Unit Ratios with Fractions

Unit Ratios with Fractions

by Kellany Bennett

​Ratios

• ​This comparison is based on division or multiplication

​Equivalent Ratios

• ​Think like equivalent fractions

• ​Super helpful in problem solving

• ​Why? Because a special equivalent ratio is called a unit ratio!

Multiple Choice

The 1st term of a ratio is 25 and its second is 20. The simplest form of that ratio is:

• 5 : 4

• 5 : 3

• 6 : 4

• 2 : 1

Multiple Choice

Look at the picture above. A and B are:

• 52 5and 28

• 54 and 28

• 54 and 24

• 28 and 24

Multiple Select

Find two equivalent ratios for 3 : 4 using multiplication

• 6 : 8

• 6 : 12

• 9 : 12

Multiple Select

Find two equivalent ratios for 12 : 18 using division

• 6 : 6

• 6 : 9

• 4 : 6

​Unit Rates (AKA Unit Ratios)

A Unit Ratio always has the second unit as one, or the "denominator"

• ​24 pencils per every $1.20 is a RATE

• ​$0.05 per pencil is a UNIT RATE

  • ​sometimes they won't write the 1

Multiple Choice

• 1

• 3

Multiple Choice

• 4

• 12

Multiple Choice

Solve the proportion:

• 15

• 5

• 10

• 12

Multiple Choice

Solve for x 

• x = 16

• x = 28

• x = 1/26

• x = 26

Multiple Choice

Enter the missing numbers to create equivalent ratios.  1 : 3 6 : 18 2 : _ 4 : _

• 4 & 8

• 4 & 12

• 6 & 12

• 6 & 8

​Complex Fractions and Complex Ratios

• ​Of course, it can't all be whole numbers and decimals! Eventually, there have to be some fractions!!

• ​If one or both parts of the ratio contain a fraction, it's a complex ratio

• ​You will still look for multiplicative or division-based relationships!

  • ​In the bottom picture, see how they divide the 2 hours by 2 to get 1 hour, and do the same to 5 ²/₃

​Solving Ratio Problems--Yes, Watch the Video!

​You need to create a proportion, or a ratio box (table). Here's another explanation of solving these, slightly different from mine! Maybe it will help.

​Quickest Possible Route

1. Choose a unit to be tops and a unit to be bottoms

2. ​Fill in the numbers you know

3. ​To get the answer, look at the row that becomes a 1

4. ​Multiply the number by its reciprocal (flipped version)

5. ​Multiply the other row by the SAME number

6. ​Remember that you get the multiplication from the row you KNOW, not the "answer" row.

Multiple Choice

You spend $40 on 5 pounds of concrete. What is the unit rate in dollars per pound?

• $8 per pound

• $5 per pound

• $35 per pound

• 0.125 pounds per dollar

Multiple Choice

If Justin can type 408 words in 4 minutes, how many words can he type per minute?

• 102 words per minute

• 100 words per minute

• 400 words per minute

• 412 words per minute

Multiple Choice

Alycia earned $20.40 in 3 hours. What is her unit rate in dollars per hour?

• $7 per hour

• $6 per hour

• $6.80 per hour

• $17.40 per hour

Multiple Choice

Your favorite restaurant sells 15 wings for $17.99. What is the cost per wing?

• $1.1

• $1.20

• $1.75

• $1.19

Multiple Select

A store had 2 blue chairs for $22.78 or 6 red chairs for $67.80. Which color chair has the lower unit price?

• 2 blue chairs for $22.78

• 6 red chairs for $67.80

Multiple Choice

If a dog can eat $$\frac{1}{3}$$  of a bag of food in $$\frac{1}{2}$$   week, how many bags of food can the dog eat in 1 week?

• $$\frac{1}{6}$$  

• $$\frac{2}{3}$$  

• $$1\frac{1}{2}$$  

• $$\frac{5}{6}$$  

Multiple Choice

Mr. Rogers needs fertilizer for his 1-acre garden.  The package suggests $$\frac{1}{2}$$   pound of fertilizer for $$\frac{1}{45}$$   of an acre.  How many pounds of fertilizer does Mr. Rogers need for his entire garden?

• $$11\frac{1}{4}$$  lb

• $$22\frac{1}{2}$$  lb

• 45 lb

• 90 lb

Multiple Choice

Over a $$3\frac{1}{2}$$   year period, $$27\frac{1}{2}$$   inches of snow fell in Jackson City.  What was the average yearly snowfall in Jackson City?

• 31 inches per year

• 24 inches per year

• $$9\frac{1}{4}$$   inches per year

• $$7\frac{6}{7}$$  inches per year

Multiple Choice

Sasha can mow $$\frac{3}{8}$$   of an acre of grass in $$\frac{3}{4}$$   an hour. How many acres of grass does Sasha mow per hour?

• $$\frac{2\ acres}{1\ hour}$$  

• $$\frac{\frac{1}{2}acre}{1\ hour}$$  

• $$\frac{\frac{9}{24}acres}{1\ hour}$$  

• $$\frac{1\frac{2}{3}acres}{1\ hour}$$  

Multiple Choice

A novelist can write $$2\frac{1}{4}$$   pages in $$\frac{3}{5}$$   of an hour. What is her speed in pages per hour?

• $$\frac{4}{15}$$  pages per hour

• $$\frac{15}{4}$$ pages per hour

• $$\frac{20}{27}$$  pages per hour

• $$\frac{27}{20}$$ pages per hour

Multiple Select

While exercising Loghan walked $$\frac{1}{8}$$   of a mile in $$\frac{1}{6}$$  of an hour. At this rate,how far will he have traveled after an hour?

• $$\frac{1}{48}$$   of a mile

• $$\frac{3}{4}$$   of a mile

• 1 mile

• $$\frac{6}{8}$$  of a mile

​ALWAYS WORKS (but sometimes not necessary)

​While most of us would easily see the relationship divide by 5...

10/5 = 2 so...

​13/5 = 2.6

​

​But you also have cross products as a method, or means and extremes. Set the products of the diagonals (means and extremes) as equal and solve.

​Divide both sides by 10

​2.6 = x

​Solving Ratio Problems--Yes, Watch the Video!

This guy really goes step by step. Check out his video on problem solving by taking a detour at the unit rate!

​12.5 / 50 = 0.25, then 0.25 * 36 = 9 problems

Multiple Choice

A 6-ounce package of fruit snacks contains 45 pieces. How many pieces would you expect in a 10-ounce package?

• 75 Pieces

• 27-ounces

• 27 pieces

• 75-ounces

Multiple Choice

The waiting time to ride a roller coaster is 20 minutes when 150 people are in line. How long is the waiting time when 240 people are in line?

• 32 People

• 32 Min.

• 12.5 Min.

• 12.5 People

Multiple Choice

A grading machine can grade 48 multiple-choice tests in 1 minute. How long will it take the machine to grade 300 tests?

• 6.25 Min

• 0.16 Tests

• 6.25 Tests

• 0.16 Min

Multiple Choice

Hamburger sells for 3 pounds for $6. If Alicia buys 10 pounds of hamburger, how much will she pay?

• $30

• $20

• $60

• $10

Multiple Choice

On his last math test, Brandon completed $$12\frac{1}{2}$$  math problems in 50 minutes. If he kept a constant rate, how many minutes would it take him to complete 8 problems?

• 28 minutes

• $$14\frac{1}{2}$$  minutes

• 16 minutes

• 32 minutes