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 minutes 3 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 burger 15 hamburgers 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, times x = 15x

$75 times 20 = 1, times x = 15x 1,500 = 15x Divide 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.