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SHAPING UP

SHAPING UP. SENIOR VCAL NUMEERACY. http:// www.mathsisfun.com /fractions- menu.html. Rules: When adding and subtracting two integers with the same sign, this changes to a positive . E.g . - 4 + + 2 = - 4 + 2 = - 2 E.g. 3 - - 2 = 3 + 2 = 5

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SHAPING UP

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  1. SHAPING UP SENIOR VCAL NUMEERACY http://www.mathsisfun.com/fractions-menu.html

  2. Rules: • When adding and subtracting two integers with the same sign, this changes to a positive. • E.g. -4 + +2 = -4 + 2 = -2 • E.g. 3 - -2 = 3 + 2 = 5 • When adding and subtracting two integers with different signs, this changes to a negative. • E.g. -3 + -4 = -3 – 4 = -7 • E.g. 4 - +5 = 4 – 5 = -1 • In Summary: • +and + gives + • –and – gives + • +and – gives – • –and + gives – ADDITION & SUBTRACTION OF POSITIVE & NEGATIVE NUMBERS

  3. 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 EXERCISE 1

  4. Rules: • When multiplying and dividing two integers with the same sign, the answer is positive. • E.g. +4 × +2 = +8 • E.g. -3 × -2 = +6 • When multiplying and dividing two integers with different sign, the answer is negative. • E.g. -3 × +4 = -12 • E.g. +4 × -5 = -20 • In Summary: • +and + gives + • –and – gives + • +and – gives – • –and + gives – MULTIPLICATION & DIVISION OF POSITIVE & NEGATIVE NUMBERS

  5. 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.-40 / -4 17. -33 / -3 18. 99 ÷ -11 EXERCISE 2

  6. BIDMAS: • Brackets, Indices, Division & Multiplication, Addition & Subtraction • Setting out is VERY IMPORTANT! • Always work left to right • Eg: 3 + 2 × 4 = 3 + 8Eg: (7 + 2) × -3 + 9 = 9 × -3 + 9 • = 11 = - 27 + 9 • = -18 BIDMAS

  7. Simplify 1. 2 + 5 × 4 2. 27 + 3 × 7 3. 46 - 5 × 3 4. 41 + 28 ÷ 4 5. 40 – 45 ÷ 5 6. 50 – 35 ÷ 7 (show all working) 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 EXERCISE 3

  8. Simplify 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. 27. 28. 29. 30. ✔ EXERCISE 3 cont’d

  9. ROUNDING • Round down when last digit is 0, 1, 2, 3, 4 • Round up when last digit is 5, 6, 7, 8, 9 • Eg: Round to 2 decimal places (dp) 34.013 = 34.01 • Eg: Round to 3 decimal places 125.1267 = 125.127 • Eg: Round to nearest 5 cents $23.22 = $23.20 ROUNDING

  10. 1. Round the following numbers to three decimal places. • 2. The following are prices of groceries bought. Add up the totals then round off using the following table. EXERCISE 4

  11. POWERS OF 10 • Dividing by powers of 10 eg. 10, 100, etc – move the decimal point to the LEFT • Eg: 3245 ÷ 100 = 32.45 • Multiplying by powers of 10 eg. 10, 100, etc – move the decimal point to the RIGHT • Eg: 0.045 × 10 = 0.45 CONVERTING

  12. 3. Without using a calculator, complete the following. (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 EXERCISE 4 cont’d

  13. COMMON FRACTIONS • 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. On the next slide is a table that shows a number of fractions in the first column. COPY the table, then 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 the teacher. Use the third column to write in the correct answer if your estimate was incorrect. COMMON FRACTION

  14. EXERCISE 5

  15. Simplifying / cancelling down fractions • To simplify a fraction, divide the top (numerator) and bottom (denominator) by the highest number that can divide into both numbers exactly • Eg: Eg: FRACTIONS

  16. Equivalent fractions • Have the same value even though they may look different. Rule:Change the bottom using multiply or divide, and the same to the top must be applied. • Eg: Eg: FRACTIONS

  17. 1. Cancel down these fractions into their simplest form. • 2. Find the missing values in the sets of equivalent fractions. EXERCISE 6

  18. Fraction • Wall • Remember: • Ascending order – smallest to largest • Descending order – largest to smallest FRACTIONS

  19. 3. Rearrange these fractions in ascending order. EXERCISE 6 cont’d

  20. Multiplying • Fractions • Eg: FRACTIONS

  21. 4. Find the answer to the following questions. Simply if needed. EXERCISE 6 cont’d

  22. 5. Find the answer to the following. ✔ • 6. Find solutions to the following: • (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? EXERCISE 6 cont’d

  23. CONVERTING • To convert Fractions or Decimals to a Percentage the rule is to multiply by 100 • Eg: Eg: 0.34 × 100 = 34% • To convert Percentages to Fractions or Decimals the rule is to divide by 100 • Eg:Eg: 56% = 56 ÷ 100 = 0.56 CONVERTING FRACTIONS, DECIMALS & PERCENTAGES

  24. 1. Write the following fractions as percentages. EXERCISE 7

  25. 2. Write the following decimals as percentages. EXERCISE 7 cont’d

  26. 3. Write the following percentages as fractions. Simply if needed. 4. Write the following percentages as decimals. Simply if needed. EXERCISE 7 cont’d

  27. CALCULATING PERCENTAGES FROM AN AMOUNT • Sometimes we need to find a specific percentage of a value e.g. 20% of $200. It is good to be able to do basic calculations with & without a calculator. • Eg. 20% of $200 = 20% ×200 • = × 200 • = $40 PERCENTAGES

  28. 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. ✔ EXERCISE 8

  29. 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? ✔ EXERCISE 8 cont’d

  30. 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. Copy the table. For each of the following items, find the GST amount and the price that the public will pay. ✔ EXERCISE 8 cont’d

  31. IN THE KITCHEN EXTENSION

  32. EXTENSION

  33. EXTENSION

  34. EXTENSION

  35. EXTENSION

  36. Garden Design Puzzles Part A: A Lovers Ultimatum I ask you, sir, to plant a grove To show that I’m your lady love. This grove though small must be composed Of twenty-five trees in 12 straight rows. In each row five trees you must place Or you shall never see my face EXTENSION

  37. Garden Design Puzzles Part B: The Economical Gardener 1. A gardener liked to make the most of plants she had and one day she found, when laying out a rose bed, that she had managed to plant 7 rose bushes in such a way that they formed 6 lines with 3 rose bushes in each line. How did she do it? 2. Pleased with herself the gardener looked for other interesting arrangements until she had 5 lines with 4 rose bushes in each line. Find her arrangement. EXTENSION

  38. SOLUTIONS TO EXTENSION EXTENSION

  39. EXTENSION

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