By Tuesday Fuller – Updated Aug 30, 2022
Fractions appear everywhere—from pizza slices to financial calculations. Understanding them is essential for everyday decision‑making and advanced math. This guide presents adult‑friendly explanations, practical examples, and clear steps to master fractions confidently.
Step 1: Notice the slash (/) that separates the two numbers. It’s called a solidus.
Step 2: The number on the left is the numerator—the part of the whole you’re considering.
Step 3: The number on the right is the denominator—the total number of equal parts that make up the whole.
Step 1: Review these examples: 1/2, 6/5, 1 1/5, 17/1.
Step 2: Proper fraction: numerator < denominator (e.g., 1/2).
Step 3: Improper fraction: numerator > denominator (e.g., 6/5). It can be rewritten as a mixed number.
Step 4: Mixed number: a whole number plus a proper fraction (e.g., 1 1/5). Its improper form is 6/5.
Step 5: Whole numbers are fractions with an invisible denominator of 1 (e.g., 17/1).
Same Denominator
Step 1: 3/7 + 2/7 = (3 + 2)/7 = 5/7.
Step 2: 9/10 – 8/10 = (9 – 8)/10 = 1/10.
Different Denominators
Step 3: 2/5 + 4/7 – find the least common multiple (LCM) of 5 and 7, which is 35.
Step 4: Convert: 2/5 = 14/35 (2 × 7), 4/7 = 20/35 (4 × 5).
Step 5: Add: 14/35 + 20/35 = 34/35.
Subtracting with Different Denominators
Step 6: 6/8 – 9/10 – LCM of 8 and 10 is 40.
Step 7: Convert: 6/8 = 30/40, 9/10 = 36/40.
Step 8: Subtract: 30/40 – 36/40 = ‑6/40 = ‑3/20 after simplification.
Multiplication
Step 1: 3/4 × 1/2 = (3 × 1)/(4 × 2) = 3/8.
Division
Step 2: 4/9 ÷ 2/3 – flip the divisor to get its reciprocal: 3/2.
Step 3: Multiply: 4/9 × 3/2 = 12/18 = 2/3 after reducing.
Step 1: Compare 6/11 and 3/12 using cross‑multiplication.
Step 2: 6 × 12 = 72; 3 × 11 = 33. Since 72 > 33, 6/11 is larger than 3/12.
Decimal
Step 1: 8/9 = 0.888… (repeating).
Mixed Number
Step 2: 10/7 = 1 3/7 (1 whole, remainder 3).
Improper Fraction
Step 3: 5 9/10 = (5 × 10 + 9)/10 = 59/10.
Percent
Step 4: 3/4 = 0.75 = 75%.
