Mathematics
Grade 7
15 min
Unit rates
Unit rates
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1
Introduction & Learning Objectives
Learning Objectives
Define and identify ratios, rates, and unit rates.
Calculate unit rates from given rates or ratios.
Compare different rates by converting them to unit rates.
Solve real-world problems involving unit rates.
Use unit rates to make informed decisions, such as comparing prices.
Explain the importance of units when working with rates.
Ever wonder which brand of cereal is the best deal at the grocery store, or who types faster? 🛒 Unit rates are your secret weapon for making smart comparisons!
In this lesson, you'll discover what unit rates are, how to calculate them, and why they are incredibly useful for comparing quantities and making informed choices in your daily life. We'll learn to simplify rates to understand 'how much per one' of s...
2
Key Concepts & Vocabulary
TermDefinitionExample
RatioA comparison of two quantities using division. It can be written as a fraction, with a colon, or with the word 'to'.The ratio of 3 red apples to 2 green apples is 3:2 or 3/2.
RateA ratio that compares two quantities measured in different units.Driving 120 miles in 2 hours is a rate.
UnitA single, individual quantity or item used as a standard of measurement.In 'miles per hour', 'hour' is a unit of time.
Unit RateA rate where the second quantity (denominator) is 1 unit. It tells you 'how much per one' of something.If you drive 60 miles in 1 hour, your unit rate (speed) is 60 miles per hour.
NumeratorThe top number in a fraction or ratio, representing the first quantity being compared.In the rate 120 miles / 2 hours, 120 mil...
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Core Formulas
Calculating Unit Rate
$ ext{Unit Rate} = \frac{ ext{Quantity 1}}{ ext{Quantity 2}}$
To find a unit rate, divide the first quantity by the second quantity. The goal is to make the denominator equal to 1 unit. The units of Quantity 1 will be 'per' the unit of Quantity 2.
Using Unit Rate to Find Total
$ ext{Total Quantity} = ext{Unit Rate} \times ext{Number of Units}$
Once you know the unit rate, you can use it to find a total amount for a different number of units. For example, if you know the cost per apple, you can find the total cost for any number of apples.
5 more steps in this tutorial
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Challenging
Maya reads at a rate of 2 pages per minute. David reads 600 words in 3 minutes. If one page contains an average of 250 words, who reads faster in terms of 'words per minute'?
A.Maya reads faster.
B.David reads faster.
C.They read at the same speed.
D.There is not enough information to compare.
Challenging
A cell phone plan costs $30 per month, which includes 2 gigabytes (GB) of data. For any data used over 2 GB, the company charges a rate of $10 per gigabyte. What is the total cost for a month where 4.5 gigabytes of data are used?
A.$45.00
B.$75.00
C.$55.00
D.$45.50
Challenging
A painter uses 2 gallons of paint to cover 900 square feet. The paint costs $35 per gallon. What is the painter's cost of paint per square foot?
A.Approximately $0.078 per square foot
B.Approximately $0.022 per square foot
C.$12.86 per square foot
D.$450 per square foot
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