Ratios, Rates, and Proportions

Learn about ratios, rates, and proportions - comparing numbers and measures, simplifying ratios, finding unit rates, and making cost comparisons. Dive into examples and visual explanations to enhance your understanding of these mathematical concepts.

• Mathematics
• Ratios
• Rates
• Proportions
• Unit Rates
• Simplifying Ratios

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1. Ratios, Rates, Proportions A _______ is a comparison of _______ numbers and measures using ______________. A ratio can be written ______ different ways. 1. ______ to _____ 2. a ____ b 3. ? Ratios do ________ have units! Ratios are often expressed as fractions in the ____________ form. 5 20=

2. To simplify ratio: 1. Write in ___________form. 2. Find greatest _________ factor (GCF) List factors of a and b Find GCF ______ a and b by _______ Write in simplest form Example 16 28 16:28 16= 1,__, __, 8,16 28=___,2,___7,14,28 16 28 =

3. Examples 8 GCF: 8= GCF: 24= 24= 40 200 27 9

4. Examples 8 24=1 GCF: 8=1,2,4,8 GCF: 24=1,2,3,4,7,8,12,24 3 40 200 =1 5 3 1 27 9 6 25

5. Rates A _________ is a ratio that ___________ two quantities with ______________ units. A rate is written as a ______________(fraction) in simplest form. Rates _______ units. A ____________ rate is which the denominator number is 1 The __ in the denominator is _____________and often the word per is used to make the comparison ex: miles per hour -- mph miles per gallon -> mpg To find: Find the unit rate, you would find the ______ or _______ for 1 Examples If it costs $78 for 13 sandwiches. $78/13= $6 or $6 per 1 sandwich

6. The cost of a 12-ounce box of Cheerios is $3.29. Publix brand Cheerios cost $4.89 for an 18 ounce box. Find the unit rate to find the better buy. 3.29/____= .274 _____/18=.271 It takes 11 gallons to drive 250 miles. What is the unit rate or m.p.g.?

7. Ratios, Rates, Proportions A ratio is a comparison of two numbers and measures using division. A ratio can be written 3 different ways. 1. A to B 2. a _:_ b 3. ? ? Ratios do not have units! Ratios are often expressed as fractions in the simplest form. 5 20=

8. To simplify ratio: 1. Write in simplest form. 2. Find greatest common factor (GCF) List factors of a and b Find GCF Divide A and B by GCF Write in simplest form Example 16 28 16:28 16= 1,2 , 4, 8,16 28=1 ,2,4, 7,14,28 4 7 16 28 4/4 =

9. Rates A rate is a ratio that compares two quantities with different units. A rate is written as a quotient (fraction) in simplest form. Rates have units. A unit rate is which the denominator number is 1 The _1_ in the denominator is dropped and often the word per is used to make the comparison ex: miles per hour -- mph miles per gallon -> mpg To find: Find the unit rate, you would find the cost or amount for 1. Examples If it costs $78 for 13 sandwiches. $78/13= $6 or $6 per 1 sandwich

10. The cost of a 12-ounce box of Cheerios is $3.29. Publix brand Cheerios cost $4.89 for an 18 ounce box. Find the unit rate to find the better buy. 3.29/12= .274 4.89/18=.271 It takes 11 gallons to drive 250 miles. What is the unit rate or m.p.g.? 250/11=22.72 mpg