
Unit Ratios with Fractions
Presentation
•
Mathematics
•
7th Grade
•
Medium
+9
Standards-aligned
Kellany Bennett
Used 5+ times
FREE Resource
15 Slides • 25 Questions
1
Unit Ratios with Fractions
by Kellany Bennett
2
Ratios
This comparison is based on division or multiplication
3
Equivalent Ratios
Think like equivalent fractions
Super helpful in problem solving
Why? Because a special equivalent ratio is called a unit ratio!
4
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
5
Multiple Choice
Look at the picture above. A and B are:
52 5and 28
54 and 28
54 and 24
28 and 24
6
Multiple Select
Find two equivalent ratios for 3 : 4 using multiplication
6 : 8
6 : 12
9 : 12
7
Multiple Select
Find two equivalent ratios for 12 : 18 using division
6 : 6
6 : 9
4 : 6
8
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
9
Multiple Choice
1
3
10
Multiple Choice
4
12
11
Multiple Choice
Solve the proportion:
15
5
10
12
12
Multiple Choice
Solve for x
x = 16
x = 28
x = 1/26
x = 26
13
Multiple Choice
Enter the missing numbers to create equivalent ratios. 1 : 3 6 : 18 2 : _ 4 : _
4 & 8
4 & 12
6 & 12
6 & 8
14
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
15
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.
16
Quickest Possible Route
Choose a unit to be tops and a unit to be bottoms
Fill in the numbers you know
To get the answer, look at the row that becomes a 1
Multiply the number by its reciprocal (flipped version)
Multiply the other row by the SAME number
Remember that you get the multiplication from the row you KNOW, not the "answer" row.
17
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
18
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
19
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
20
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
21
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
22
23
24
25
26
Multiple Choice
If a dog can eat 31 of a bag of food in 21 week, how many bags of food can the dog eat in 1 week?
61
32
121
65
27
Multiple Choice
Mr. Rogers needs fertilizer for his 1-acre garden. The package suggests 21 pound of fertilizer for 451 of an acre. How many pounds of fertilizer does Mr. Rogers need for his entire garden?
1141 lb
2221 lb
45 lb
90 lb
28
Multiple Choice
Over a 321 year period, 2721 inches of snow fell in Jackson City. What was the average yearly snowfall in Jackson City?
31 inches per year
24 inches per year
941 inches per year
776 inches per year
29
Multiple Choice
Sasha can mow 83 of an acre of grass in 43 an hour. How many acres of grass does Sasha mow per hour?
1 hour2 acres
1 hour21acre
1 hour249acres
1 hour132acres
30
Multiple Choice
A novelist can write 241 pages in 53 of an hour. What is her speed in pages per hour?
154 pages per hour
415 pages per hour
2720 pages per hour
2027 pages per hour
31
Multiple Select
While exercising Loghan walked 81 of a mile in 61 of an hour. At this rate,how far will he have traveled after an hour?
481 of a mile
43 of a mile
1 mile
86 of a mile
32
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
33
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!
34
35
12.5 / 50 = 0.25, then 0.25 * 36 = 9 problems
36
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
37
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
38
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
39
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
40
Multiple Choice
On his last math test, Brandon completed 1221 math problems in 50 minutes. If he kept a constant rate, how many minutes would it take him to complete 8 problems?
28 minutes
1421 minutes
16 minutes
32 minutes
Unit Ratios with Fractions
by Kellany Bennett
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