Solved Exercises on Fractions of a Whole Number Word Problems in Grade 3

Comprehensive practice on real-world applications of fractions of whole numbers: solving various word problems with detailed solutions and visual aids.

Complete Summary: Fractions of a Whole Number Word Problems

Definitions

Word Problem: A mathematical problem presented in a real-world context using words instead of symbols.

Fraction of a Whole Number: A calculation that finds a part of a whole number in a real-world scenario.

Contextual Understanding: Interpreting mathematical operations within real-world situations.

Problem Solving: Using mathematical concepts to answer questions about real-life situations.

Core Rules and Laws

Fraction of a Number Rule: ab of n = (n ÷ b) × a

Word Problem Steps: Read → Identify → Calculate → Answer → Check

Context Recognition: Identify key information from the word problem.

Units Consistency: Maintain units throughout the problem-solving process.

Step-by-Step Method

  1. Read the problem carefully: Understand what is being asked
  2. Identify key information: Find the whole number and the fraction
  3. Determine the operation: Recognize that you need to find a fraction of a number
  4. Calculate: Apply the fraction of a number rule
  5. Answer the question: Provide the answer in the context of the problem
  6. Check your answer: Verify it makes sense in the context

Examples (Simple to Advanced)

Simple: "Sarah has 12 cookies. She gives 14 to her friend. How many does she give?" → 12 ÷ 4 × 1 = 3

Intermediate: "A class has 24 students. 23 are girls. How many girls are there?" → 24 ÷ 3 × 2 = 16

Advanced: "A store has 30 books. They sell 35 of them. How many remain?" → 30 ÷ 5 × 3 = 18 sold, so 30 - 18 = 12 remain

Tips, Tricks, and Common Pitfalls

Tips: Underline key numbers and fractions, draw pictures when needed.

Tricks: Look for clue words like "of", "part", "portion", "fraction", "share".

Common Pitfalls: Misreading the question, forgetting to answer in context, calculation errors.

Key Notes for Memorization

Memory Aid: "Read the story, find the numbers, do the math, answer the question!"

Visual Memory: Picture the problem situation before calculating.

Quick Check: Does your answer make sense in the real-world context?

Solution: Exercises 1 to 3
1 Food Sharing Problems
Exercise 1
Maria baked 16 cupcakes for her birthday party.
She ate 14 of the cupcakes herself. How many cupcakes did Maria eat?
Definition:

Food sharing problem: A real-world scenario where fractions represent parts of food items shared or consumed.

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Method for solving word problems:
  1. Read: Understand the situation (Maria has 16 cupcakes)
  2. Identify: Find the fraction (14) and whole number (16)
  3. Calculate: Apply the fraction rule: (16 ÷ 4) × 1 = 4
  4. Answer: State the answer in context (4 cupcakes)
Step 1: Identify total cupcakes: 16
Step 2: Find the fraction to eat: 14
Step 3: Calculate: (16 ÷ 4) × 1 = 4
Step 1: Read the problem

Maria has 16 cupcakes and eats 14 of them

Step 2: Identify the numbers

Whole number = 16, Fraction = 14

Step 3: Apply the formula

(16 ÷ 4) × 1 = 4 × 1 = 4

Maria ate 4 cupcakes
Final answer:

Maria ate 4 cupcakes

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Context preservation: Answer in terms of cupcakes

• Verification: 4 + 12 = 16, confirming the calculation

2 Population Problems
Exercise 2
A soccer team has 18 players.
If 23 of the players are boys, how many boys are on the team?
Definition:

Population problem: A real-world scenario where fractions represent parts of a group of people.

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Step 1: Identify total players: 18
Step 2: Find the fraction: 23
Step 3: Calculate: (18 ÷ 3) × 2 = 6 × 2 = 12
Step 1: Read the problem

There are 18 players total, 23 are boys

Step 2: Identify the numbers

Whole number = 18, Fraction = 23

Step 3: Apply the formula

(18 ÷ 3) × 2 = 6 × 2 = 12

Step 4: Answer in context

There are 12 boys on the team

12 boys are on the team
Final answer:

There are 12 boys on the team

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Context preservation: Answer in terms of players

• Verification: 12 + 6 = 18, confirming the calculation

3 Collection Problems
Exercise 3
Emma has 20 stickers in her collection.
She decides to give 34 of her stickers to her little sister. How many stickers does Emma give away?
Definition:

Collection problem: A real-world scenario where fractions represent parts of a collection of items.

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Step 1: Identify total stickers: 20
Step 2: Find the fraction: 34
Step 3: Calculate: (20 ÷ 4) × 3 = 5 × 3 = 15
Step 1: Read the problem

Emma has 20 stickers, gives away 34 of them

Step 2: Identify the numbers

Whole number = 20, Fraction = 34

Step 3: Apply the formula

(20 ÷ 4) × 3 = 5 × 3 = 15

Step 4: Answer in context

Emma gives away 15 stickers

Emma gives away 15 stickers
Final answer:

Emma gives away 15 stickers

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Context preservation: Answer in terms of stickers

• Verification: 15 + 5 = 20, confirming the calculation

Rules and methods, laws,...
ab of n = (n ÷ b) × a
Fraction of a Whole Number
Rule 1
12 of n = n ÷ 2
Half of a number
Rule 2
13 of n = n ÷ 3
Third of a number
Rule 3
nn of m = m
All of a number
Key definitions:

Numerator: The top number in a fraction (how many parts taken)

Denominator: The bottom number in a fraction (total equal parts)

Whole number: Any positive integer including zero

Context: The real-world situation described in the word problem

Complete methodology:
  1. Read carefully: Understand the situation and question
  2. Identify key info: Find the whole number and fraction
  3. Determine operation: Recognize it's a fraction of a number problem
  4. Calculate: Apply the fraction rule (divide by denominator, multiply by numerator)
  5. Answer in context: Provide answer using the problem's units
  6. Check reasonableness: Verify the answer makes sense
Tip 1: Underline important numbers and fractions in the problem.
Tip 2: Draw pictures or use objects to visualize the problem.
Tip 3: Always answer with the same units as the problem.
Tip 4: Check if your answer is reasonable compared to the original number.
Common errors: Misreading the problem, calculation mistakes, forgetting context.
Key insights: Word problems connect math to real life situations.
Formulas to know by heart:

• Fraction of a number: ab of n = (n ÷ b) × a

• Half of a number: 12 of n = n ÷ 2

• Third of a number: 13 of n = n ÷ 3

Solution: Exercises 4 to 5
4 Transportation Problems
Exercise 4
A school bus has 24 seats.
If 56 of the seats are occupied, how many seats are occupied?
Definition:

Transportation problem: A real-world scenario involving capacity and occupancy of vehicles.

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Step 1: Identify total seats: 24
Step 2: Find the fraction: 56
Step 3: Calculate: (24 ÷ 6) × 5 = 4 × 5 = 20
Step 1: Read the problem

The bus has 24 seats total, 56 are occupied

Step 2: Identify the numbers

Whole number = 24, Fraction = 56

Step 3: Apply the formula

(24 ÷ 6) × 5 = 4 × 5 = 20

Step 4: Answer in context

20 seats are occupied

20 seats are occupied
Final answer:

20 seats are occupied

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Context preservation: Answer in terms of seats

• Verification: 20 + 4 = 24, confirming the calculation

5 Shopping Problems
Exercise 5
A store received 30 boxes of toys.
They sold 25 of the boxes on the first day. How many boxes did they sell?
Definition:

Shopping problem: A real-world scenario involving inventory and sales of goods.

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Step 1: Identify total boxes: 30
Step 2: Find the fraction: 25
Step 3: Calculate: (30 ÷ 5) × 2 = 6 × 2 = 12
Step 1: Read the problem

The store has 30 boxes, sells 25 of them

Step 2: Identify the numbers

Whole number = 30, Fraction = 25

Step 3: Apply the formula

(30 ÷ 5) × 2 = 6 × 2 = 12

Step 4: Answer in context

The store sold 12 boxes

The store sold 12 boxes
Final answer:

The store sold 12 boxes

Applied rules:

• Fraction of a number rule: ab of n = (n ÷ b) × a

• Context preservation: Answer in terms of boxes

• Verification: 12 + 18 = 30, confirming the calculation

Questions & Answers

Question: Sometimes word problems have extra information that I don't need. How do I know what to use?

Answer: Good observation! Here's how to identify the important information:

  • Find the question: What are they asking you to find?
  • Look for numbers related to that question: Find the total amount and the fraction
  • Ignore unrelated details: Colors, names, or other facts not needed for the calculation

For example, if the question is "How many cupcakes did Maria eat?", you only need the total cupcakes and the fraction she ate. Details about the party theme or decorations aren't needed.

Question: My child struggles to identify whether to multiply or divide in word problems. Any suggestions?

Answer: For fraction of a number problems, the process is always the same:

  • First divide: Divide the whole number by the denominator
  • Then multiply: Multiply the result by the numerator

You can remember: "Divide by the bottom number, multiply by the top number." The fraction tells you to split into equal parts (divide) and then take some of those parts (multiply).

Practice with visual models to help build understanding before moving to abstract calculations.

Question: What if the word problem asks for how many are left after giving away a fraction?

Answer: That's a two-step problem! Here's how to solve it:

  1. Step 1: Find how many were given away using the fraction formula
  2. Step 2: Subtract that amount from the original number

For example, if you start with 20 items and give away 14:

  • Give away: (20 ÷ 4) × 1 = 5
  • Left over: 20 - 5 = 15

Always read the question carefully to know what it's asking for!