Grade 6 proportions word problems worksheet with decimal-based math exercises.

Let’s go through each problem one by one, step by step.

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Problem 1: A bus travels 350 km in 4 hours (with a constant speed). How far can it travel in 7 hours (with the same speed)?

Step 1: Find the speed of the bus.
Speed = Distance ÷ Time
→ 350 km ÷ 4 hours = 87.5 km/hour

Step 2: Use that speed to find distance in 7 hours.
Distance = Speed × Time
→ 87.5 km/hour × 7 hours = 612.5 km

✔ Check: 87.5 × 7 → 80×7=560, 7.5×7=52.5 → 560+52.5=612.5 ✔️

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Problem 2: If two water towers can hold 905 gallons of water, how much water can 11 water towers hold?

Step 1: Find how much one tower holds.
→ 905 ÷ 2 = 452.5 gallons per tower

Step 2: Multiply by 11 towers.
→ 452.5 × 11

Let’s calculate:
452.5 × 10 = 4525
452.5 × 1 = 452.5
Add them: 4525 + 452.5 = 4977.5

✔ Check: 452.5 × 11 = 4977.5 ✔️

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Problem 3: If it takes four moving trucks to move 48 boxes, how many trucks are needed to move 840 boxes?

Step 1: Find how many boxes one truck can move.
→ 48 ÷ 4 = 12 boxes per truck

Step 2: Divide total boxes by boxes per truck.
→ 840 ÷ 12 = ?

Let’s divide:
12 × 70 = 840 → So, 70 trucks

✔ Check: 12 × 70 = 840 ✔️

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Problem 4: A factory can produce 60 TV in 7 days. How long does it take to finish 400 TVs?

Step 1: Find how many TVs are made per day.
→ 60 ÷ 7 ≈ 8.5714 TVs/day (we’ll keep more decimals for accuracy)

Step 2: Divide total TVs needed by daily production.
→ 400 ÷ (60/7) = 400 × (7/60) = (400 × 7) ÷ 60

Calculate:
400 × 7 = 2800
2800 ÷ 60 = 46.666...

Round to 2 decimal places → 46.67 days

✔ Check: 60 TVs in 7 days → rate = 60/7 ≈ 8.5714
8.5714 × 46.67 ≈ let’s check:
8.5714 × 46 = 394.2844
8.5714 × 0.67 ≈ 5.7428
Total ≈ 394.28 + 5.74 = 400.02 → close enough ✔️

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Problem 5: 500 lemons were packed in 8 boxes. How many lemons can be packed in 20 boxes?

Step 1: Find lemons per box.
→ 500 ÷ 8 = 62.5 lemons per box

Step 2: Multiply by 20 boxes.
→ 62.5 × 20 = 1250

✔ Check: 62.5 × 20 = 1250 ✔️

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Problem 6: A pack of four cans of coffee cost $10.90. How much would 17 cans of coffee cost?

Step 1: Find cost per can.
→ $10.90 ÷ 4 = $2.725 per can

Step 2: Multiply by 17 cans.
→ 2.725 × 17

Break it down:
2.725 × 10 = 27.25
2.725 × 7 = 19.075
Add: 27.25 + 19.075 = 46.325

Round to 2 decimal places → $46.33

✔ Check: 2.725 × 17
Or: 10.90 ÷ 4 = 2.725 → 2.725 × 17 = 46.325 → rounds to 46.33 ✔️

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Final Answer:
612.5 km
4977.5 gallons
70 trucks
46.67 days
1250 lemons
$46.33