Direct proportion

Direct proportiontwo 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

Best buyswhen 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

Advanced direct proportionPercentage increase/decrease = (actual increase/decrease divided by original value) x 100We 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.

Inverse proportionInverse 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