Measurement Word Problems for Class 4 | Solved Exercises

Advanced Measurement Concepts for Class 4

Length: Inches, Feet, Yards, Miles

Advanced Length Measurement

Weight: Ounces, Pounds, Tons

Advanced Weight Measurement

Capacity: Cups, Pints, Quarts, Gallons

Advanced Capacity Measurement

Time: Seconds, Minutes, Hours, Days

Advanced Time Measurement

Advanced Concepts for Class 4:

Word Problem: A complex math question written in sentences that tells a multi-step story.

Measurement: Using numbers to describe how long, heavy, full, or how much time something is.

Units: Standard amounts used to measure (inches, pounds, cups, minutes).

Operations: Addition (+), subtraction (-), multiplication (×), division (÷).

Multi-step: Problems requiring more than one operation to solve.

Fractions: Parts of a whole (½, ¼, ¾).

Decimals: Numbers with tenths and hundredths (.5, .25).

Addition

Combining amounts

Subtraction

Taking away

Multiplication

Repeated addition

Division

Sharing equally

Fractions

Parts of a whole

Decimals

Decimal places

Advanced Problem-Solving Steps:

Read Carefully: Understand the full story in the problem

Find Information: Identify all numbers and what they measure

Plan Steps: Decide the order of operations needed

Solve Step-by-Step: Work through each operation carefully

Check Answer: Make sure it makes sense

Advanced Skills:

Converting between different units (feet to inches, cups to quarts)
Solving multi-step problems with multiple operations
Using multiplication and division in word problems
Working with fractions in measurement (½ cup, ¾ inch)
Calculating with decimals (.5 feet, 1.25 pounds)
Finding averages and totals
Working with elapsed time

Solution: Exercises 1 to 3

1 Advanced Length Problem

Exercise 1

A carpenter needs to cut 4 pieces of wood for a project. The first piece is 3.5 feet long, the second is 2.75 feet long, the third is 4.25 feet long, and the fourth is 1.5 feet long. How many total feet of wood does the carpenter need? If the carpenter buys wood in 8-foot boards, how many boards does he need to buy?

Problem Context:

The carpenter needs to calculate total wood needed and determine how many boards to purchase.

Key Information:

First piece: 3.5 feet

Second piece: 2.75 feet

Third piece: 4.25 feet

Fourth piece: 1.5 feet

Board length: 8 feet

Question: Total feet needed and number of boards?

Solution Method:

This is a multi-step problem. First add all decimal lengths, then divide by board length and round up.

Step 1: Add all wood lengths

3.5 + 2.75 + 4.25 + 1.5 = 12 feet total

Step 2: Calculate number of boards needed

12 ÷ 8 = 1.5 boards

Since we can't buy half a board, round up to 2 boards

Step 3: Write the complete answer

The carpenter needs 12 feet of wood and must buy 2 boards.

Total: 12 feet, Boards: 2.

Final Answer:

The carpenter needs 12 feet of wood and must buy 2 boards.

Applied Rules:

• Addition Rule: 3.5 + 2.75 + 4.25 + 1.5 = 12

• Division Rule: 12 ÷ 8 = 1.5

• Rounding Rule: Round up when dealing with materials

Key Point to Remember:

When working with physical materials, always round up to ensure you have enough.

2 Advanced Weight Problem

Exercise 2

A baker needs to make 6 batches of cookies. Each batch requires 3/4 pound of flour. The baker has 2 pounds of flour in stock. How much more flour does the baker need to buy? If flour costs $2.50 per pound, how much will it cost to buy the needed flour?

Problem Context:

The baker wants to know how much additional flour to buy and the cost.

Key Information:

Batches needed: 6

Flour per batch: 3/4 pound

Flour in stock: 2 pounds

Cost per pound: $2.50

Question: Additional flour needed and cost?

Solution Method:

This is a multi-step problem with fractions. First multiply to find total flour needed, then subtract what's in stock, then multiply by cost per pound.

Step 1: Calculate total flour needed

6 × 3/4 = 18/4 = 4.5 pounds

Step 2: Calculate additional flour needed

4.5 - 2 = 2.5 pounds more needed

Step 3: Calculate cost

2.5 × $2.50 = $6.25

Step 4: Write the complete answer

The baker needs 2.5 more pounds of flour, which will cost $6.25.

Additional flour: 2.5 pounds, Cost: $6.25.

Final Answer:

The baker needs 2.5 more pounds of flour, which will cost $6.25.

Applied Rules:

• Fraction Multiplication: 6 × 3/4 = 18/4 = 4.5

• Subtraction Rule: 4.5 - 2 = 2.5

• Decimal Multiplication: 2.5 × $2.50 = $6.25

Key Point to Remember:

When multiplying fractions by whole numbers, multiply the numerator by the whole number.

3 Advanced Capacity Problem

Exercise 3

A water tank can hold 24.5 gallons of water. It currently has 8.75 gallons. Water flows into the tank at a rate of 2.25 gallons per minute. How long will it take to fill the tank completely? If the tank starts empty, how long would it take to fill it?

Problem Context:

The water system engineer wants to know fill times under different conditions.

Key Information:

Tank capacity: 24.5 gallons

Current water: 8.75 gallons

Flow rate: 2.25 gallons per minute

Question: Time to fill from current level and from empty?

Solution Method:

This is a multi-step problem with decimals. First calculate remaining capacity, then divide by flow rate for first scenario. For second scenario, divide total capacity by flow rate.

Step 1: Calculate remaining capacity

24.5 - 8.75 = 15.75 gallons needed

Step 2: Calculate time to fill from current level

15.75 ÷ 2.25 = 7 minutes

Step 3: Calculate time to fill from empty

24.5 ÷ 2.25 = 10.89 minutes (approximately 10.9 minutes)

Step 4: Write the complete answer

It takes 7 minutes to fill from current level and 10.9 minutes to fill from empty.

Current: 7 minutes, Empty: 10.9 minutes.

Final Answer:

It takes 7 minutes to fill from current level and 10.9 minutes to fill from empty.

Applied Rules:

• Subtraction Rule: 24.5 - 8.75 = 15.75

• Division Rule: 15.75 ÷ 2.25 = 7

• Division Rule: 24.5 ÷ 2.25 = 10.89 ≈ 10.9

Key Point to Remember:

When calculating time with rates, divide the amount by the rate.

Solution: Exercises 4 to 5

4 Advanced Time Problem

Exercise 4

A factory produces 3.5 tons of steel per hour. The factory operates for 8 hours each day. If the factory needs to produce 140 tons of steel, how many days will it take? If production increases to 4.2 tons per hour, how many days will it take to produce the same amount?

Problem Context:

The factory manager wants to plan production schedules.

Key Information:

Original rate: 3.5 tons per hour

Operating hours: 8 hours per day

Total needed: 140 tons

New rate: 4.2 tons per hour

Question: Days needed at original rate and new rate?

Solution Method:

This is a multi-step problem with decimals. First calculate daily production, then divide total needed by daily production for both scenarios.

Step 1: Calculate daily production at original rate

3.5 tons/hour × 8 hours/day = 28 tons per day

Step 2: Calculate days needed at original rate

140 ÷ 28 = 5 days

Step 3: Calculate daily production at new rate

4.2 tons/hour × 8 hours/day = 33.6 tons per day

Step 4: Calculate days needed at new rate

140 ÷ 33.6 = 4.17 days (approximately 4.2 days)

Step 5: Write the complete answer

It takes 5 days at the original rate and 4.2 days at the new rate.

Original: 5 days, New: 4.2 days.

Final Answer:

It takes 5 days at the original rate and 4.2 days at the new rate.

Applied Rules:

• Multiplication Rule: 3.5 × 8 = 28

• Division Rule: 140 ÷ 28 = 5

• Multiplication Rule: 4.2 × 8 = 33.6

• Division Rule: 140 ÷ 33.6 = 4.17 ≈ 4.2

Key Point to Remember:

When calculating time for production, divide total amount needed by daily production rate.

5 Complex Multi-Step Problem

Exercise 5

A farmer has 3 fields. The first field is 2.5 acres, the second is 3.75 acres, and the third is 1.25 acres. He plants corn on 3/4 of the total area and wheat on the remaining area. If corn yields 180 bushels per acre and wheat yields 120 bushels per acre, how many total bushels does the farmer harvest?

Problem Context:

The farmer wants to predict total harvest yield.

Key Information:

Field 1: 2.5 acres

Field 2: 3.75 acres

Field 3: 1.25 acres

Corn area: 3/4 of total

Corn yield: 180 bushels per acre

Wheat yield: 120 bushels per acre

Question: Total bushels harvested?

Solution Method:

This is a complex multi-step problem with decimals and fractions. First add field areas, then calculate corn and wheat areas, then calculate yields for each crop.

Step 1: Calculate total area

2.5 + 3.75 + 1.25 = 7.5 acres total

Step 2: Calculate corn area

7.5 × 3/4 = 5.625 acres for corn

Step 3: Calculate wheat area

7.5 - 5.625 = 1.875 acres for wheat

Step 4: Calculate corn yield

5.625 × 180 = 1,012.5 bushels of corn

Step 5: Calculate wheat yield

1.875 × 120 = 225 bushels of wheat

Step 6: Calculate total yield

1,012.5 + 225 = 1,237.5 bushels total

Step 7: Write the complete answer

The farmer harvests 1,237.5 bushels in total.

Total harvest: 1,237.5 bushels.

Final Answer:

The farmer harvests 1,237.5 bushels in total.

Applied Rules:

• Addition Rule: 2.5 + 3.75 + 1.25 = 7.5

• Fraction Multiplication: 7.5 × 3/4 = 5.625

• Subtraction Rule: 7.5 - 5.625 = 1.875

• Decimal Multiplication: 5.625 × 180 = 1,012.5

• Decimal Multiplication: 1.875 × 120 = 225

• Addition Rule: 1,012.5 + 225 = 1,237.5

Key Point to Remember:

For complex problems, solve one step at a time and keep track of what you've calculated.

Advanced Measurement Word Problems for Class 4 Students

Class 4 Questions & Answers