UNIT 1: Proportional Reasoning with Ratios and Rates
PART 1: INTRO TO RATIOS
1. Basic Ratios
Description:
A ratio compares two quantities. It tells us how much of one thing there is compared to another. Ratios can compare part to part or part to whole.
Explanation (TEKS 6.4C & 6.4D):
Write ratios in three ways:
Using "to" → 3 to 5
Using a colon → 3:5
As a fraction → 3/5
Critical rule: Keep the order exactly as the problem asks.
"Ratio of boys to girls" is different from "ratio of girls to boys"
Example 1:
A class has 8 boys and 12 girls.
Ratio of boys to girls = 8 to 12 = 8:12 = 8/12 (simplifies to 2/3)
Ratio of girls to boys = 12 to 8 = 12:8 = 12/8 (simplifies to 3/2)
Ratio of boys to total students (part to whole) = 8 to 20 = 8:20 = 8/20
Example 2:
A fruit basket has 6 apples and 4 oranges.
Ratio of apples to oranges = 6:4 = 3:2 (simplified)
Ratio of oranges to total fruit = 4:10 = 2:5
Practice Questions (Basic Ratios):
A pet store has 15 dogs and 10 cats. Write the ratio of dogs to cats in simplest form.
A recipe uses 2 cups of flour and 3 cups of sugar. Write the ratio of flour to sugar as a fraction.
In a bag, there are 7 red marbles, 5 blue marbles, and 8 green marbles. What is the ratio of blue marbles to total marbles?
A soccer team scored 12 goals and allowed 8 goals. Write the ratio of goals scored to goals allowed using a colon.
A parking lot has 24 cars and 6 trucks. What is the ratio of trucks to cars in simplest form?
2. Ratios as Fractions and Decimals
Description:
A ratio written as a fraction can also be converted to a decimal. This helps when comparing ratios or working with real-world measurements.
Explanation:
A ratio of a:b means a/b
To convert fraction to decimal: divide numerator by denominator
The decimal represents the relative size of one quantity to another
Example 1:
Ratio of 3:4 as fraction = 3/4
3/4 as decimal = 3 ÷ 4 = 0.75
Example 2:
A class has 5 boys for every 8 students.
Ratio = 5:8
Fraction = 5/8
Decimal = 5 ÷ 8 = 0.625
This means 62.5% of the class are boys.
Example 3:
In a juice mix, ratio of concentrate to water is 1:3.
Fraction of concentrate = 1/4 = 0.25
Fraction of water = 3/4 = 0.75
Practice Questions (Ratios as Fractions and Decimals):
Write the ratio 7:10 as a fraction and as a decimal.
A recipe has a ratio of oil to vinegar of 2:5. What fraction of the mixture is oil? What is that as a decimal?
In a game, the ratio of wins to losses is 9:6. Simplify the ratio, write as a fraction, then convert to decimal.
A school has 240 boys and 360 girls. What decimal represents the ratio of boys to girls?
A paint mixture has a ratio of blue to white paint of 3:8. What fraction and decimal represent the amount of blue paint compared to white paint?
✅ QUIZ 1: Basic Ratios + Ratios as Fractions/Decimals
A zoo has 24 lions, 18 tigers, and 30 bears. Write the ratio of tigers to total animals.
Convert the ratio 5:8 to a decimal.
In a box, the ratio of pens to pencils is 9:15. Simplify and write as a fraction.
A basketball team made 18 free throws and missed 12. What is the ratio of made to missed as a decimal?
A punch recipe uses 2 parts orange juice to 3 parts soda. What fraction of the punch is orange juice?
PART 2: VISUALIZE EQUIVALENT RATIOS
3. Ratios with Tape Diagrams
Description:
A tape diagram is a visual tool that uses rectangular strips (tapes) to represent quantities. Each "tape" represents an equal part. This helps see the relationship between quantities.
Explanation (TEKS 6.5A):
Draw rectangles (tapes) for each part of the ratio
Each rectangle has the same size (equal groups)
Label each tape with its quantity
Use total to find the value of one tape
Example 1:
The ratio of red to blue marbles is 3:2. There are 15 red marbles. How many blue marbles?
Step 1: Draw 3 tapes for red, 2 tapes for blue
Step 2: 3 tapes = 15 marbles → 1 tape = 5 marbles
Step 3: Blue has 2 tapes → 2 × 5 = 10 blue marbles
Example 2:
Ratio of boys to girls is 4:5. Total students = 36. How many boys?
Step 1: Total tapes = 4 + 5 = 9 tapes
Step 2: 9 tapes = 36 students → 1 tape = 4 students
Step 3: Boys have 4 tapes → 4 × 4 = 16 boys
Example 3:
The ratio of flour to sugar is 3:1. If there are 12 cups of flour, how much sugar?
3 tapes = 12 cups → 1 tape = 4 cups
Sugar = 1 tape = 4 cups
Practice Questions (Ratios with Tape Diagrams):
Ratio of cats to dogs is 2:3. There are 8 cats. How many dogs? Draw a tape diagram.
Ratio of apples to oranges is 5:2. Total fruits = 49. How many apples?
In a bag, ratio of pennies to nickels is 4:1. There are 20 pennies. How many nickels?
Ratio of adults to children at a movie is 3:7. There are 60 adults. How many children?
A school's ratio of teachers to students is 1:25. Total people = 520. How many teachers?
4. Equivalent Ratios with Equal Groups
Description:
Equivalent ratios are different ratios that represent the same relationship. You find them by multiplying or dividing both parts of a ratio by the same nonzero number.
Explanation:
Multiply or divide the numerator and denominator by the same number
Like finding equivalent fractions
2:3 is equivalent to 4:6, 6:9, 8:12, etc.
Example 1:
Find 3 equivalent ratios to 4:5
Multiply by 2: 8:10
Multiply by 3: 12:15
Multiply by 4: 16:20
Example 2:
Are 6:9 and 10:15 equivalent?
Simplify 6:9 = ÷3 → 2:3
Simplify 10:15 = ÷5 → 2:3
Yes, they are equivalent (both simplify to 2:3)
Example 3:
Find the missing value: 3:7 = 9:x
3 × 3 = 9, so multiply 7 × 3 = 21
x = 21
Practice Questions (Equivalent Ratios with Equal Groups):
Write three equivalent ratios to 2:5.
Are 8:12 and 14:21 equivalent? Show your work.
Find the missing value: 5:6 = 15:x
Write the simplest form of 18:24.
A ratio is 7:9. Write an equivalent ratio where the first term is 21.
5. Create Double Number Lines
Description:
A double number line has two parallel lines with matching tick marks. The top line shows one quantity, the bottom line shows the related quantity. It helps visualize scaling ratios.
Explanation:
Draw two parallel lines
Mark 0 on both lines at the left
Place given ratio on matching tick marks
Add more tick marks by adding the same increments
Example 1:
Create a double number line for the ratio 2:3 (miles to hours)
Top (miles): 0, 2, 4, 6, 8
Bottom (hours): 0, 3, 6, 9, 12
(Each step adds 2 miles and 3 hours)
Example 2:
A recipe uses 1 cup of sugar for every 4 cups of flour. Create a double number line for 0 to 5 cups of sugar.
Sugar: 0, 1, 2, 3, 4, 5
Flour: 0, 4, 8, 12, 16, 20
Practice Questions (Create Double Number Lines):
Create a double number line for the ratio 3:5. Show 4 increments beyond the given ratio.
A car travels 30 miles per hour. Create a double number line for time (hours) and distance (miles) from 0 to 4 hours.
For ratio 4:7, what is the bottom number when the top is 12? (Use double number line reasoning)
A paint mix uses 2 drops of blue for every 5 drops of yellow. Create a double number line from 0 to 8 drops of blue.
On a map, 1 inch represents 10 miles. Create a double number line from 0 to 5 inches.
6. Ratios with Double Number Lines
Description:
Using a pre-drawn or self-created double number line to find missing values in a proportional relationship.
Explanation:
Find the scale factor (how much you multiply to go from one known value to another)
Apply same scale factor to the other quantity
Or count increments on the double number line
Example 1:
On a double number line: Top (cups flour): 0, 2, 4, 6; Bottom (cups sugar): 0, 1, 2, 3
How much sugar for 10 cups flour?10 is 5 increments of 2 → 5 × 1 = 5 cups sugar
Example 2:
Ratio is 3 tickets for $12. How much for 5 tickets?
Tickets: 0, 3, 6, 9...
Cost ($): 0, 12, 24, 36...
Find 5 tickets: between 3 and 6. Use proportional: 3 tickets = $12, so 1 ticket = $4, 5 tickets = $20
Practice Questions (Ratios with Double Number Lines):
On a double number line, 4 apples cost $2. How much for 10 apples?
A runner runs 6 miles in 48 minutes. At this rate, how long for 9 miles?
On a double number line, 5 notebooks cost $7.50. How many notebooks for $15?
A recipe uses 2 eggs for 3 cups of flour. How many eggs for 12 cups of flour?
A bike travels 15 miles in 1 hour. Use a double number line to find distance in 2.5 hours.
7. Relate Double Number Lines and Ratio Tables
Description:
Ratio tables and double number lines show the same information in different formats. You can convert between them. A ratio table organizes equivalent ratios in rows/columns.
Explanation:
Double number line → Ratio table: List each tick mark pair as a row
Ratio table → Double number line: Plot each row as a point on two lines
Both show multiplicative relationships
Example 1:
Double number line:
Hours: 0, 1, 2, 3, 4
Miles: 0, 50, 100, 150, 200Ratio table:
Hours Miles 1 50 2 100 3 150 4 200
Example 2:
Ratio table:
x y 2 6 4 12 6 18 This is ratio 2:6 = 1:3. Double number line: top (x): 0,2,4,6; bottom (y): 0,6,12,18
Practice Questions (Relate Double Number Lines and Ratio Tables):
Convert this double number line to a ratio table: Top (cups water): 0, 3, 6, 9; Bottom (cups rice): 0, 1, 2, 3
Convert this ratio table to a double number line (describe the tick marks):
Packets Seeds 1 20 2 40 3 60 A double number line shows 5 meters = 2 seconds. Create a ratio table for 10, 15, and 20 meters.
From a ratio table, how do you know if the relationship is proportional?
The ratio table shows 3 pens cost $4.50. Draw what the double number line would look like for 0, 3, 6, 9 pens.
✅ QUIZ 2: Visualize Equivalent Ratios
(Topics: Tape diagrams, equal groups, double number lines, relating tables and lines)
Draw a tape diagram for ratio 4:7 where the smaller quantity is 12. Find the larger quantity.
Find the missing value: 3:8 = 9:x
Create a double number line for 2 gallons of paint covering 500 square feet. Show up to 10 gallons.
Convert this ratio table to a double number line: Minutes: 0, 5, 10, 15; Words typed: 0, 75, 150, 225
Is 5:8 equivalent to 15:20? Explain.
PART 3: EQUIVALENT RATIOS
8. Ratio Tables
Description:
A ratio table is an organized way to list equivalent ratios. Each column (or row) shows a pair of numbers that keep the same multiplicative relationship.
Explanation:
Multiply or divide both terms by the same number to get a new column
Use ratio tables to solve problems with missing values
Also called "proportional tables" on STAAR
Example 1:
Complete the ratio table for the ratio 2:3
2 4 6 8 10 3 6 9 12 15 (Multiply both by 1,2,3,4,5)
Example 2:
Find the missing value:
5 10 15 x 8 16 24 32 Pattern: multiply top by 1.6 (or bottom ÷ top = 1.6)
x = 20 because 32 ÷ 1.6 = 20
Practice Questions (Ratio Tables):
Complete the ratio table for ratio 4:9:
Find the missing value:
A recipe uses 2 cups flour to 5 cups milk. Complete the table:
Is this a proportional ratio table? Explain:
9. Equivalent Ratios
Description:
Equivalent ratios represent the same relationship between quantities. You can find them by multiplying or dividing both terms by the same number (scale factor).
Explanation:
Scale factor = new value ÷ original value
Multiply BOTH terms by the scale factor
Or find the simplest form (like simplifying fractions)
Example 1:
Are 6:10 and 9:15 equivalent?
Method 1: Simplify 6:10 = 3:5; 9:15 = 3:5 → Yes
Method 2: Cross-multiply: 6×15 = 90, 10×9 = 90 → Yes
Example 2:
Find an equivalent ratio to 8:20
Simplify: ÷4 → 2:5
Multiply: ×3 → 24:60
Practice Questions (Equivalent Ratios):
Are 4:7 and 12:21 equivalent? Prove your answer.
Find three equivalent ratios to 9:12.
Simplify 25:35 to lowest terms.
Which ratio is NOT equivalent to 5:8? A) 10:16 B) 15:24 C) 20:30 D) 25:40
A ratio is 6:14. Write an equivalent ratio where the second term is 35.
10. Equivalent Ratio Word Problems
Description:
Real-world problems where you must find a missing value using equivalent ratios. Often involves recipes, mixtures, speeds, or prices.
Explanation (TEKS 6.4B - Readiness Standard):
Identify the two quantities being compared
Set up a proportion: known ratio = unknown ratio
Solve by cross-multiplication or scale factor
Strategy:
Write what you know as a ratio (simplify if helpful)
Write what you need to find with a variable
Cross-multiply: a/b = c/d → a×d = b×c
Solve for the variable
Example 1:
A recipe calls for 3 cups of flour for every 2 cups of sugar. How much sugar is needed for 9 cups of flour?
Ratio: flour:sugar = 3:2
3/2 = 9/x
Cross-multiply: 3×x = 2×9 → 3x = 18 → x = 6 cups sugar
Example 2:
On a map, 2 inches represent 15 miles. How many miles are represented by 5 inches?
2/15 = 5/x → 2x = 75 → x = 37.5 miles
Example 3:
A factory produces 240 toys in 4 hours. At this rate, how many toys in 7 hours?
240/4 = x/7 → 4x = 1680 → x = 420 toys
Practice Questions (Equivalent Ratio Word Problems):
A smoothie uses 2 bananas for every 3 cups of yogurt. How many bananas for 9 cups of yogurt?
A car travels 210 miles on 7 gallons of gas. How far on 10 gallons?
A recipe for 8 muffins uses 2 cups of flour. How much flour for 20 muffins?
The ratio of boys to girls in a club is 3:5. If there are 24 boys, how many girls?
A printer prints 45 pages in 3 minutes. At this rate, how many minutes for 120 pages?
11. Equivalent Ratios in the Real World
Description:
Applying equivalent ratios to everyday situations like shopping (unit price), cooking (scaling recipes), mixing (paint or concrete), and maps (scale drawings).
Explanation:
Look for the "per one" relationship (unit rate)
Use that unit rate to solve for any quantity
Real-world problems often require rounding or interpreting remainders
Example 1 (Shopping):
A 12-ounce box costs $3.60. A 20-ounce box costs $5.80. Which is the better buy?
Unit price: $3.60 ÷ 12 = $0.30 per ounce
$5.80 ÷ 20 = $0.29 per ounce
The 20-ounce box is cheaper per ounce.
Example 2 (Scaling a recipe):
A recipe for 4 servings uses 1.5 cups of broth. How much broth for 10 servings?
1.5/4 = x/10 → 4x = 15 → x = 3.75 cups
Practice Questions (Real-World Equivalent Ratios):
A 6-pack of water bottles costs $4.50. A 12-pack costs $8.40. Which is the better unit price?
Concrete is mixed with 1 part cement to 3 parts sand. How much cement for 45 pounds of sand?
A photo is 4 inches wide and 6 inches tall. If enlarged to 10 inches wide, how tall will it be?
A map scale is 1 cm = 5 km. Two cities are 8 cm apart on the map. How far apart in reality?
A juice blend uses 2 parts orange to 5 parts apple juice. To make 14 cups of blend, how many cups of orange juice?
12. Understand Equivalent Ratios in the Real World
Description:
Moving beyond just computing to interpreting what equivalent ratios mean in context. This includes explaining why two ratios are equivalent and using reasoning to compare situations.
Explanation:
Understanding "per" statements (miles per hour, price per pound)
Recognizing constant of proportionality (k = y/x)
Explaining why a real-world relationship is proportional
Example 1:
"A car travels 120 miles in 2 hours." This means 60 miles per hour. The ratio is constant: 240 miles in 4 hours, 360 in 6 hours.
Example 2:
Two mixtures: Mix A has 2 tsp salt to 5 cups water. Mix B has 3 tsp salt to 8 cups water. Which is saltier?
Mix A: 2/5 = 0.4 tsp per cup
Mix B: 3/8 = 0.375 tsp per cup
Mix A is saltier (higher ratio of salt to water).
Practice Questions (Understand Equivalent Ratios):
Explain why 4:6 and 8:12 are equivalent ratios using words.
A store sells 3 shirts for $45. Another store sells 5 shirts for $70. Which is the better deal? Explain.
Two paint mixtures: Mix X (2 blue:3 white), Mix Y (3 blue:5 white). Which is bluer? Explain.
"This car gets 25 miles per gallon." What does this mean? Write two equivalent ratios.
A student says 3:5 is equivalent to 9:20. Is she correct? Explain why or why not.
✅ QUIZ 3: Equivalent Ratios
Complete: | 3 | 9 | 15 | 21 |
|---|---|---|---|
| 4 | 12 | | |Are 7:11 and 21:33 equivalent? Show work.
A factory produces 300 widgets in 5 hours. How many in 8 hours?
Which is the better buy: 10 pencils for $2.50 or 16 pencils for $3.68?
A map scale is 0.5 inch = 20 miles. How many miles for 3 inches?
PART 4: RATIO APPLICATION
13. Ratios on Coordinate Plane
Description:
Plotting ratio pairs as points (x, y) on a coordinate grid. For equivalent ratios, the points will lie on a straight line that passes through the origin (0,0).
Explanation (TEKS 6.4A):
Each ratio pair (a, b) becomes point (a, b)
For equivalent ratios, all points are collinear with (0,0)
The slope of the line = constant of proportionality (b/a)
Example 1:
Plot points for ratio 1:2 → (1,2), (2,4), (3,6), (4,8)
All points lie on line y = 2x through (0,0)
Example 2:
Which points represent equivalent ratios to 2:3?
(4,6) → 4/6 = 2/3 ✓
(6,9) → 6/9 = 2/3 ✓
(3,4) → 3/4 = 0.75, not 2/3 ✗
Practice Questions (Ratios on Coordinate Plane):
Plot these points from a ratio table: (1,5), (2,10), (3,15). Do they form a straight line? What is the ratio?
Is (4,10) equivalent to ratio 2:5? Explain.
A point (6,9) lies on a proportional line. What is the missing point if x=8?
Graph the ratio 3:4 from x=1 to x=4. Describe the line.
Two points are (2,6) and (5,15). Are they on a proportional line? What is the constant?
14. Ratios and Units of Measurement
Description:
Using ratios to convert between different units of measurement (customary and metric). Requires knowing conversion factors.
Explanation:
Write conversion factor as a ratio equal to 1 (e.g., 12 inches/1 foot)
Multiply the given quantity by the conversion ratio
Cancel units to get desired unit
Example 1:
Convert 3 feet to inches
3 ft × (12 in / 1 ft) = 36 inches
Example 2:
A snake is 60 inches long. How many feet?
60 in × (1 ft / 12 in) = 5 feet
Example 3:
A car travels 2 miles per minute. How many feet per second?
Step 1: 2 miles/min × 5280 ft/mile = 10,560 ft/min
Step 2: 10,560 ft/min ÷ 60 sec/min = 176 ft/sec
Practice Questions (Ratios and Units of Measurement):
Convert 5 yards to feet. (1 yd = 3 ft)
Convert 48 ounces to pounds. (1 lb = 16 oz)
A recipe calls for 2 liters of water. How many milliliters? (1 L = 1000 mL)
A runner runs 6 meters per second. How many meters per minute?
Convert 2.5 hours to minutes.
15. Part-Part-Whole Ratios
Description:
Ratios that compare two parts to each other (part-part) or a part to the whole (part-whole). Often used with tape diagrams.
Explanation:
Part + Part = Whole
If ratio of part A : part B = a:b, then:
Part A = (a/(a+b)) × Whole
Part B = (b/(a+b)) × Whole
Whole : Part A = (a+b):a
Example 1:
Ratio of cats to dogs is 3:4. Total animals = 28.
Total parts = 3+4 = 7
Each part = 28 ÷ 7 = 4 animals
Cats = 3 × 4 = 12, Dogs = 4 × 4 = 16
Example 2:
Ratio of red to blue marbles is 5:2. There are 20 red marbles. How many total marbles?
5 parts = 20 → 1 part = 4
Blue = 2 × 4 = 8
Total = 20 + 8 = 28 marbles
Practice Questions (Part-Part-Whole Ratios):
Ratio of boys to girls is 2:3. There are 30 students total. How many boys?
Ratio of apples to oranges is 5:1. There are 25 apples. How many total fruits?
In a bag, ratio of quarters to dimes is 3:4. There are 21 dimes. How many total coins?
A class has 18 girls. Ratio of boys to girls is 4:9. How many total students?
Ratio of fiction to nonfiction books is 7:2. There are 49 fiction books. How many total books?
✅ QUIZ 4: Ratio Application
Plot these points: (1,4), (2,8), (3,12). What is the ratio? Do they form a line through origin?
Convert 7 gallons to quarts. (1 gal = 4 qt)
Convert 150 centimeters to meters. (100 cm = 1 m)
Ratio of blue to red marbles is 4:5. Total marbles = 54. How many blue?
Ratio of left-handed to right-handed students is 1:8. There are 36 right-handed. How many total?
PART 5: INTRO TO RATES
16. Unit Rates
Description:
A rate is a ratio comparing two quantities with different units (e.g., miles per hour, price per pound). A unit rate has a denominator of 1.
Explanation (TEKS 6.4B & 6.5A):
To find unit rate: divide first quantity by second quantity
Unit rate = "per one" (something per 1 unit of something else)
Written as: $5 per pound, 60 miles per hour
Example 1:
240 miles in 4 hours → 240 ÷ 4 = 60 miles per hour (unit rate)
Example 2:
$12 for 3 pounds → 12 ÷ 3 = $4 per pound
Example 3:
120 words in 2 minutes → 60 words per minute
Practice Questions (Unit Rates):
Find the unit rate: 300 miles on 15 gallons.
24 ounces cost $6.00. What is the unit price per ounce?
A plane flies 1,200 miles in 3 hours. What is the unit rate (speed)?
8 shirts cost $96. What is the cost per shirt?
A machine produces 450 bottles in 5 hours. How many per hour?
17. Rate Problems
Description:
Word problems that involve rates. Usually ask: find total for a different quantity, or find time/distance given the rate.
Explanation:
Find the unit rate first
Then multiply by the new quantity
Or set up a proportion: rate1 = rate2
Example 1:
A car travels at 55 miles per hour. How far in 3.5 hours?
55 × 3.5 = 192.5 miles
Example 2:
A faucet fills a tub at 8 gallons per minute. How long to fill 120 gallons?
120 ÷ 8 = 15 minutes
Example 3:
A baker makes 24 cupcakes in 2 hours. At this rate, how many in 5 hours?
Unit rate = 12 cupcakes/hour → 12 × 5 = 60 cupcakes
Practice Questions (Rate Problems):
A runner runs at 12 feet per second. How far in 10 seconds?
A printer prints 30 pages per minute. How long for 450 pages?
A car uses 0.05 gallons of gas per mile. How many gallons for 200 miles?
A typist types 45 words per minute. How many words in 20 minutes?
A water pump moves 15 gallons per minute. How long to pump 900 gallons?
18. Comparing Rates
Description:
Determining which rate is faster, cheaper, or more efficient by comparing unit rates.
Explanation:
Find the unit rate for each option
Compare the unit rates directly
Smaller unit cost = better deal; larger unit speed = faster
Example 1:
Store A: 5 pounds for $20 → $4/lb
Store B: 8 pounds for $28 → $3.50/lb
Store B is cheaper.
Example 2:
Car A: 300 miles in 5 hours → 60 mph
Car B: 280 miles in 4 hours → 70 mph
Car B is faster.
Practice Questions (Comparing Rates):
Which is faster: 240 miles in 4 hours or 210 miles in 3 hours?
Which is cheaper: $4.50 for 3 pounds or $7.20 for 6 pounds?
Job A pays $360 for 30 hours. Job B pays $420 for 35 hours. Which pays more per hour?
Which is a better deal: 12 eggs for $3.60 or 18 eggs for $5.40?
Truck A uses 15 gallons for 300 miles. Truck B uses 12 gallons for 270 miles. Which gets better gas mileage (miles per gallon)?
✅ QUIZ 5: Intro to Rates
Find the unit rate: 360 miles in 6 hours.
A gardener plants 24 flowers per hour. How many in 4.5 hours?
Which is faster: 90 meters in 10 seconds or 150 meters in 15 seconds?
A school buys 8 computers for $4,800. What is the unit price?
A train travels 75 miles per hour. How far in 2.8 hours?
UNIT TEST PRACTICE (Cumulative)
Write the ratio 8:14 in simplest form.
Complete:
A recipe uses 3 eggs for 5 cups of flour. How many eggs for 20 cups of flour?
On a map, 1 cm = 8 km. Two towns are 6.5 cm apart. How many km?
Convert 4.5 feet to inches.
Ratio of boys to girls is 5:7. Total students = 48. How many girls?
Plot (2,6), (4,12), (6,18). Are they proportional? What is the constant?
Which is the better buy: 8 oranges for $3.20 or 12 oranges for $4.80?
A car travels 180 miles in 3 hours. What is the unit rate? How far in 5 hours?
A faucet leaks 3 mL per minute. How much in 2 hours (120 minutes)?
Write the ratio 8:14 in simplest form.
Complete:
A recipe uses 3 eggs for 5 cups of flour. How many eggs for 20 cups of flour?
On a map, 1 cm = 8 km. Two towns are 6.5 cm apart. How many km?
Convert 4.5 feet to inches.
Ratio of boys to girls is 5:7. Total students = 48. How many girls?
Plot (2,6), (4,12), (6,18). Are they proportional? What is the constant?
Which is the better buy: 8 oranges for $3.20 or 12 oranges for $4.80?
A car travels 180 miles in 3 hours. What is the unit rate? How far in 5 hours?
A faucet leaks 3 mL per minute. How much in 2 hours (120 minutes)?
