Understanding Fractions
Master the fundamentals of fractions - the building blocks for all fraction operations on the ParaPro math test.
What You'll Learn
- β Parts of a fraction (numerator and denominator)
- β Types of fractions (proper, improper, mixed numbers)
- β Finding equivalent fractions
- β Simplifying fractions to lowest terms
- β Comparing and ordering fractions
What is a Fraction?
A fraction represents a part of a whole. It consists of two numbers separated by a line:
Top number - parts we have
Bottom - total equal parts
Visual Example
Think of a pizza cut into 4 equal slices. If you eat 3 slices, you've eaten 3/4 of the pizza.
3 out of 4 slices = 3/4
Types of Fractions
Proper Fractions
Numerator < Denominator
Value is less than 1
Improper Fractions
Numerator β₯ Denominator
Value is 1 or greater
Mixed Numbers
Whole number + fraction
Combination form
Converting Between Improper Fractions and Mixed Numbers
Improper β Mixed
Divide numerator by denominator
7/4 = 7 Γ· 4 = 1 R 3
= 1 3/4
Mixed β Improper
Multiply whole Γ denominator + numerator
2 3/5 = (2 Γ 5 + 3)/5
= 13/5
Equivalent Fractions
Equivalent fractions are different fractions that represent the same value. To create equivalent fractions, multiply or divide both the numerator and denominator by the same number.
Example: Equivalent Fractions for 1/2
All these fractions equal 0.5 or 50%
The Golden Rule
Whatever you do to the numerator, you must do to the denominator.
Multiply by 3:
2/5 = (2Γ3)/(5Γ3) = 6/15
Divide by 2:
8/12 = (8Γ·2)/(12Γ·2) = 4/6
Simplifying Fractions
A fraction is in simplest form (lowest terms) when the numerator and denominator have no common factors other than 1.
Steps to Simplify
- 1 Find the Greatest Common Factor (GCF) of numerator and denominator
- 2 Divide both numerator and denominator by the GCF
- 3 Check that no common factors remain
Example: Simplify 12/18
Step 1: Find GCF of 12 and 18
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
GCF = 6
Step 2: Divide both by 6
12/18 = (12Γ·6)/(18Γ·6) = 2/3
Comparing Fractions
Same Denominator
Compare numerators directly
3/8 < 5/8
Because 3 < 5
Different Denominators
Cross multiply to compare
2/3 vs 3/4
2Γ4=8, 3Γ3=9 β 2/3 < 3/4
Practice Problems
1. Convert 15/4 to a mixed number
Show Answer
15 Γ· 4 = 3 R 3, so 3 3/4
2. Convert 2 5/6 to an improper fraction
Show Answer
(2 Γ 6 + 5)/6 = 17/6
3. Simplify 24/36
Show Answer
GCF = 12, so 24/36 = 2/3
4. Which is larger: 3/5 or 4/7?
Show Answer
Cross multiply: 3Γ7=21, 4Γ5=20. Since 21 > 20, 3/5 > 4/7
Key Takeaways
- β Numerator = parts you have, Denominator = total equal parts
- β Proper fractions are less than 1, improper are 1 or greater
- β Equivalent fractions have the same value with different numbers
- β To simplify, divide by the GCF
- β Cross-multiply to compare fractions with different denominators
Related Lessons
Ready for the Next Lesson?
Now that you understand fraction basics, learn how to add and subtract fractions!