What fraction of the pizza did Emma eat?
What fraction of the pizza did Emma and her brother eat together?
Word Problem: 6 slices total, Emma ate 2, brother ate 1.
Word problem: A math problem presented in a real-life story format that requires mathematical thinking to solve.
- Read the problem carefully
- Identify the total amount (denominator)
- Identify the part(s) being used (numerator)
- Write the fraction as part/total
- Solve the specific question asked
The pizza has 6 equal slices (total = 6)
Emma ate 2 slices
Emma's part over total = 2/6
Emma ate 2 + brother ate 1 = 3 slices total
Together over total = 3/6
Emma ate 2/6 of the pizza. Emma and her brother ate 3/6 of the pizza together.
• Word problems: Extract numbers and relationships
• Addition: Combine parts to find total
• Same denominator: Parts come from same whole
What fraction of the apple halves did she give away?
What fraction of the apple halves are left?
Word Problem: 4 apples × 2 halves each = 8 halves total, 3 given away.
Multiplication in word problems: When we have multiple groups of the same size, we multiply.
4 apples × 2 halves each = 8 apple halves
3 halves were given away
Given over total = 3/8
Remaining = 8 - 3 = 5 halves
Remaining over total = 5/8
She gave away 3/8 of the apple halves. 5/8 of the apple halves are left.
• Multiplication: Groups × items per group = total
• Subtraction: Total - given away = remaining
• Fraction: Part over whole
What fraction of the bags did she sell?
What fraction of the cookies did she sell?
Word Problem: 3 bags total, 2 sold. Each bag has 4 cookies (12÷3).
Division in word problems: When we split a total into equal groups, we divide.
Sarah made 3 equal bags
She sold 2 bags
Bags sold over total bags = 2/3
12 cookies ÷ 3 bags = 4 cookies per bag
2 bags × 4 cookies per bag = 8 cookies sold
Cookies sold over total cookies = 8/12 = 2/3
She sold 2/3 of the bags. She sold 8/12 (or 2/3) of the cookies.
• Division: Total ÷ number of groups = items per group
• Multiplication: Groups × items per group = total items
• Equivalent fractions: 8/12 = 2/3
Definitions:
Word problem: A math problem presented in a real-life story format that requires mathematical thinking to solve.
Fraction: A number that shows part of a whole. It has a top number (numerator) and bottom number (denominator).
Numerator: The top number showing how many parts we have or take.
Denominator: The bottom number showing how many equal parts there are in total.
Equal parts: All sections must be the same size for valid fractions.
Multiplication in word problems: When we have multiple groups of the same size.
Division in word problems: When we split a total into equal groups.
Core Rules:
1. Read the problem carefully
2. Identify the total amount (denominator)
3. Identify the part being used (numerator)
4. All parts must be equal in size
5. Fraction = numerator/denominator
6. Multiplication: groups × items per group = total
7. Division: total ÷ groups = items per group
Step-by-Step Method:
Step 1: Read the word problem carefully
Step 2: Identify what the total is (denominator)
Step 3: Identify what the part is (numerator)
Step 4: Check if parts are equal
Step 5: Write the fraction as part/total
Step 6: Answer the specific question asked
Step 7: Verify your answer makes sense
Examples:
Simple: 2 slices out of 6 pizza slices = 2/6
Medium: 3 apple halves out of 8 halves = 3/8
Advanced: 2 bags out of 3 bags = 2/3
Tips:
- Read the problem twice to understand it
- Underline important numbers
- Draw pictures to visualize
- Check if parts are equal
- Make sure the fraction makes sense
- Practice with real-life scenarios
Key Notes:
- Word problems connect math to real life
- Always identify what the "whole" is first
- Look for words like "each," "per," "out of" to identify relationships
- Practice helps build problem-solving skills
8 pieces, 3 eaten
5 apples, 2 halved
10 cookies, 4 bags
6 slices, 2 friends
What fraction of the juice cups did the teacher drink?
What fraction of the juice cups were given to students?
What fraction of the juice cups are left?
Word Problem: 8 cups total, 1 to teacher, 3 to students.
Multiple operations: Word problems that require multiple steps to solve, including addition and subtraction.
There were 8 cups of juice prepared (total = 8)
Teacher drank 1 cup, so fraction = 1/8
Students got 3 cups, so fraction = 3/8
Used = 1 (teacher) + 3 (students) = 4 cups
Left = 8 - 4 = 4 cups
Left over total = 4/8 = 1/2
The teacher drank 1/8 of the juice cups. Students received 3/8 of the juice cups. 4/8 (or 1/2) of the juice cups are left.
• Multiple fractions: Same denominator for comparison
• Addition: Combine different uses of the same resource
• Subtraction: Find remaining after use
What fraction of the candy did each friend receive?
What fraction of the candy did Tom keep for himself?
Word Problem: 15 candies, 3 friends, 3 kept by Tom.
Equal sharing: Distributing items equally among a group, requiring division.
Total = 15, Tom keeps 3, so shared = 15 - 3 = 12 candies
12 candies ÷ 3 friends = 4 candies per friend
Each friend gets 4 out of 15 total = 4/15
Tom keeps 3 out of 15 total = 3/15
Friends get: 3 × 4 = 12, Tom keeps: 3, Total: 12 + 3 = 15 ✓
Each friend received 4/15 of the candy. Tom kept 3/15 of the candy for himself.
• Division: Total ÷ number of recipients = amount per recipient
• Subtraction: Remove reserved amount from total
• Verification: Ensure all parts add up to original total
Word problem: A math problem presented in a real-life story format
Numerator: Top number showing parts we have/use
Denominator: Bottom number showing total parts
Equal parts: All sections must be the same size
Problem solving: Systematic approach to finding solutions
- Read carefully: Understand the story situation
- Identify key information: Numbers and relationships
- Determine the operation: What needs to be calculated
- Set up the fraction: Part over total
- Calculate: Perform the necessary math
- Verify: Check if answer makes sense
• Read carefully: Understand the full context
• Identify total: Find the denominator
• Find part: Identify the numerator
• Equal parts: Required for valid fractions
• Multiple steps: Some problems require several calculations
• Verification: Check if answer is reasonable