Fractions and Mixed Numbers
Fraction = Part / Whole
Fraction Concept
3
4
Three Fourths
1
1
2
Numerator
Top Number
Denominator
Bottom Number
Mixed Number
Whole + Fraction
Definition:
Fraction: A number representing part of a whole
Tip: Top number is how many parts you have.
Tip: Bottom number is how many equal parts make the whole.
Multi-Step Fraction Problems with Solutions
1 Basic Fraction Problem
Problem 1
Sarah ate 1/4 of a pizza. Then she ate another 1/4 of the same pizza. How much of the pizza did Sarah eat in total?
Definition:
Adding Fractions: When denominators are the same, add numerators
Method:
- Identify fractions with the same denominator
- Add the numerators
- Keep the denominator the same
1
First, Sarah ate 1/4 of the pizza
2
Then, she ate another 1/4 of the pizza
3
Add the fractions: 1/4 + 1/4 = 2/4
4
Simplify: 2/4 = 1/2
1
4
+
1
4
=
2
4
=
1
2
1/4 + 1/4 = 2/4 = 1/2
Final answer:
Sarah ate 1/2 of the pizza in total.
2 Mixed Number Problem
Problem 2
Tom walked 1 1/2 miles in the morning. He walked another 1/2 mile in the evening. How far did Tom walk in total?
1
Tom walked 1 1/2 miles in the morning
2
He walked 1/2 mile in the evening
3
Add: 1 1/2 + 1/2 = 1 + 1/2 + 1/2
4
Combine fractions: 1/2 + 1/2 = 2/2 = 1
5
Total: 1 + 1 = 2 miles
1
1
2
+
1
2
=
2
1 1/2 + 1/2 = 2 miles
Final answer:
Tom walked 2 miles in total.
3 Complex Fraction Problem
Problem 3
A recipe calls for 2 1/3 cups of flour. If you want to make half the recipe, how much flour do you need?
1
The full recipe needs 2 1/3 cups of flour
2
We want half of that amount
3
Convert mixed number to improper fraction: 2 1/3 = 7/3
4
Multiply by 1/2: 7/3 × 1/2 = 7/6
5
Convert back to mixed number: 7/6 = 1 1/6
2
1
3
× 1/2 =
7
3
× 1/2 =
7
6
=
1
1
6
2 1/3 × 1/2 = 1 1/6 cups
Final answer:
You need 1 1/6 cups of flour for half the recipe.
Fraction Rules and Methods
a/b + c/b = (a+c)/b
Fraction Addition
Key definitions:
Fraction: A number representing part of a whole
Numerator: The top number in a fraction
Denominator: The bottom number in a fraction
Mixed Number: A combination of a whole number and a fraction
Multi-Step Fraction Method:
- READ: Understand what the problem is asking
- IDENTIFY: Find the fractions involved
- OPERATION: Determine if you need to add, subtract, multiply, or divide
- SOLVE: Perform the operation step by step
- VERIFY: Check if your answer makes sense
Tip 1: When adding fractions with same denominator, add numerators.
Tip 2: Convert mixed numbers to improper fractions to make calculations easier.
Tip 3: Always simplify your final answer if possible.
Tip 4: Draw pictures to visualize the problem if needed.
Key insight: Fractions represent equal parts of a whole.
Memory trick: "Same bottom, add tops" for fraction addition.
Essential rules:
• When adding fractions with the same denominator, add numerators only
• To convert mixed numbers to improper fractions: (whole × denominator) + numerator
• Always simplify fractions to lowest terms when possible
• Check if your answer is reasonable in the context of the problem
• Visual representations can help understand the problem