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Perform addition, subtraction, multiplication, and division with fractions and mixed numbers.

Computing with Parts: Fraction Operations

Fraction operations β€” addition, subtraction, multiplication, and division β€” extend the four basic arithmetic operations to numbers expressed as parts of a whole. Mastering these operations lets students combine measurements, scale recipes, split quantities, and solve equations that involve non-whole amounts.

Components of Fraction Operations

This section covers the four operations with fractions:

  • Adding Fractions: Find a common denominator, add the numerators, and simplify the result.
  • Subtracting Fractions: Find a common denominator, subtract the numerators, and simplify.
  • Multiplying Fractions: Multiply numerators together and denominators together, then simplify.
  • Dividing Fractions: Multiply by the reciprocal of the divisor (flip and multiply), then simplify.

Examples of Fraction Operations

Adding Fractions Examples

  • Add 1/4 + 2/4: Same denominator, so add numerators: 1 + 2 = 3, giving 3/4.
  • Add 2/3 + 1/5: The LCM of 3 and 5 is 15, so rewrite as 10/15 + 3/15 = 13/15.
  • A trail mix recipe uses 1/3 cup of nuts and 1/6 cup of raisins. Rewrite 1/3 as 2/6, then add 2/6 + 1/6 = 3/6, which simplifies to 1/2 cup total.

Subtracting Fractions Examples

  • Subtract 5/8 - 3/8: Same denominator, so 5 - 3 = 2, giving 2/8, which simplifies to 1/4.
  • Subtract 3/4 - 1/3: The LCM of 4 and 3 is 12, so rewrite as 9/12 - 4/12 = 5/12.
  • A water bottle was 7/10 full and you drank 2/5. Rewrite 2/5 as 4/10, then 7/10 - 4/10 = 3/10 remaining.

Multiplying Fractions Examples

  • Multiply 2/3 Γ— 4/5: Multiply numerators 2 Γ— 4 = 8 and denominators 3 Γ— 5 = 15, giving 8/15.
  • Multiply 3/4 Γ— 2/9: Multiply to get 6/36, then simplify by dividing both by 6 to get 1/6.
  • A garden plot is 3/4 acre, and you plant flowers on 2/3 of it. The flower area is 3/4 Γ— 2/3 = 6/12 = 1/2 acre.

Dividing Fractions Examples

  • Divide 3/4 Γ· 1/2: Flip the second fraction and multiply, 3/4 Γ— 2/1 = 6/4, which simplifies to 3/2 or 1 1/2.
  • Divide 5/6 Γ· 2/3: Flip and multiply, 5/6 Γ— 3/2 = 15/12, which simplifies to 5/4 or 1 1/4.
  • A board 7/8 meter long is cut into pieces of 1/4 meter each. Divide 7/8 Γ· 1/4 = 7/8 Γ— 4/1 = 28/8 = 3 1/2 pieces.