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Practice
with Unit Rates
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What is a unit rate?
A unit rate tells the price of one item.
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Johnny bought $75 on 15 hamburgers. At this rate, how much does 1 hamburger cost?
Would it make sense for 1 hamburger to cost $75? Why? (*Hint- do not just say $75 is too much for a hamburger. )
+ = $75 = ??
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Johnny bought $75 on 15 hamburgers. At this rate, how much does 1 hamburger
cost?
Why wouldn’t it make sense for 1 hamburger to cost $1?
=$75 = 1?? NOOO!
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Johnny bought $75 on 15 hamburgers. At this rate, how much does 1 hamburger
cost?
Should you add, subtract, multiply, or divide to solve the problem in yellow? WHY?
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Johnny bought $75 on 15 hamburgers. At this rate, how much does 1 hamburger
cost?
1. Solve the problem above. Show your work.
+ = $75 = ?????
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The answer…
$75 ÷ 15 = $5 per every 1 hamburger
That means we took all over our money ($75) and split it evenly. Each hamburger was $5.
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If each hamburger costs $5, how much do 15 hamburgers cost? What are some different ways
you can find out?
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It takes Mary 12 minutes to play 3 songs on her piano. How many
minutes long is 1 song?
2. Solve the problem in yellow. Show your work.
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The answer….
12 ÷ 3 = 4 minutes per every song
That means we took all over the minutes she played (12 minutes) and split it evenly. Each song was 4 minutes.
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So far you have found unit rates.
A Unit Rate is the ratio of two measurements in which the second term is 1.
$5_____ 4 minutes 1 burger 1 song
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This is what we were actually solving….
$75______ = $5___15 burgers 1 burger
How did we get from 15 to 1 on the bottom?What did we divide by?How did we get from $75 to $5 on the top?What did we divide by?
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This is actually what we were solving….
12 minutes = 4 minutes3 songs 1 song
How did we get from 3 to 1 on the bottom?What did we divide by?How did we get from $12 to $4 on the top?What did we divide by?
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But…..sometimes you have to do more than just divide
to find an answer.
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For example…..
Johnny bought $75 on 15 hamburgers. At this rate, how much does 20 hamburgers cost?
- Just dividing will not work. - Let’s find out why…..
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Soooo…..
$75__________ = ___x_________ 15 hamburgers 20 hamburgers
Look at the ratios above. The x means that we do not know what number goes there yet. Remember you have to multiply or divide to find equivalent ratios. So, I cannot add 5 on the bottom and add 5 on the top. I have to multiply or divide.
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We know that if Johnny paid $75 for 15 hamburgers each hamburger costs $5. So how
much would 20 burgers cost?
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$75______ = $100____ 15 burgers 20 burgers
Where did the $100 come from?
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Now, let’s find out how to solve a proportion without pictures.
$75______ = __x_____15 burgers 20 burgers
The x means we are trying to find out what number goes there. We already know that $100 goes there. Let’s solve this proportion without pictures.
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$75__________ = $5 per burger15 hamburgers
If we want to know how much 20 burgers would cost, what should we multiply?
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If we want to know how much 20 burgers would cost, what should we multiply?
We should multiply 20 burgers times $5 per burger which gives us $100 for 20 burgers.$75______ = $100____ 15 burgers 20 burgers
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Cross multiplying is exactly what it sounds like. You multiply the numbers that are across from
each other.$75______ = __x_____15 burgers 20 burgers
$75 times 20 = 1,50015 times x = 15x
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$75 times 20 = 1,50015 times x = 15x1,500 = 15xDivide both sides by the number with the letter beside it.1,500 divided by 15 =15 divided by 15=So, x =
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We still get
$75______ = $100_ 15 burgers 20 burgers
$75____÷ 15 = $5__ 15 burgers ÷15 1 burger
$100____÷20 = $5__20 burgers ÷20 1 burger
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The end.