1. Ratio and proportion

2. Definition of a ratio If a and b are two quantities that are measured in the same units, then the ratio of a to b is a/b. If a and b are two quantities that are measured in the same units, then the ratio of a to b is a/b. This ratio is written as a : b. This ratio is written as a : b. Ratios are preferably expressed in simplified form. Ratios are preferably expressed in simplified form.

3. A ratio is a comparison of two numbers and can be written several ways. Each of the following are ways to write the ratio of 3 to 4.

4. If the quantities to be compared include units, then the units should be the same. To find the ratio of 1 ft to 15 in, express both quantities in inches and then find the ratio.

5. For Practice Simplify the following ratios: Simplify the following ratios:

6. Definition of proportion An equation that equates two ratios is a proportion. For instance, if the ratio a/b is equal to the ratio c/d, then the following proportion can be written: An equation that equates two ratios is a proportion. For instance, if the ratio a/b is equal to the ratio c/d, then the following proportion can be written:

7. A proportion has four terms. In the proportion the first term is 2, the second term is 5 the third term is 4, and the fourth term is 10. The first and fourth terms are called the extremes and the second and third terms are called the means.

8. In a proportion the product of the means is equal the product of the extremes.

9. A proportion is often used to solve such applications in which we are given one of the ratios and then asked to find one part of the other ratio equal to the first one.

10. To solve a proportion means to find the value of the missing term. To do this use cross products to write an equation then solve the equation. Solve:

11. Practice: Solve each of the following proportions.

12. Solve the following proportions.

13. Some Related Examples

14. If 125 bolts cost $7.50, how much do 200 bolts cost?

15. Suppose 826 bricks are used to build a wall 14 ft long. How many bricks are needed for a similar wall 35 ft long?

16. The perimeter of rectangle ABCD is 60 centimeters. The ratio of AB:BC is 3:2. Find the length and width of the rectangle. The perimeter of rectangle ABCD is 60 centimeters. The ratio of AB:BC is 3:2. Find the length and width of the rectangle.

17. The measure of the angles in triangle JKL are in the extended ratio of 1:2:3. Find the measures of the angles. The measure of the angles in triangle JKL are in the extended ratio of 1:2:3. Find the measures of the angles.

18. 1 If 32 rulers cost £3.52 what would 25 rulers cost ? 2 32 boxes of crayons cost £47.36 What would 48 boxes cost ? 3 25 bottles of wine cost £ 143.75 What would 15 bottles cost ? 4 If 40 set squares cost £7.60, what would 64 cost ? 5 19 metres of curtain material cost £ 149.15 19 metres of curtain material cost £ 149.15 What would 12 metres cost ? 6 A set of 8 dental mirrors cost £ 110 A set of 8 dental mirrors cost £ 110 What would a set of 12 cost ? 7 56 books cost £266 What would 40 books cost ? 8 80 tennis balls cost £84. What would 64 tennis balls cost ? Some more Examples

19. 9 A box of 250 toothbrushes cost £315 How much should you pay for the larger box which contains 480 toothbrushes ? 10 A package containing 52 ties can be bought at a warehouse for £621·40. How much should you pay if you wanted to buy the smaller package containing 20 ties ? 11 A store buys 140 childrens shirts from their supplier for £539. The store wish to buy in a further 360 of the same shirts. How much would they pay for them ? 12 A shoe shop buy 12 pairs of the slippers shown from the manufacturer for £107.40 If they wish to order a further 20 pairs, how much would they pay for them ? 13 A jeweler buys 50 bangles for his shop for £997·50. As they sell so well, he decides to buy a further 40 bangles. How much will these cost ? 14 If 56 calendars cost £277.20 how much would 44 cost ?