Direct proportion

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Direct proportion

two quantities are in direct proportion if there is a constant factor linking them (eg, the cost of 12 items is 12 times the cost of 1 item)

8 snacks makes 18 lunches, how many lunches can 20 snacks make

18 divided by 8 = 2.23

2.25 x 20 = 45

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Best buys

when looking for "best buys" one side of the ratio must be the same

500 snacks for 2.34 or 200 snacks for 0.98

divide 500 and 2.34 by 5 to get 100:0.47

divide 200 and 0.98 by 2 to get 100:0.49

0.47 is lower so, 500 snacks for 2.34 is the best buy

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Advanced direct proportion

Percentage increase/decrease = (actual increase/decrease divided by original value) x 100

We sometimes need to find an equation for two quantities that are in proportion.

If a and b are in direct proportion then we can write this as a ∝ b, ∝ is the symbol for proportionality but can be replaced with "= K"

It costs 72p for 12 pencils, work out an equation connecting cost and number of pencils, then find out how much 30 pencils will cost.

Let a be the cost in pence and b the number of pencils, a ∝ b

a = k x b so 72 = k x 12

k = 72 ÷ 12 so k = 6

We can find the equation is a = 6b.

Now, we can calculate the price for 30 by substituting b with 30.

a = 6 x 30 so a = 180p

If a and b are in indirect proportion then a ∝ 1/b.

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Inverse proportion

Inverse proportion occurs where one variable is proportional to the reciprocal of the other - as one gets bigger the other gets smaller

m is inversely proportional to r, what's m when r=2

m=9 when r =4

m=k/r 9=k/r k=36

m=36/2=18