Ratio

Definition and rules

• The ratio of two quantities of the same kind and same units is a : b = a/b; it is a pure number, it has no unit.
• Multiplying or dividing both terms by the same non-zero number gives an equivalent ratio, so 12 : 18 = 2 : 3.
• The ratio is always written in its lowest terms, and the order of the terms matters: the ratio of a to b is not the ratio of b to a.

Dividing a quantity in a given ratio

To divide Q in the ratio a : b : c, find the total number of parts a + b + c, then the share of each part is Q ÷ (a + b + c); multiply by a, b, c.

• Divide 240 feddans in the ratio 3 : 5. Parts = 8, one part = 30, so the shares are 90 and 150 feddans.
• Divide EGP 1,200 in the ratio 2 : 3 : 7. Parts = 12, one part = 100, so 200, 300, 700.

Ratio problems with two changing quantities

• The ratio of the ages of two friends is 4 : 5 and the difference of their ages is 6 years. One part = 6, so their ages are 24 and 30 years.
• If a : b = 2 : 3 and b : c = 4 : 5, make b common: a : b : c = 8 : 12 : 15.