How to Calculate Fractions (The Ultimate Guide)
Fractions represent parts of a whole. While calculators make the math instant, understanding the core concepts of fractions is essential for middle school math, standardized tests (like the SAT), and real-world baking or construction.
Adding and Subtracting Fractions
To add or subtract fractions, they must have a common denominator (the bottom number). If they don't, you must find the Least Common Multiple (LCM). For example, to add 1/4 and 1/3, the LCM of 4 and 3 is 12. Convert them to 3/12 + 4/12, which equals 7/12.
Multiplying and Dividing Fractions
Multiplication is simple: multiply the numerators straight across, and the denominators straight across. (e.g., 1/2 × 3/4 = 3/8).
For division, use the "Keep-Change-Flip" rule. Keep the first fraction, change the division sign to multiplication, and flip the second fraction upside down. (e.g., 1/2 ÷ 3/4 becomes 1/2 × 4/3 = 4/6, which simplifies to 2/3).
Simplifying Fractions
Always reduce your final answer to its lowest terms. Find the Greatest Common Factor (GCF) of both the numerator and denominator, and divide both by that number. For instance, in 8/12, the GCF is 4. Dividing both by 4 yields 2/3.