Class Notes: Finding Equivalent Fractions

Objective

Learn how to find equivalent fractions by determining the missing number in a given fraction.

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Key Concepts

• Equivalent fractions: Fractions that have the same value, even though they may look different.
• To make two fractions equivalent, multiply (or divide) both the numerator and denominator by the same number.

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Steps to Find the Missing Number

1. Determine what you multiply or divide the known part of one fraction to get the corresponding part of the other fraction.
2. Apply the same operation to the other part of the fraction to find the missing number.
3. Make sure you do the same operation to both the numerator and denominator.

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Example Problems & Solutions

Example 1

• Problem: Find the missing number in (\frac{4}{5} = \frac{?}{20})
• Solution:
  • (5 \times ? = 20 \Rightarrow 20 / 5 = 4)
  • Multiply numerator by 4: (4 \times 4 = 16)
  • Equivalent fraction: (\frac{16}{20})

Example 2

• Problem: Find the missing numerator in (\frac{7}{15} = \frac{?}{21})
• Solution:
  • (21 / 7 = 3)
  • Multiply numerator and denominator by 3: ((7 \times 3) = 21), ((15 \times 3) = 45)
  • Equivalent fraction: (\frac{15}{21})

Example 3

• Problem: Find the missing denominator in (\frac{2}{5} = \frac{6}{?})
• Solution:
  • (6 / 2 = 3)
  • Multiply denominator by 3: (5 \times 3 = 15)
  • Equivalent fraction: (\frac{6}{15})

Example 4

• Problem: Find the missing denominator in (\frac{5}{8} = \frac{30}{?})
• Solution:
  • (30 / 5 = 6)
  • Multiply denominator by 6: (8 \times 6 = 48)
  • Equivalent fraction: (\frac{30}{48})

Example 5 (missing on left)

• Problem: Find the missing numerator in (\frac{?}{14} = \frac{18}{42})
• Solution:
  • (42 / 14 = 3)
  • (18 / 3 = 6)
  • Equivalent fraction: (\frac{6}{14})

Example 6 (missing on left)

• Problem: Find the missing numerator in (\frac{?}{9} = \frac{28}{36})
• Solution:
  • (36 / 9 = 4)
  • (28 / 4 = 7)
  • Equivalent fraction: (\frac{7}{9})

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Summary

• To find a missing value in equivalent fractions:
  • Find the multiplication or division factor between the numerators or denominators.
  • Apply the same factor to the missing part.
• This method ensures both fractions represent the same value.