Comparing Ratios
Team A mixes 3 cups of powder to 5 cups of water.
Team B mixes 4 cups of powder to 6 cups of water.
Which team’s drink has a stronger powder taste?
Explain how you know.
Sports Drinks
Team A: 3 : 5
Team B: 4 : 6 → simplifies to 2 : 3
Compare:
Team A = 3/5 = 0.6
Team B = 2/3 ≈ 0.67
✅ Answer: Team B has the stronger powder taste.
Juice Boxes
Pack A has 6 juice boxes for $3.00.
Pack B has 10 juice boxes for $4.50.
Which pack is the better deal?
Pack A: $3.00 ÷ 6 = $0.50 per box
Pack B: $4.50 ÷ 10 = $0.45 per box
✅ Pack B is the better deal.
Running Practice
Runner A runs 3 miles in 30 minutes.
Runner B runs 5 miles in 1 hour.
Who runs at a faster rate?
Running Practice
Runner A: 3 miles / 30 min = 3 / 0.5 hr = 6 mph
Runner B: 5 miles / 1 hr = 5 mph
✅ Answer: Runner A
Water Bottles
Bottle A holds 750 milliliters for $1.50.
Bottle B holds 1 liter for $1.80.
Which bottle gives more water per dollar?
Bottle A: 750 mL / $1.50 = 500 mL per $1
Bottle B: 1 L = 1,000 mL → 1,000 / $1.80 ≈ 556 mL per $1
✅ Answer: Bottle B
Walking vs. Biking
Lena walks 3 miles to the library. Her brother bikes 8,800 feet to the same place.
Convert both distances to the same unit.
Who traveled farther?
How much farther did they travel?
Walking vs. Biking
Lena walks 3 miles.
Her brother bikes 8,800 feet.
Conversion: 1 mile = 5,280 feet
Step 1: Convert miles to feet (Lena)
3 miles×5,280 feet/mile=15,840 feet3 \text{ miles} \times 5,280 \text{ feet/mile} = 15,840 \text{ feet}3 miles×5,280 feet/mile=15,840 feet
Step 2: Compare distances
Lena: 15,840 ft
Brother: 8,800 ft
Step 3: Who traveled farther?
Lena traveled farther.
Step 4: How much farther?
15,840−8,800=7,040 feet15,840 - 8,800 = 7,040 \text{ feet}15,840−8,800=7,040 feet
✅ Answer: Lena traveled 7,040 ft farther.
In Class 6A, the ratio of markers to students is 12 : 24.
In Class 6B, the ratio of markers to students is 10 : 20.
Which class has more markers per student, or are the ratios the same?
Classroom Supplies
Class 6A: 12 : 24 → 1 : 2
Class 6B: 10 : 20 → 1 : 2
✅ Answer: The ratios are equivalent.
Apples
Bag A has 4 pounds of apples for $6.00.
Bag B has 6 pounds of apples for $8.40.
Which bag is the better buy?
Bag A: $6.00 ÷ 4 = $1.50 per lb
Bag B: $8.40 ÷ 6 = $1.40 per lb
✅ Bag B is the better deal.
I ran 2 miles in 12 minutes.
Max ran 12 miles in 1 hour.
Who ran faster?
I ran 10 miles in 1 hour.
Answer- Max ran faster.
Better Deal - Notebook Paper
Pack A has 150 sheets for $3.75.
Pack B has 200 sheets for $4.80.
Which pack costs less per sheet?
Pack A: $3.75 ÷ 150 = $0.025 per sheet
Pack B: $4.80 ÷ 200 = $0.024 per sheet
✅ Pack B is the better deal.
A family drives 120 kilometers on one highway and 75 miles on another highway.
Convert the kilometers to miles (1 mile ≈ 1.6 km).
Which highway segment was longer?
How many more miles was it?
Road Trip Comparison
Highway 1: 120 km
Highway 2: 75 miles
Conversion: 1 mile ≈ 1.6 km
Step 1: Convert km to miles
120÷1.6=75 miles120 \div 1.6 = 75 \text{ miles}120÷1.6=75 miles
Step 2: Compare distances
Highway 1 = 75 miles
Highway 2 = 75 miles
Step 3: Which is longer?
They are the same distance.
✅ Answer: Both highways are the same length (75 miles).
Pets at Two Shelters
At Shelter X, the ratio of cats to dogs is 8 : 12.
At Shelter Y, the ratio of cats to dogs is 10 : 15.
Which shelter has a greater proportion of cats?
Pets at Two Shelters
Shelter X: 8 : 12 → 2 : 3
Shelter Y: 10 : 15 → 2 : 3
✅ Answer: Both shelters have the same proportion of cats.
Movie Tickets
Theater A charges $18 for 3 tickets.
Theater B charges $24 for 4 tickets.
Which theater offers the lower price per ticket?
Theater A: $18 ÷ 3 = $6 per ticket
Theater B: $24 ÷ 4 = $6 per ticket
✅ Both deals are the same.
Juice Production
Machine A produces 750 milliliters of juice in 3 minutes.
Machine B produces 1.2 liters of juice in 4 minutes.
Which machine produces more juice per minute?
Machine A: 750 mL / 3 min = 250 mL/min
Machine B: 1.2 L = 1,200 mL → 1,200 / 4 = 300 mL/min
✅ Answer: Machine B
Better Deal-Yogurt Cups
Pack A has 6 yogurt cups for $4.20.
Pack B has 8 yogurt cups for $5.60.
Which pack gives more yogurt for the money?
Pack A: $4.20 ÷ 6 = $0.70 per cup
Pack B: $5.60 ÷ 8 = $0.70 per cup
✅ Both deals are equal.
Running Practice
During practice, Jordan runs 2.5 miles. Maya runs 13,200 feet.
Convert both distances to miles.
Who ran farther?
What is the difference in distance?
Running Practice
Jordan: 2.5 miles
Maya: 13,200 feet
Conversion: 1 mile = 5,280 feet
Step 1: Convert Jordan’s distance to feet
2.5×5,280=13,200 feet2.5 \times 5,280 = 13,200 \text{ feet}2.5×5,280=13,200 feet
Step 2: Compare distances
Jordan: 13,200 ft
Maya: 13,200 ft
Step 3: Who ran farther?
They ran the same distance
✅ Answer: Same distance; no one ran farther.
Paint Mixtures
Paint Mix A uses 2 cups of red paint for every 3 cups of white paint.
Paint Mix B uses 4 cups of red paint for every 5 cups of white paint.
Which paint mix will look more red?
Paint Mixtures
Mix A: 2 : 3
Mix B: 4 : 5
Compare:
Mix A = 2/3 ≈ 0.67
Mix B = 4/5 = 0.8
✅ Answer: Paint Mix B looks more red
Water Bottles
Pack A has 12 bottles for $6.60.
Pack B has 18 bottles for $9.90.
Which pack costs less per bottle?
Pack A: $6.60 ÷ 12 = $0.55 per bottle
Pack B: $9.90 ÷ 18 = $0.55 per bottle
✅ Both packs cost the same.
Emma watches 90 minutes of movies for every 3 hours of reading.
Liam watches 2 hours of movies for every 100 minutes of reading.
Who watches more movies compared to reading time?
Emma: 90 min / 3 hr = 90 / 180 = 1/2
Liam: 2 hr = 120 min → 120 / 100 = 1.2
✅ Answer: Liam
Typing Practice
Ava types 450 words in 15 minutes.
Noah types 1,200 words in 40 minutes.
Who types faster?
Ava: 450 / 15 = 30 wpm
Noah: 1,200 / 40 = 30 wpm
✅ Answer: Same speed
Hiking Trails
Trail A is 4,200 meters long. Trail B is 3.8 kilometers long.
Convert both distances to meters.
Compare the lengths of the two trails.
How much longer is one trail than the other?
Hiking Trails
Trail A: 4,200 meters
Trail B: 3.8 km
Conversion: 1 km = 1,000 m
Step 1: Convert Trail B to meters
3.8×1,000=3,800 meters3.8 \times 1,000 = 3,800 \text{ meters}3.8×1,000=3,800 meters
Step 2: Compare distances
Trail A: 4,200 m
Trail B: 3,800 m
Step 3: Difference
4,200−3,800=400 meters4,200 - 3,800 = 400 \text{ meters}4,200−3,800=400 meters
✅ Answer: Trail A is 400 meters longer.
Reading Time
Liam spends 15 minutes reading for every 45 minutes of screen time.
Noah spends 20 minutes reading for every 40 minutes of screen time.
Who spends more time reading compared to screen time?
Reading Time
Liam: 15 : 45 → 1 : 3
Noah: 20 : 40 → 1 : 2
✅ Answer: Noah spends more time reading compared to screen time.
Granola Bars
Box A has 8 granola bars for $4.00.
Box B has 12 granola bars for $5.40.
Which box is the better deal?
Box A: $4.00 ÷ 8 = $0.50 per bar
Box B: $5.40 ÷ 12 = $0.45 per bar
✅ Box B is the better deal.
Store A sells 300 grams of candy for $2.40.
Store B sells 0.5 kilograms of candy for $3.50.
Which store has the lower cost per 100 grams?
Store A: $2.40 / 300 g = $0.80 per 100 g
Store B: 0.5 kg = 500 g → $3.50 / 500 g = $0.70 per 100 g
✅ Answer: Store B
Snack Prices
Snack A costs 75 cents for 150 grams.
Snack B costs $1.20 for 200 grams.
Which snack is the better buy?
Snack Prices
Snack A: $0.75 / 150 g = $0.50 per 100 g
Snack B: $1.20 / 200 g = $0.60 per 100 g
✅ Answer: Snack A
Delivery Routes
A delivery truck travels 18 miles on Route A and 28,800 yards on Route B.
Convert both distances to miles.
Which route is longer?
Explain how you know using ratios or unit rates.
Delivery Routes
Route A: 18 miles
Route B: 28,800 yards
Conversion: 1 mile = 1,760 yards
Step 1: Convert Route A to yards
18×1,760=31,680 yards18 \times 1,760 = 31,680 \text{ yards}18×1,760=31,680 yards
Step 2: Compare distances
Route A: 31,680 yd
Route B: 28,800 yd
Step 3: Difference
31,680−28,800=2,880 yards31,680 - 28,800 = 2,880 \text{ yards}31,680−28,800=2,880 yards
✅ Answer: Route A is longer by 2,880 yards.