Understanding Ratios and Unit Rates in Mathematics
Exploring the concepts of ratios, unit rates, and their applications involving rational numbers, fractions, and complex fractions in mathematics. The content covers the basics of writing and simplifying ratios, creating ratios in different forms, and understanding how ratios can be expressed in various ways.
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11.13.2018 Ticket out the Door Ticket in the door Ticket in the door review Introduction Video Lesson of the Day; Unit Rates Unit 3 Vocabulary Quiz on Friday. Ticket in the door n + 2 = -4 + 2n R+2+3 = 4 3m+4m = -14
Introduction Video https://www.youtube.com/watch?v=liW_A Lj4Qj8
Format your papers for Cornell notes Topic: Ratio and Unit Rates E.Q. How Can you Compute Unit Rates involving rational numbers, fractions, and complex fractions?
A ratio is a comparison of two numbers or measures using division. A ratio can be written three ways: 3:5 3/5 3 to 5 BACK BACK
Ratios are often expressed as fractions in simplest or as a decimal. 5 1 = or .25 20 4 BACK BACK
A ratio is the comparison of two numbers with the same units by division. A ratio may be written in three ways. 2 to 2 3 2 : 3 3 What ratios can we form from the tiles above? whole part 12 20 part part whole 12 to 8 20 part 12 BACK BACK
Create as many ratios as possible. Write each ratio three different ways. BACK BACK
Simplest Form Write the ratio 50 to 300 in simplest form. 50 1 = 6 300 BACK BACK
Simplest Form Write the ratio 60 per dozen in simplest form. 60 5 = 1 12 BACK BACK
Look over the ratios you have written. Is there another way that you can write those ratios? The ratio illustrated here is four filled cells to ten total cells. The ratio shown here is twofilled cells to five total cells. What do you know about these two ratios? How can you prove your answer? BACK BACK
UNIT RATES A unit rate is a rate in which the denominator number is 1. The 1 in the denominator is dropped often the word per is used to make the comparison. Ex: miles per hour mph miles per gallon mpg
Unit Rate To find the Unit Rate, you would find the cost or amount for 1. Or the rate when the denominator is 1. How much for just 1? BACK BACK
Unit Rate If it costs $78 for 13 sandwiches, What is the unit rate? = 13 78 $ $ each 6 BACK BACK
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. 29 . 3 274 . = . 4 89 = 271 . 12 18 BACK BACK
Mile per Gallon M.P.G. stands for miles per gallon and is usually used for gas mileage in cars. BACK BACK
Unit Rate If it takes 11 gallons to drive 250 miles, What is the unit rate or m.p.g.? BACK BACK
Solving Word Problems 250 x = Write problem as proportions: 11 1 Solve using cross multiplication. 250(1) = 250= 11X 11X 11 11 X=22.7 mpg BACK BACK
Now you try it! BACK BACK
1. A skydiver falls 144 feet in three seconds. How far does the skydiver fall per second? 2. A pump moves 42 gallons in seven minutes. Find the unit rate. 3. You score 84 points in six games. How much do you score per game? 4. Steve drives 78 miles on 3 gallons of gas. Find the miles per gallon. 5. Maria walks 12 miles in 3 hours. How many miles does she walk per hour?
Reference https://www.msjc.edu/.../Ratio%20Rates%2 0Proportions/14%20PROPORTIONS.ppt https://1.cdn.edl.io/DKFLbKdN2no9i1bybz vJgFk29nXpLnVogNdVhtgeFXeimt3i.pptx https://www.nrcs.net/Downloads/UNIT%20 RATE%20word%20problems.pdf
