reteach - st. brigid-st. frances cabrini catholic academy...you are in charge of making punch for an...

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Course 1 • Ratios and Rates

ReteachRatios

Refer to the diagram at the right.

Write the ratio in simplest form that compares the number of circles to the number of triangles.

4 − 5 The GCF of 4 and 5 is 1.

So, the ratio of circles to triangles is 4 − 5 , 4 to 5, or 4:5.

For every 4 circles, there are 5 triangles.

Write the ratio in simplest form that compares the number of circles to the total number of figures.

4 − 10

= 2 − 5 The GCF of 4 and 10 is 2.

The ratio of circles to the total number of figures is 2 − 5 , 2 to 5, or 2:5.

For every two circles, there are five total figures.

Divide 24 roses into two groups so the ratio is 3 to 5.

Use a bar diagram. Show a group of 3 24 rosesand a group of 5.

Because there are 8 sections, each section 24 roses

3 3 3

3 3 3 3 3represents 24 ÷ 8, or 3 roses.

There are 9 roses in the first group and 15 roses in the second group.

Exercises

Write each ratio as a fraction in simplest form. Then explain its meaning.

1. 2 guppies to 6 seahorses

2. 12 puppies to 15 kittens

3. SPELLING A sentence has 5 misspelled words and 15 correctly spelled words. Find the ratio of misspelled words to correctly spelled words.

A ratio is a comparison of two numbers by division. A common way to express a ratio is as a fraction in simplest form. Ratios can also be written in other ways. For example, the ratio 2 −

3 can be written as

2 to 3, 2 out of 3, or 2:3.

Examples

circles triangles

circles total figures

→→

÷2

÷2

→→

Example 3

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Name Class Date

ffimftHos amd Ratesffiornrng fiSeeperEssential question: How do youfi,nd equiualent ratios and unit rates?

A ratio is a comparison of two numbers by division. The twonumbers in a ratio are called terms. A ratio can be written inseveral different ways:5 dogs to 3 cats 5 to 3 5:3

X A lVl P L E'.,Writing Ratios

The party mlr recipe requires cup(s) of pretzels andcup(s) of bagel chips. Write the ratio of pretzels to bagel

chips in three different ways.

The recipe makes a total of -_-.r0, o, Ourty mix. Write the

ratio of pretzels to total party mix in three different ways.

5

Party MixMakes 8 cups4 cups pretzels2 cups bagel chips1 cup cheese crackers1 cup peanuts

EXATUPLE

Tttv T1!t5!

Write each ratio in three different ways.

1a. bagel chips to peanurs

1b. total party mix to pretzels

1c. cheese crackers to Deanuts

ffiFFIFCT

1d. \.A/hat does it mean when the terms in a ratio are equal?

1e. The ratio of floor seats to balcony seats in a theater is 20:1"have more floor seats or more balcony seats? How do you

Does this theaterknow?

1f. At another theater, the ratio of floor seats to balcony seats is 20:19, How do thenumber of floor seats and the number of balcony seats compare at this theater?

Chapter 7 283 Lesson 1

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For Exercises 1–10, write each ratio as a fraction in simplest form. Then explain its meaning.

1. 3 sailboats to 6 fan boats 2. 4 tulips to 6 daffodils

3. 5 ducks to 30 geese 4. 5 baseballs to 25 softballs

5. 6 poodles to 18 beagles 6. 10 brown eggs to 12 white eggs

7. WALLPAPER The design on Santana’s wall includes 16 pink stripes and 20 green stripes. Find the ratio of pink stripes to green stripes.

8. JAZZ BAND In the jazz band at Wyatt’s school, there are 15 trumpets and 9 trombones. Find the ratio of trombones to trumpets.

9. WILDLIFE PARK At a wildlife park, Zoey counted 10 lions and 14 tigers. What is the ratio of lions to tigers?

10. MAILBOX In one week, Latrina received 18 letters and 8 bills. What was the ratio of bills to letters?

11. GYM CLASS Mr. Riley allowed a class of sixth graders to Gym Class ActivitiesActivity StudentsVolleyball 12Softball 21Soccer 3

choose an activity for their gym class. What is the ratio of students playing volleyball to the total number of students? Write the ratio as a fraction in simplest form. Then explain its meaning.

12. FRUIT SALAD In a fruit salad, there are 12 strawberries, 14 grapes, 6 kiwis, and 4 papayas. Find the ratio of kiwis to the total number of pieces of fruit in the fruit salad. Write the ratio as a fraction in simplest form. Then explain its meaning.

Skills PracticeRatios


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1. FRUITS Find the ratio of bananas to oranges in the graphic at the right. Write the ratio as a fraction in simplest form. Then explain its meaning.

2. MODEL TRAINS Hiroshi has 4 engines and 18 box cars. Find the ratio of engines to box cars. Write the ratio as a fraction in simplest form. Then explain its meaning.

ANALYZE TABLES For Exercises 3 and 4, refer Animals Found in a Tide PoolAnimal Number

Anemones 11Limpets 14Snails 18Starfish 9

to the table showing tide pool animals. Write each ratio in simplest form.

3. Find the ratio of limpets to snails. Then explain its meaning.

4. Find the ratio of snails to the total number of animals. Then explain its meaning.

5. ZOOS A petting zoo has 5 lambs, 11 rabbits, 4 goats, and 4 piglets. Find the ratio of goats to the total number of animals. Write the ratio in simplest form. Then explain its meaning.

6. FOOD At the potluck, there were 6 pecan pies, 7 lemon pies, 13 cherry pies, and 8 apple pies. Find the ratio of apple pies to the total number of pies. Write each ratio in simplest form. Then explain its meaning.

7. BAKERY Rolls are being prepared to go to grocery stores. Divide 72 rolls into 2 groups so the ratio is 3 to 5.

8. LAUNDRY A basket of laundry is being separated. Divide 48 pieces of clothing into 2 groups so the ratio is 1 to 3.

Homework PracticeRatios

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Two ratios are said to be equivalent ratios if they have the same unit rate.

ReteachEquivalent Ratios

Determine if each pair of rates are equivalent. Explain your reasoning.

$35 for 7 balls of yarn; $24 for 4 balls of yarn.

Write each rate as a fraction. Then find its unit rate.

$35 −

7 balls of yarn = $5

− 1 ball of yarn

$24 −

4 balls of yarn = $6

− 1 ball of yarn

Since the rates do not share the same unit rate, they are not equivalent.

Determine if each pair of ratios are equivalent. Explain your reasoning.

8 boys out of 24 students; 4 boys out of 12 students

Write each ratio as a fraction.

8 boys −

24 students =

4 boys −

12 students The numerator and the denominator are divided by the same number.

Since the fractions are equivalent, the ratios are equivalent.

Exercises

Determine if each pair of ratios or rates are equivalent. Explain your reasoning.

1. $12 saved after 2 weeks; $36 saved after 6 weeks

2. $9 for 3 magazines; $20 for 5 magazines

3. 135 miles driven in 3 hours; 225 miles driven in 5 hours

4. 24 computers for 30 students; 48 computers for 70 students

Example 1

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You are in charge of making punch for an upcoming schoor dance.The punch recipe makes 5 cups of punch by mixing 3 cups of cranberryjuice with 2 cups of apple juice.

EXPLORE, EquivalentRatios

A \A/hat is the ratio of cranberry juice to apple juice?

Do you think the punch will taste more like cranberry iuice or more like applejuice? Explain.

You must increase the recipe to serve a large number of people. Fill in the boxesto find the ratio of cranberry iuice to apple juice when the recipe is cloubledand tripled.

$r il -\;-

)i x'tTo double the recipe, you need --- cups of cranberry iuice ancl --_ cupsof apple juice" This makes a totalof --- cups of punch.

To triple the recipe, you need cups of cranberry juice and _---- cupsof apple juice. This makes a total of

-- cups of punch.

The ratios you found in B are equivalent to ]. Eina three other rariosthat are equivalent to j,

How much of each juice would you need to make a total of 40 cups ofpunch?

TRY THIS!$omplete each pair of equivalent ratios.

1/12a. 3 2b. +: u

Find

2d.

three

6

ratios equivalent to the given ratio.

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2c. T=

2f. +36

Chapter 7 284 Lesson 1

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Skills PracticeEquivalent Ratios


1. $18 for 3 bracelets; $30 for 5 bracelets

2. 120 Calories in 2 servings; 360 Calories in 6 servings

3. 4 hours worked for $12; 7 hours worked for $28

4. 15 blank CDs for $5; 45 blank CDs for $15

5. 24 points scored in 4 games; 48 points scored in 10 games

6. 15 out of 20 students own hand-held games; 105 out of 160 students own

hand-held games.

7. 30 minutes to jog 3 miles; 50 minutes to jog 5 miles

8. $3 for 6 muffins; $9 for 18 muffins

9. 360 miles driven on 12 gallons of fuel; 270 miles driven on 9 gallons of fuel

10. SHOPPING Miguel bought 2 pairs of jeans for $50, and Han bought 4 pairs of jeans for $90. Did they pay the same rate? Explain your reasoning.


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Homework Practice Equivalent Ratios


1. 18 vocabulary words learned in 2 hours; 27 vocabulary words learned in 3 hours

2. $15 for 5 pairs of socks; $25 for 10 pairs of socks

3. 20 out of 45 students attended the concert; 12 out of 25 students

attended the concert

4. 78 correct answers out of 100 test questions; 39 correct answers out of 50 test questions

5. 15 minutes to drive 21 miles; 25 minutes to drive 35 miles

ANIMALS For Exercises 6–8, refer to the table on lengths of some animals with long tails. Determine if each pair of animals has the same ratio of body length to tail length. Explain your reasoning.

6. brown rat and opossum

7. hamster and lemming

8. opossum and prairie dog

Animal Lengths (mm)Animal Head & Body Tail

Brown Rat 240 180Hamster 250 50Lemming 125 25Opossum 480 360Prairie Dog 280 40

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