Practice

with Unit Rates

What is a unit rate?

A unit rate tells the price of one item.

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 = ??

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!

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?

Johnny bought $75 on 15 hamburgers. At this rate, how much does 1 hamburger

cost?

1. Solve the problem above. Show your work.

+ = $75 = ?????

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.

If each hamburger costs $5, how much do 15 hamburgers cost? What are some different ways

you can find out?

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.

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.

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

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?

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?

But…..sometimes you have to do more than just divide

to find an answer.

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…..

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.

We know that if Johnny paid $75 for 15 hamburgers each hamburger costs $5. So how

much would 20 burgers cost?

$75______ = $100____ 15 burgers 20 burgers

Where did the $100 come from?

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.

$75__________ = $5 per burger15 hamburgers

If we want to know how much 20 burgers would cost, what should we multiply?

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

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

$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 =

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

The end.