Fractions and Operations
"Add, subtract, and discover equivalent parts with like denominators."
A Today you'll learn
- Understand equivalent fractions and simplify fractions to lowest terms
- Add and subtract like fractions and solve word problems
- Convert between improper fractions and mixed numbers
B Let's understand
Fractions describe parts of a whole. Equivalent fractions are fractions that represent the exact same value or proportion even though they look different (for example, 1/2 = 2/4 = 3/6 = 4/8). You find equivalent fractions by multiplying or dividing both the numerator and denominator by the same non-zero number. When fractions have the same denominator (like fractions), adding or subtracting them is straightforward: simply add or subtract the numerators while keeping the denominator unchanged: 2/7 + 3/7 = 5/7. A fraction where the numerator is greater than or equal to the denominator is called an improper fraction (like 7/4), which can also be expressed as a mixed number (1 3/4).
C See it step by step
- Multiply numerator and denominator by 2: (3 × 2) / (5 × 2) = 6/10.
- Multiply numerator and denominator by 3: (3 × 3) / (5 × 3) = 9/15.
- Two equivalent fractions are 6/10 and 9/15.
- Divide the numerator by the denominator: 11 ÷ 4 = 2 with a remainder of 3.
- The quotient (2) becomes the whole number.
- The remainder (3) becomes the new numerator, keeping the same denominator (4).
- Mixed number: 2 3/4.
D Your turn
E Ready to practise?
Equivalent fractions have equal values
Equivalent fractions have equal values: multiply or divide top and bottom by the same number.
To add/subtract like fractions
To add/subtract like fractions, operate on numerators only: a/c + b/c = (a+b)/c.
Key idea 3
A proper fraction has a numerator smaller than its denominator (e.g., 3/8).
Key idea 4
An improper fraction has a numerator equal to or greater than its denominator (e.g., 9/5).
Key idea 5
A mixed number combines a whole number and a proper fraction (e.g., 1 4/5).