Decimal Word Problems
Apply your decimal skills to solve real-world problems!
1. Problem-Solving Strategy
Steps to Solve Word Problems:
- Read carefully - What information is given? What are you asked to find?
- Identify the operations - Do you need to add, subtract, multiply, or divide?
- Check units - Make sure all units are the same before calculating
- Show your working - Write out each step clearly
- Check your answer - Does it make sense? Include the correct units!
Tip: Estimation helps! Round the numbers first to get an approximate answer, then check if your final answer is close to your estimate.
2. Single-Step Word Problems
Example: Multiplication
A packet of rice has a mass of 2.5 kg. What is the mass of 3 such packets?
Given: 1 packet = 2.5 kg
Find: Mass of 3 packets
Mass of 3 packets = 3 × 2.5 kg
= 7.5 kg
The mass of 3 packets of rice is 7.5 kg.
Example: Division
A ribbon is 4.8 m long. It is cut into 6 equal pieces. What is the length of each piece?
Given: Total length = 4.8 m, Number of pieces = 6
Find: Length of each piece
Length of each piece = 4.8 m ÷ 6
= 0.8 m
Each piece of ribbon is 0.8 m long.
3. Multi-Step Word Problems
Example: Multiple Operations with Unit Conversion
A worker had 150 m of cable at first. He used 73.6 m of cable and cut the remaining cable into 40 equal pieces. What was the length of each shorter piece of cable in centimetres?
Estimation:
150 m − 70 m = 80 m, and 80 m ÷ 40 = 2 m. So each piece should be about 2 m, which is 200 cm.
Step 1: Find the remaining cable
150 m − 73.6 m = 76.4 m
Step 2: Find the length of each piece
76.4 m ÷ 40 = 1.91 m
Step 3: Convert to centimetres
1.91 m = 1.91 × 100 cm = 191 cm
The length of each shorter piece of cable was 191 cm.
Example: Combining Different Units
The mass of one packet of rice is 2.5 kg. The mass of one packet of flour is 820 g. Find the total mass of 3 packets of rice and 5 packets of flour. Express your answer in kilograms.
Important:
We need to make sure both measurements have the same unit before adding!
Step 1: Find the mass of 3 packets of rice
3 × 2.5 kg = 7.5 kg
Step 2: Find the mass of 5 packets of flour
5 × 820 g = 4100 g
4100 g = 4.1 kg
Step 3: Add the masses together
7.5 kg + 4.1 kg = 11.6 kg
The total mass of 3 packets of rice and 5 packets of flour is 11.6 kg.
4. Bar Model Problems
Example: Comparison Problem
3 identical pens and 3 identical storybooks cost $46.80. Each pen costs $3.10 less than each storybook. How much does a storybook cost?
Bar Model:
Step 1: Find the total of the three "$3.10" parts
3 × $3.10 = $9.30
Step 2: Add the three parts to the total, so that each pen costs as much as a storybook
$46.80 + $9.30 = $56.10
(This is the cost of 6 storybooks)
Step 3: Find the cost of 1 storybook
$56.10 ÷ 6 = $9.35
Check:
Cost of 1 pen = $9.35 − $3.10 = $6.25
Total = 3 × $6.25 + 3 × $9.35 = $18.75 + $28.05 = $46.80 ✓
A storybook costs $9.35.
Practice Problems
Practice 1: Mass Problem
Cindy had 5.1 kg of beads. She bought another 2.34 kg of beads and packed all of them equally into 8 packets. What was the mass of beads in each packet? Leave your answer in grams.
ShowHide solution
Step 1: Total mass = 5.1 kg + 2.34 kg = 7.44 kg
Step 2: Mass in each packet = 7.44 kg ÷ 8 = 0.93 kg
Step 3: Convert to grams: 0.93 kg = 0.93 × 1000 g = 930 g
Practice 2: Length Problem
The perimeter of a rectangular photo is 56.8 cm. Its length is 3 times as long as its breadth. What is the length of the photo?
ShowHide solution
Let breadth = 1 unit, length = 3 units
Perimeter = 2 × (length + breadth) = 2 × (3 units + 1 unit) = 8 units
8 units = 56.8 cm
1 unit = 56.8 cm ÷ 8 = 7.1 cm
Length = 3 units = 3 × 7.1 cm = 21.3 cm
Practice 3: Money Problem
Ahmad bought 9 identical pencils for $13.05 and 6 identical glue sticks for $12.90. How much did 2 such pencils and 3 such glue sticks cost altogether?
ShowHide solution
Step 1: Cost of 1 pencil = $13.05 ÷ 9 = $1.45
Step 2: Cost of 1 glue stick = $12.90 ÷ 6 = $2.15
Step 3: Cost of 2 pencils = 2 × $1.45 = $2.90
Step 4: Cost of 3 glue sticks = 3 × $2.15 = $6.45
Total = $2.90 + $6.45 = $9.35
Practice 4: Volume Problem
The total volume of 4 identical cups of juice and 5 identical glasses of water is 3440 ml. The total volume of 2 such cups of juice and 2 such glasses of water is 1530 ml. Find the total volume of 1 cup of juice and 2 glasses of water. Give your answer in litres.
ShowHide solution
2 cups of juice + 2 glasses of water = 1530 ml
Double everything: 4 cups + 4 glasses = 2 × 1530 ml = 3060 ml
The question tells us: 4 cups + 5 glasses = 3440 ml
The difference is 1 glass of water: 3440 ml − 3060 ml = 380 ml
1 cup + 1 glass = 1530 ml ÷ 2 = 765 ml
1 cup + 2 glasses = 765 ml + 380 ml = 1145 ml
1145 ml = 1145 ÷ 1000 ℓ = 1.145 ℓ
Key Takeaways
- Read carefully to understand what is given and what to find
- Check units - convert to the same unit before calculating
- Use estimation to check if your answer is reasonable
- Bar models help you visualise comparison problems
- Show all your working and include units in your answer
- For multi-step problems, solve one step at a time