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4-1 Ratios
Warm UpWarm Up
Lesson PresentationLesson Presentation
Problem of the DayProblem of the Day
Lesson QuizzesLesson Quizzes
4-1 Ratios
Warm UpWrite each fraction in simplest terms.
1.
3640
3.
5. 1580
2. 2135
4. 4290
6. 5684
23
35
23
910
715
316
812
4-1 Ratios
Problem of the Day
If June 1 falls on a Tuesday, on which day of the week does September 1 fall?
Wednesday
4-1 Ratios
Prep for MA.7.A.1.1 Distinguish between situations that are proportional or not proportional and use proportions to solve problems.Review of MA.6.A.2.2
Sunshine State Standards
4-1 Ratios
Vocabulary
ratio
4-1 Ratios
In basketball practice. Kathlene made 17 baskets in 25 attempts. She compared the number of baskets she made to the total number of attempts she made by using the
ratio . A ratio is a comparison of two
quantities by division.
1725
Kathlene can write her ratio of baskets madeto attempts in three different ways.
1725
17 to 25 17:25
4-1 Ratios
Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.
Additional Example 1: Writing Ratios
A. rock to hip hop
57
, 5 to 7, 5:7
The ratio of rock to hip hop is 5 to 7, which can be written as follows:
B. hip hop to popThe ratio of hip hop to pop is 7 to 8, which can be written as follows:78
, 7 to 8, 7:8
4-1 Ratios
Twenty students are asked to choose their favorite music category. Eight chose pop, seven chose hip hop, and five chose rock. Write each ratio in all three forms.
Additional Example 1: Writing Ratios
C. rock to pop and hip hop
The ratio of rock to pop is 5 to 8 and rock to hip hop is 5 to 7, which can be written as follows:
515
, 5 to 15, 5:15
4-1 Ratios
Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.
Check It Out: Example 1
A. snow boarding to rock climbing
69
, 6 to 9, 6:9
The ratio of snow boarding to rock climbing is 6 to 9, which can be written as follows:
B. kite surfing to snow boardingThe ratio of kite surfing to snow boarding is 4 to 6, which can be written as follows:46
, 4 to 6, 4:6
4-1 Ratios
Check It Out: Example 1
C. rock climbing to kite surfing and snowboarding
The ratio of rock climbing to kite surfing is 9 to 4 and rock climbing to snow boarding is 9 to 6, which can be written as follows:
910
, 9 to 10, 9:10
Nineteen students are asked to choose their favorite sport. Nine chose rock climbing, four chose kite surfing, and six chose snow boarding. Write each ratio in all three forms.
4-1 Ratios
Sometimes a ratio can be simplified. To simplify a ratio, first write it in fraction form and then simplify the fraction.
4-1 Ratios
A fraction is in simplest form when the GCF of the numerator and denominator is 1.
Remember!
4-1 Ratios
On average, most people can read about 600 words in 3 minutes. Write the ratio of words to minutes in all three forms. Write your answer in simplest form.
Additional Example 2: Writing Ratios in Simplest Form
wordsminute
Write the ratio as a fraction.
600 ÷ 33 ÷ 3
= 6003
Simplify.
For every minute, there are 200 words read.
wordsminute
=
wordsminute
= 2001
The ratio of words to minutes is 200 to 1.
4-1 Ratios
At Casitas Middle School there are 456 microscopes for 152 students. Write the ratio of microscopes to students in all three forms. Write your answer in simplest form.
Check It Out: Example 2
microscopesstudents
Write the ratio as a fraction.
456 ÷ 152152 ÷ 152
= 456152
Simplify.
For every microscope, there are 3 children.
microscopestudents
=
microscopestudents
= 31
The ratio of microscopes to students is 3 to 1.
4-1 Ratios
To compare ratios, write them as fractions with common denominators. Then compare the numerators.
4-1 Ratios
Honey lemon cough drops come in packages of 30 drops per 10-ounce bag. Cherry cough drops come in packages of 24 drops per 6-ounce bag. Tell which package has the greater ratio of drops to ounces.
Additional Example 3: Comparing Ratios
610Ounces
2430Drops
CherryHoney lemon
Honey lemon: dropsounces
= 3010
= 31
Cherry: dropsounces
= 246
= 41
Because 4 > 3 and the denominators are the same, the drops to ounces is greater in the bag of cherry cough drops.
Write the ratios as fractions with common denominators.
4-1 Ratios
Jelly beans come in small packages of 25 per 5 ounce package and large packages of 56 per 8 ounce package. Tell which package has the greater ratio of jelly beans to ounces.
Check It Out: Example 3
58Ounces
2556Jelly beans
SmallLarge
Large:jelly beans ounces
= 568
= 71
Small: jelly beans ounces
= 255
= 51
Because 7 > 5 and the denominators are the same, jelly beans to ounces is greater in the small package.
Write the ratios as fractions with common denominators.
4-1 Ratios
Standard Lesson Quiz
Lesson Quizzes
Lesson Quiz for Student Response Systems
4-1 Ratios
Lesson Quiz: Part I
A coin bank contains 16 quarters, 12 dimes, and 8 nickels. Write the given ratio in all three forms.
1. nickels to quarters
2. dimes to nickels
3. nickels and dimes to quarters
816
, 8 to 16, 8:16 or 12
, 1 to 2, 1:2
128
, 12 to 8, 12:8 or 32
, 3 to 2, 3:2
2016
, 20 to 16, 20:16 or 54
, 5 to 4, 5:4
4-1 Ratios
Lesson Quiz: Part II
4. There are 220 calories in 5 crackers. Write the ratio of calories to crackers in all three forms. Write your answers in simplest form.
5. On a school trip, bus 1 has 3 teachers and 14 students. Bus 2 has 4 teachers and 28 students. Which bus has the greater ratio of teachers to students?
bus 1
44 calories 1 cracker
, 44 to 1, 44:1
4-1 Ratios
1. A box contains 18 violet tops, 15 red tops, and 6 white tops. Identify the ratio of white tops to violet tops in all three forms.
A. , 6 to 18, 6:18 or , 1 to 3, 1:3
B. , 6 to 15, 6:15 or , 2 to 5, 2:5
C. , 6 to 18, 6:18 or , 2 to 5, 2:5
Lesson Quiz for Student Response Systems
6 18
1 3
6 15
2 5
6 18
2 5
4-1 Ratios
2. A box contains 15 black pens, 12 blue pens, and 9 white pens. Identify the ratio of black pens to white pens in all three forms.
A. , 12 to 9, 12:9 or , 4 to 3, 4:3
B. , 15 to 9, 15:9 or , 5 to 3, 5:3
C. , 12 to 9, 12:9 or , 5 to 3, 5:3
Lesson Quiz for Student Response Systems
12 9
4 3
15 9
5 3
12 9
5 3
4-1 Ratios
3. In a book shelf, there are 20 math books, 14 science books, and 2 history books. Identify the ratio of history books and science books to math books in all three forms.
A. , 16 to 20, 16:20 or , 7 to 10, 7:10
B. , 14 to 20, 14:20 or , 4 to 5, 4:5
C. , 16 to 20, 16:20 or , 4 to 5, 4:5
Lesson Quiz for Student Response Systems
16
20
7 10
14
20
4 5
16
20
4 5
4-1 Ratios
4. In a school, there are 350 students in 5 classes. Identify the ratio of students to classes in all three forms. Write your answers in simplest form.
A. , 70 to 1, 70:1 C. , 70 to 4, 70:4
B. , 4 to 70, 4:70 D. , 1 to 70, 1:70
Lesson Quiz for Student Response Systems
70 1
70 4
70 4
70 1
4-1 Ratios
5. In Family 1, there are 6 adults and 14 children. Which of the following families will have a greater ratio of adults to children than Family 1?
A. Family 2: 9 adults and 19 children
B. Family 3: 3 adults and 10 children
C. Family 4: 4 adults and 12 children
D. Family 5: 7 adults and 18 children
Lesson Quiz for Student Response Systems