Understanding Fractions

Learn what fractions represent and how to compare them

Understanding Fractions

What is a Fraction?

A fraction represents a part of a whole. It has two parts:

numeratordenominator\frac{\text{numerator}}{\text{denominator}}

  • Numerator: The top number (how many parts we have)
  • Denominator: The bottom number (how many equal parts in the whole)

Example: 34\frac{3}{4} means 3 parts out of 4 equal parts

Types of Fractions

Proper Fraction

Numerator is less than denominator: 25\frac{2}{5}, 710\frac{7}{10}

Improper Fraction

Numerator is greater than or equal to denominator: 74\frac{7}{4}, 99\frac{9}{9}

Mixed Number

A whole number and a fraction: 2132\frac{1}{3}, 5385\frac{3}{8}

Comparing Fractions

Same Denominator

Compare the numerators: 38<58\frac{3}{8} < \frac{5}{8}

Different Denominators

Find a common denominator first, then compare

Equivalent Fractions

Fractions that represent the same value: 12=24=36=48\frac{1}{2} = \frac{2}{4} = \frac{3}{6} = \frac{4}{8}

Multiply or divide both numerator and denominator by the same number.

📚 Practice Problems

1Problem 1easy

❓ Question:

Convert the improper fraction 114\frac{11}{4} to a mixed number.

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Solution:

Divide the numerator by the denominator: 11÷4=2 remainder 311 \div 4 = 2 \text{ remainder } 3

This means:

  • Whole number: 2
  • Numerator of fraction: 3 (remainder)
  • Denominator stays: 4

Answer: 114=234\frac{11}{4} = 2\frac{3}{4}

2Problem 2medium

❓ Question:

Which is greater: 56\frac{5}{6} or 79\frac{7}{9}?

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Solution:

Find a common denominator (LCM of 6 and 9 is 18):

56=5×36×3=1518\frac{5}{6} = \frac{5 \times 3}{6 \times 3} = \frac{15}{18}

79=7×29×2=1418\frac{7}{9} = \frac{7 \times 2}{9 \times 2} = \frac{14}{18}

Compare: 1518>1418\frac{15}{18} > \frac{14}{18}

Answer: 56\frac{5}{6} is greater

3Problem 3hard

❓ Question:

Order from least to greatest: 23\frac{2}{3}, 58\frac{5}{8}, 34\frac{3}{4}

💡 Show Solution

Solution:

Find a common denominator (LCM of 3, 8, and 4 is 24):

23=1624\frac{2}{3} = \frac{16}{24}

58=1524\frac{5}{8} = \frac{15}{24}

34=1824\frac{3}{4} = \frac{18}{24}

Order: 1524<1624<1824\frac{15}{24} < \frac{16}{24} < \frac{18}{24}

Answer: 58,23,34\frac{5}{8}, \frac{2}{3}, \frac{3}{4}

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