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“Kickstart”

Exercise 1

Simplify. 1. (-6) + (-4) 2. (-8) + (-4) 3. (-16) + (-9) 4. (-2) + (-4) + (-3) 5. (-9) + (-2) + (-6) 6. (-4) + (-3) + (-9) 7. –(8) + (-13) + (-15) 8. 7 + (-4) 9. 15 + (-6) 10. (-10) + 13

11. 3 + 2 + (-7) 12. (-11) + 2 + 6 13. 8 + (-5) + (-3) 14. 18 + (-12) + (-6) 15. (-16) + (-10) + 15 16. 18 – 5 17. 22 – 15 18. 14 – (-13) 19. 11 – (-14) 20. (-12) – 24

NB: denotes that a calculator can be used ✪✪

Exercise 2

Simplify. 1. 15 • 8 2. (-2)(-5) 3. (-6) × (-5) 4. 2(-8) 5. 4(-7) 6. -5 × 12 7. (-5)(4)(-1) 8. (-9)(1)(6) 9. 4 × -3 × -6 10. (-1)(-9)(3) 11. (-2)(-4)(-3) 12. –(-2)(-7)(-4) 13. –(-3)(-2)(2) 14. -42 ÷ -7 15. -24 ÷ -8

16. 440−

−

17. 333−

−

18. 99 ÷ -11

Exercise 3 Simplify by following order of operations (BODMAS). 1. 2 + 5 × 4 2. 27 + 3 × 7 3. 46 - 5 × 3 4. 41 + 28 ÷ 4 5. 40 – 45 ÷ 5 6. 50 – 35 ÷ 7 7. 24 ÷ 6 + 3 × 4 - 8 8. 7 × 3 + 8 – 12 ÷ 4 9. (9 + 2) × 3 - 9

10. 24 + 3(4 – 1) 11. 12 - 32 12. 23 – 6 × 7 13. 31 – 3 × (-2) 14. 2 + 2(6 – 10) 15. -15 + 45 ÷ 5 16. 7 × 8 – 5 + 6 ÷ 3 17. 10 – 45 ÷ 5 + 4 × (-7) 18. 35 ÷ 7 – 2 + 4 × 3

19. 7 × 3 + 8 – 12 ÷ (-4) 20. (7 + 2) × (-3) + 9 21. (5 – 8) × 6 - 4 22. (16 – 46) ÷ (5 × 3) 23. 3(8 – 6) + 42 ÷ 7 24. 8(3 + 2) – 35 ÷ 5 25. 20 ÷ 4 – 12 ÷ 2 + 3 × (-6)

26. 43636÷

×

27. 59236

−

+×

28. ( )2242105×+

−

29. ( )252376×−

−

30. 62)2(85

+

−÷×

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Multiplying Fractions

1. Cancel down these fractions into their simplest form.

(a) 3672

= (b) 18300

= (c) 50225

=

2. Find the missing values in the sets of equivalent fractions.

(a) 20 430 18

= = (b) 15 4575 25

= = (c) 75 15100 20

= =

3. Rearrange these fractions in ascending order (smallest to biggest).

(a) 5 2 7 3 1, , , ,6 5 8 7 2

(b) 3 15 3 6, , ,20 16 4 7

(c) 2 3 5 4, , ,5 10 6 11

(d) 8 8 8 8, , ,9 11 10 12

4. Cancel down these fractions and then find the answer in simplified form.

(a) 4 105 12× (b) 14 6

18 21× (c) 11 8

12 9×

5. Multiply these fractions and whole numbers. Make sure the answers are cancelled down into their simplest form.

(a) 45

of 70 (b) 1525

of 30 (c) 614

of 35

6. (a) In a pine plantation of 5850 trees, 1/9 of them died from a lack of water. How many trees survived the drought?

(b) A small population of 220 lyrebirds living in a protected forest were attacked by feral animals. If 2/5 of the birds were killed, how many survived the attack?

(c) A farmer lost 1/3 of his crop to hail. He expected to harvest 12 tonnes; how much did he lose?

(d) 3/5 of a group of 220 students catch a bus to school. How many students is this?

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Converting Decimals to Fractions

1. Round off the following numbers to three decimal places. (a) 418.34901 (b) 29.99999 (c) 0.3973845 (d) 99.988888 (e) 0.00600 (f) 8.90961 2. The followings are prices of groceries bought. Add up the totals, then round them off using the following table.

1c 2c 3c 4c 5c 6c 7c 8c 9c Round down to 0c Round to 5c Round up to 10c (a) $2.58 + $13.76 + $8.32 (b) $16.21 + $3.98 + $5.99 + $20.04 (c) $129.99 + $36.95 + $155.22 (d) $1.09 + $22.05 + $18.02 3. It is not uncommon to need to change a fraction into a decimal or a decimal into a fraction. There are some common conversions that people use regularly. Below is a table that shows a number of fractions in the first column. Without using a calculator, estimate the decimal equivalent and write it in the second column. When you have filled the second column, check your answers with a calculator. Use the third column to write in the correct answer if your estimate was incorrect.

Fraction Estimate Correction Fraction Estimate Correction 23

1

3

12

4

5

14

1

8

34

75

100

15

1

10

4. Without using a calculator, complete the following. Remember: move the decimal point to the left when dividing, move the decimal point to the right when multiplying. (a) 64.725×100 (b) 3812.4 × 10 (c) 0.3914 × 1000 (d) 298.3 ÷ 10 (e) 34.231 ÷ 100 (f) 0.03 ÷ 10 (g) 0.00582 × 1000 (h) 234 ÷ 1000 (i) 980 × 100

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Percentage Skills

1. Write each of these fractions as a percentage.

(a) 12

(b) 34

(c) 110

(d) 15

(e) 13

(f) 23

2. Write each of these decimals as a percentage. (a) 0.2 (b) 0.15 (c) 0.3 (d) 0.8 (e) 0.95 (f) 1 3. Write each of these percentages as a fraction. (a) 25% (b) 50% (c) 40% (d) 75% (e) 90% (f) 100% 4. Write each of these percentages as a decimal. (a) 35% (b) 70% (c) 30% (d) 65% (e) 50% (f) 100%

Percentages ✪✪

1. Find the following amounts. (a) 20% of 300 (b) 25% of 800 (c) 70 % of 700 2. Write each of these fractions as a percentage.

(a) 120

(b) 312

(c) 210

(d) 35

(e) 23

(f) 26

3. In a box of 40 chocolates, 15% were peanut centres. How many peanut centres were there? 4. In a group of 240 students, 80% will be attending the school concert. How many students is this? 5. The most popular ride at a fun fair is the roller coaster; 68% of people go on this ride. If 350 people visit the fun fair during one week, how many rides on the roller coaster during the week is this? 6. The local supermarket decides to increase its workforce by 15%. (a) How many new employees will there be if there are currently 40 people employed? (b) What will now be the total number of employees? 7. Vanessa works 10 hours a week in her part-time job. Her boss offers her an increase in hours of 10%. How many hours will she work each week if she accepts the offer? 8. A shopkeeper has to add 10% to the cost of all goods for sale to cover the GST. For each of the following items, find the GST amount and the price that the public will pay. Price before GST Value of GST Price with GST added $20.50 $17.00 $315.00 $2430.00