Ratio and Proportion mathematics simple.pptx

Math

1. RATIO and PROPORTION - Josephine D. Llanas BSED Math 4

2. Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. The ratio formula for two numbers, a and b is expressed as a:b or a/b. The formula for ratio is expressed as a:b ⇒ a/b, where, a = the first term or antecedent. b = the second term or consequent.

3. Example: 3:9 also represented as 3/9, where; 3 is the antecedent and 9 is the consequent If we divide each term of the ratio by the same number (non-zero), it doesn’t affect the ratio.

4. Proportion refers to the equality of two ratios. Two equivalent ratios are always in proportion. Proportions are denoted by the symbol (: :). Proportion formula: a/b = c/d or a:b :: c:d where, b and c = mean or mean terms a and d = extremes or extreme terms

5. Example: 3:5 :: 4:8 or 3/5 = 4/8 3 and 8 = extremes 5 and 4 = means Note: The ratio value does not affect when the same non-zero number is multiplied or divided on each term.

6. Example 1: F ind out if the ratios 6:8 and 24:32 are in proportion. Solution: The given ratios are 6:8 and 24:32. *6:8= 3/4 = 0.75 *24:32 = 3/4= 0.75. Here, both the ratios are equal. Therefore, 6:8 and 24:32 are in proportion.

7. F ind out if the ratios 3:6 and 8:16 are in proportion. Solution: *3:6 = ½ = 0.5 *8:16 = ½ = 0.5

8. There are 30 students in a class. The number of students who like Math and the ones who like Science is expressed in the ratio 2:3. Find the number of students who like Math and the ones who like Science.

9. Solution: *Total number of students = 30 *Number of students who like Math = 2x *Number of students who like Science = 3x We can say that 2x + 3x = 30 ⇒ 5x = 30 5x = 30 5 5 x = 6 *Substituting the value of x = 6 We can get the number of students who like; Math = 2x = 2 x 6 = 12 Science = 3x = 3 x 6 = 18 *Therefore, 12 students like Math, and 18 Students like Science.

10. A recipe calls for 3 eggs for every 8 cups of flour. A head chef will use 32 cups of flour, so how many eggs must he have? 3: 8 x : 32 8x= 96 x=12

11. TRUE OR FALSE: 1. Two ratios are said to be in proportion only if they are equivalent. TRUE - Two ratios are said to be in proportion only if they are equivalent.

12. TRUE OR FALSE: 2. In the ratio 1:2, 1 is the consequent, and 2 is the antecedent. FALSE - In the ratio 1:2, 1 is the antecedent, and 2 is the consequent.