LO I can use direct and indirect proportion

LO: I can use direct and indirect proportion. Date 24/05/2021 Word Bank: 1. 2. 3. 4. 5. 6. Share £ 120 in the ratio of 2 : 1 Expand & simplify: x(x + 2) - x(x + 3): Estimate the answer to: 253 ÷ 0. 46 Write down the HCF of 24 and 32 Factorise: p 2 – q 2 Work out (4 x 108 ) ÷ (8 x 102) Give your answer in standard form Challenge. A = πr 2 - πrs Find A when r = 4. 2 s = 3. Give your answer correct to 3 sf Proportion Unitary

LO: I can use direct and indirect proportion. Date 24/05/2021 Word Bank: 1. 2. 3. 4. 5. 6. Share £ 120 in the ratio of 2 : 1 80: 40 Expand & simplify: -x Estimate the answer to: 253 ÷ 0. 46 600 Write down the HCF of 24 and 32 8 Factorise: p 2 – q 2 (p-q)(p+q) Work out (4 x 108 ) ÷ (8 x 102) 5 x 105 Challenge. A = πr 2 - πrs Find A when r = 4. 2 s = 3 5. 28 Proportion Unitary

Proportion LO: 24/05/2021 I can : I can use direct and indirect proportion Is to: Understand the terms direct proportion and indirect proportion. Keywords Developing Percentage Unitary Is to: Work out whether two quantities are directly or inversely proportional. Emerging Find an equation linking two quantities which are directly or inversely proportional. Secure

What do these all have in common? Apples cost 12 p each. I buy x apples. They cost y pence in total. y y x x y = 7. 2 x When x increases, y increases. y and x are in proportion. x y -3 -9 -2 -6 -1 -3 0 0 1 3 2 6 3 9

Direct proportion

Direct proportion If two values are in direct proportion, as one value increases, the other increases at the same rate. For example: Two pencils cost 10 p × 2 Four pencils cost 20 p × 3 Six pencils cost 30 p ×½ × 0 ×½ One pencil costs 5 p Zero pencils cost 0 p × 0

When y is directly proportional to x. . . we write if one value is zero, the other is zero, if one value doubles, the other doubles, if one value trebles, the other trebles. . . y their graph is a straight line going through the origin the ratio between x and y is constant: therefore x (k is called the ‘constant of proportionality’)

Examples of direct proportion s 1 2 3 4 6 12 t 5 10 15 20 30 60 5 5 5 is constant, therefore (in fact, ) We could also show that the graph is a straight line going through the origin: Are s and t directly proportional?

Examples of direct proportion p and q are directly proportional. When q is 7, p is 28. a) Find the constant of proportionality, k. b) Write an equation linking p and q. c) When q is 3, find p. d) When p is 1. 6, find q. therefore a) b) writing this equation helps us remember if we need to calculate p/q or q/ p c) d)

Inverse proportion

Inverse proportion A taxi costs £ 24. Complete this table to show the cost for each person as the number of passengers changes: Passengers (p) Cost per passenger (c) 1 £ 24 1 × 24 = 24 2 £ 12 2 × 12 = 24 3 £ 8 3 × 8 = 24 4 £ 6 4 × 6 = 24 6 £ 4 6 × 4 = 24 12 £ 2 12 × 2 = 24 These values are not in direct proportion, as constant. What value is constant? is not

When y is inversely proportional to x. . . therefore the product of x and y is constant: this is the same as y being proportional to : if one value doubles, the other halves, if one value trebles, the other is divided by three. . . but neither value can ever be zero, or the other would be infinite! y their graph is a hyperbola: a special curve which never quite reaches either axis. x

Examples of inverse proportion s 1 2 3 4 6 12 t 36 18 12 8 6 3 36 36 36 32 36 36 Are s and t inversely proportional? is not constant, so s and t are not inversely proportional. What would need to change so When , t should be 9: ?

Examples of inverse proportion The time to paint a fence is inversely proportional to the number of painters. Two painters (p), take 8 hours (t). a) Find the constant of proportionality, k b) Write an equation linking p and t. c) How long would 3 painters take to paint the fence? therefore a) c) hours b)

Summary directly y is _____ proportional to x. inversely y is _____ proportional to x. If one value doubles, doubles the other _____. If one value doubles, halves the other _____. Their graph is. . . a straight line through the origin. Their graph is. . . a hyperbola (a curve which doesn’t touch either axis). k is called. . . the constant of proportionality.