13+Ratios+and+Proportions

Ratios and Proportions

Ratio - A comparison of two numbers that shows how many times one number can go into another number. Proportion - A comparison of two ratios in which the ratios are set to equal each other.

If a both ratios in a proportion are equal to each other then they are equal to each other. If one side is different then the other side of the equal sign then it is known as a proportion that has no solution.
 * Proportion Rules**

Example 1: 8/10= 4/5.......this works because if you multiply the numerator by the other denominator they will equal each other. 8x5=4x10 ... 40=40

Example 2: 6/12=5/11...this does not work because one side does not equal the other side of the proportion. 6x11=12x5 ... 66=60 ***no solution***

A ratio is a comparison between two numbers. If someone says the ratio of cats to dogs is five to three, this can be expressed as 5:3 or 5/3. These two notations are ratios. Just like fractions, ratios can be simplified. Simplifying a ratio changes the numbers in the expression, but the relationship between the numbers stays the same.
 * Ratio Rules

Example 1: There are 12 pens and 9 pencils, what is the ratio of pens to pencils in simplest form? 12:9 = 4:3 (4 is the common factor, 12 / 3 = 4 and 9 / 3 = 3) Answer: 4:3

Example 2: In a certain class, the ratio of girls to boys is 7:5. There are 36 students in the class. How many are boys? 7+ 5 = 12 5 boys Ratio says of every 12 students, 5 are boys Use a proportion to solve: 5/12 = x/36 Start by cross multiplying: 5*36 = 180 180 = 12x /12 /12 x = 15 Fifteen students in the class are boys.

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Explanation of Ratios: http://www.math.com/school/subject1/lessons/S1U2L1GL.html
 * Helpful Link**

Solving Proportions and Word Problems: http://www.purplemath.com/modules/ratio4.htm

Ratio Explanation and Example: http://aaamath.com/g62a_rx1.htm