =
4. If 6x = 7y/2, y =
5. If 3x = 8y/5, y =

Find y
1. if 3x + 4y = 8
2. if 4x + 7y = 3
3. if 5x + 3y = 7
4. if 2x - 8y = 3
5. if 9x - 3y = 4