Fractions

A fraction shows part of a whole, written as numerator/denominator. The denominator says how many equal parts the whole is cut into; the numerator says how many of those parts you have. If you cut a chapati into 4 equal pieces and eat 3 of them, you have eaten 3/4 of the chapati.

Types of fractions you'll meet in CBC:

• A proper fraction has a numerator smaller than its denominator (3/4, 2/5). It is less than one whole.
• An improper fraction has a numerator equal to or larger than its denominator (5/4, 7/3). It is at least one whole.
• A mixed number is a whole number with a fraction next to it (1 1/4, 2 2/3). It is the same amount as an improper fraction, written differently.

You can convert between improper fractions and mixed numbers freely — they describe the same quantity. To go from improper to mixed, divide the numerator by the denominator: the quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.

Equivalent fractions are different ways to write the same value. Multiply (or divide) the numerator and denominator by the same number and the value doesn't change: 1/2 = 2/4 = 5/10 = 50/100. This single idea is the trick behind every other fraction operation.

To add or subtract fractions you need a common denominator. If the denominators differ, find the LCM (Least Common Multiple) of the two denominators, convert both fractions to equivalent fractions with that LCM as the new denominator, then add or subtract the numerators. The denominator stays the same in the answer.

To multiply fractions, multiply numerator × numerator and denominator × denominator. No common denominator needed.

To divide fractions, flip the second fraction (find its reciprocal) and multiply. The shortcut is "keep, change, flip": keep the first fraction, change ÷ to ×, flip the second.

Always simplify the final answer by dividing the top and bottom by the same number — keep going until they share no common factor other than 1. 4/8 is not wrong, but the marker wants 1/2.

Common mistakes to avoid:

• Adding numerators and denominators (1/2 + 1/3 is not 2/5). You must find a common denominator first.
• Forgetting to simplify the final answer.
• Mixing up multiplication and division. Divide is "flip and multiply", never "flip and divide".
• Multiplying just one part of an improper-to-mixed conversion — divide, don't multiply.

Fractions sit between decimals and percentages: 1/2 = 0.5 = 50%. The same value, three notations. CBC Grade 3 introduces halves and quarters with shapes; Grade 4 introduces equivalent fractions; Grade 5 covers operations with like denominators; Grade 6 brings all four operations with unlike denominators; Grade 7 uses fractions inside ratio, rate and percentage problems for KPSEA and Junior Secondary.