Understanding Ratios and Unit Rates in Mathematics
Exploring the concepts of ratios, unit rates, and their applications in real-life scenarios. Examples include comparing pepperoni pizzas to total pizzas ordered, wins to games played in sports, gas mileage calculations, paint coverage for a room, and cost per pound of items. Learn how to interpret and calculate ratios and unit rates effectively.
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Vocabulary A ratio is a comparison of two quantities by division.
Example 1: program, the Youth Center orders 8 pepperoni pizzas out of every 10 pizzas that they order. What is the ratio of pepperoni pizzas to the total number purchased? For lunch during the summer recreation pepperoni pizzas Write a verbal model of what you are comparing. total pizzas 8= 4 Substitute in the values given for each quantity, and simplify the fraction. 10 5
Example 2: wins out of 64 games played. What was the ratio of wins to games played? Last year, Andy s hockey team had a record of 48 games won Write a verbal model of what you are comparing. total played Substitute in the values given for each quantity, and simplify the fraction. 48= 3 64 4
Vocabulary A rate is a special type of ratio comparing two quantities with different kinds of units. Traveling 180 miles on 9 gallons of gas $8.00 for 2 pounds of roast beef A verbal model can help us write rates. A unit rate is a rate that is simplified so that it has a denominator of 1 unit. A unit rate compares a quantity to 1 unit of another quantity. The speed limit on I-86 is 65 miles per hour. NYS minimum wage is currently $7.25 per hour
Example 3: 161 miles on 7 gallons of gas. What was his gas mileage on the trip in miles per gallon? On his trip to Pittsburgh, Alex drove miles Write a verbal model of what you are comparing. gallons 161 miles Substitute in the values given for each quantity. gallons 7 Since a unit rate has a denominator of 1 unit, divide the numerator and denominator by 7. 161 7 miles 23 = 7 7 gallon 1 Alex s car got 23 miles per gallon on his trip.
Example 4: paint covers of her walls, how much paint does she need for her entire room? Lola is painting her room. If gallon of gallons Write a verbal model of what you are comparing. room 1 gallon Substitute in the values given for each quantity. 2 1 room 6 1 6 Divide the numerator and denominator by to find the unit rate. 1 1 gallons 3 2 1 2 6 = = 1 1 1 room 1 Lola will need 3 gallons of paint for her room. 6 6
Sometimes, we are asked to compare unit rates.. Example 5: pounds of fudge and $23.85 for 5 pounds of wrapped candy. Which item costs less per pound? By how much? cost Write a verbal model of what you are comparing. During the holidays, Emily spends $12.50 for 2 pound For the fudge, For the wrapped candy, $12.50 2 $6.25 $23.85 5 $4.77 = = 2 2 pound 1 5 5 pound 1 The wrapped candy costs less by $1.48 per pound. To find the difference in price, subtract. $6.25 $4.77 = $1.48.
Example 6: who tried out for the lacrosse team, 12 were selected and of the forty boys who tried out, 16 were selected. Are the ratios of number of students on the team to number of students trying out the same for both boys and girls? How do you know? selected At Euclid Middle School, of the thirty girls for the team Write a verbal model of what you are comparing. tried out for the team For the girls, 12 For the boys, 16 6 2 8 2 = = 6 30 5 8 40 5 Yes, the ratios are the same. The value of each ratio is the same.
