Fractions
Types of Fractions & Equivalent Fractions
A proper fraction has a numerator smaller than the denominator (¾). An improper fraction has a numerator equal to or larger than the denominator (5/4). A mixed fraction has a whole number and a fraction together (1¼).
Equivalent fractions show the same value, like ½ = 2/4 = 3/6. We get them by multiplying or dividing the numerator and denominator by the same number.
- Proper: numerator < denominator; improper: numerator ≥ denominator.
- Mixed = whole number + fraction.
- Equivalent fractions show the same value (½ = 2/4 = 3/6).
Comparing Fractions & Fraction of a Number
To compare fractions with unlike denominators, make the denominators the same and compare the numerators. To compare ⅔ and ¾, change both to twelfths: 8/12 and 9/12, so ¾ is bigger.
To find a fraction of a number, divide by the denominator and multiply by the numerator. ¾ of 12 = (12 ÷ 4) × 3 = 9.
- Make denominators equal, then compare numerators.
- Fraction of a number: divide by the denominator, multiply by the numerator.
Adding & Subtracting Fractions
To add or subtract like fractions, keep the denominator and work with the numerators: ⅗ + ⅕ = ⅘.
For unlike fractions where one denominator is a multiple of the other, change them to the same denominator first. ½ + ¼ = 2/4 + ¼ = ¾, and ⅚ − ⅓ = 5/6 − 2/6 = ½.
- Like fractions: keep the denominator, add/subtract numerators.
- Unlike fractions: make denominators the same first.