Number · StudentHub Lesson
Fractions and Ratios
Understand fractions as parts of a whole and ratios as comparisons between quantities.
What you will learn
- Explain what a fraction represents
- Identify numerator and denominator
- Simplify fractions to lowest terms
- Understand ratios as comparisons
- Convert between fractions and ratios in context
Watch the lesson
What Are Fractions? - Math Antics · mathantics
Watch on YouTubeTopic notes
Main Idea
A fraction represents a relationship between two numbers involving division: a part compared to a whole. A ratio compares two quantities directly.
Key Concepts
- Fractions have a numerator (top, part) and denominator (bottom, whole)
- Equivalent fractions represent the same value with different numbers
- Ratios compare two or more quantities, written as a:b
- Simplifying means dividing by the greatest common factor
Definitions
- Numerator: the top number of a fraction, showing parts taken
- Denominator: the bottom number, showing total equal parts
- Ratio: a comparison of two numbers by division
Formulas
- Simplify: divide numerator and denominator by their GCF
- Ratio a:b equals fraction a/b
Examples
- 6/8 simplifies to 3/4 (divide by 2)
- A ratio of 3:2 apples to oranges means for every 3 apples there are 2 oranges
Common Mistakes
- Confusing numerator and denominator
- Not fully simplifying fractions
- Treating ratios like subtraction instead of comparison by division
Key concepts
Important terms
- Numerator
- Top number of a fraction representing parts.
- Denominator
- Bottom number of a fraction representing the whole.
- Ratio
- A comparison of two quantities by division.
Worked examples
Problem
Simplify 8/12
- 1. Find GCF of 8 and 12, which is 4
- 2. Divide numerator and denominator by 4
- 3. 8/4=2, 12/4=3
Answer: 2/3
Problem
Write the ratio of 4 red balls to 6 blue balls in simplest form
- 1. Write as 4:6
- 2. Divide both by GCF 2
- 3. Result 2:3
Answer: 2:3
Quick revision
- Numerator is on top, denominator on the bottom
- Simplify using the GCF
- Ratios compare quantities
- a:b can be written as the fraction a/b
- Equivalent fractions have the same value
- Always simplify the final ratio
Check your understanding
Question 1 · Multiple choice
What is the simplified form of 10/15?
Question 2 · Multiple choice
In the fraction 3/7, what is the denominator?
Question 3 · Short answer
Simplify the ratio 12:18
Question 4 · Short answer
Convert the ratio 5:4 into a fraction.
Question 5 · True or false
A fraction is always a comparison between a part and a whole.
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