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UNIT 3

UNIT 3. Ratio and Proportion. Key Terms. Extremes Means Proof Proportion Ratio. Ratios. Ratio: Way of expressing relationship between two similar components Example: The relationship of 3 to 1 is written as 3 : 1 May be expressed as quotient, fraction, or decimal. Ratio Expressions.

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UNIT 3

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  1. UNIT 3 Ratio and Proportion

  2. Key Terms Extremes Means Proof Proportion Ratio

  3. Ratios Ratio: Way of expressing relationship between two similar components Example: The relationship of 3 to 1 is written as 3 : 1 May be expressed as quotient, fraction, or decimal

  4. Ratio Expressions As a quotient One number divided by the other As a fraction Breaking whole number into parts As a decimal Based on multiples of 10

  5. Proportions Proportion: Way of expressing comparative relationships In mathematics, proportions show relationship between two ratios Example: 3 : 5 = 12 : 20 (continues)

  6. Proportions Must determine unknown by solving for x When part of problem is unknown, x represents the unknown factor

  7. Solving for X Steps to solve for x Set up proportion: 3 : 5 = 12 : x Multiply outer terms (extremes): 3x Multiply inner terms (means): 5 x 12 = 60 Divide product of x into other terms: 60 / 3 x = 20

  8. Prove Your Answer Once you find the unknown, prove your answer using the following steps: Replace x with the answer you obtained Multiply the means by the means Multiply the extremes by the extremes Results will equal each other

  9. Solving for X Using Fractions Steps to solve for x Set up proportion: 1/4x : 250 = 1 : 500 2. Multiply outer terms (extremes): 1/4x x 500 = 125x 3. Multiply inner terms (means): 250 x 1 = 250 4. Divide product of x into other terms: 250 / 125 = 2 5. x = 2

  10. Solving for X Using Decimals Steps to solve for x Set up proportion: 0.25 : 0.5 = 0.5 : x 2. Multiply outer terms (extremes): 0.25x 3. Multiply inner terms (means): 0.5 x 0.5 = 0.25 4. Divide product of x into other terms: 0.25 / 0.25 = 1 5. x = 1

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