University:
Felician University
Course:
MATH-002 | Basic Math Skills-Algebra
Academic year:

2019
Views:

62

Pages:

2
Author:

StellarSymphony

**Ratios and Proportions** **Essential Understanding** You can write a ratio to compare two quantities. A ratio is a comparison of two quantities using division. You can write a ratio of two quantities a and b, where b ≠ 0, as a/b, a to b, or a:b. You can usually express a ratio in simplest form. **Write the ratio of the first measurement to the second measurement.** 1. length of a tennis racket: 2 ft 4 in. = 28 in. length of a table tennis paddle: 10 in. 28/10 = 14/5 **The measures of two supplementary angles are in the ratio 1:4. What are the measures of the angles?** x + 4x = 180 5x = 180 x = 36 36°, 144° **Baseball** A baseball team played 154 regular season games. The ratio of the number of games they won to the number of games they lost was 3/2. How many games did they win? How many games did they lose? WON: 3x LOST: 2x 3x + 2x = 154 5x = 154 x = 22 WON: 66 LOST: 44 **An extended ratio compares three (or more) numbers. In the extended ratio a:b:c, the ratio of the first two numbers is a:b, the ratio of the last two numbers is b:c, and the ratio of the first and last numbers is a:c.** The lengths of the sides of a triangle are in the extended ratio 6:7:9. The perimeter of the triangle is 88 cm. What are the lengths of the sides? **Essential Understanding** If two ratios are equivalent, you can write an equation stating that the ratios are equal. If the equation contains a variable, you can solve the equation to find the value of the variable. For parts (a) and (b), use the proportion x/6 = y/7. What ratio completes the equivalent proportion? Justify your answer. a. x/6 = 4/7 b. 95/17 = (y + 7)/7 An equation that states that two ratios are equal is called a proportion. The first and last numbers in a proportion are the extremes. The middle two numbers are the means. x/6 = 4/7 extremes 15m = 3(m + 1) 15m = 3m + 3 12m = 3 m = 1/4 means a/b = 3/4 extremes In a proportion, the products of terms that are diagonally across the equal sign from each other are the same. This is called the Cross Products Property because the products cross at the equal sign. a/b = c/d a x d = b x c Proportions have other properties: Property (1): a/b = c/d is equivalent to b/d = d/c. (Use reciprocals of the ratios.) Property (2): a/b = c/d is equivalent to a/c = b/d. (Switch b and c in the proportion.) Property (3): a/b = c/d is equivalent to (a+b)/b = (c+d)/d. (Add the denominator to the numerator.) A band director needs to purchase new uniforms. The ratio of small to medium to large uniforms is 3:4:6. a. If there are 260 total uniforms to purchase, how many will be small? b. How many of these uniforms will be medium? c. How many of these uniforms will be large? 3x + 4x + 6x = 260 13x = 260 x = 20 a. 60 b. 80 c. 120