askvity

How Do You Solve Mixed Fractions With Mixed Fractions?

Published in Fractions Arithmetic 2 mins read

Solving problems involving mixed fractions with mixed fractions depends on the operation (addition, subtraction, multiplication, or division). Here's a breakdown of the methods:

Addition and Subtraction

  1. Convert Mixed Fractions to Improper Fractions: This is the most reliable method. An improper fraction has a numerator larger than or equal to the denominator. To convert a mixed fraction to an improper fraction:

    • Multiply the whole number by the denominator.
    • Add the numerator to the result.
    • Place the sum over the original denominator.

    For example, convert 2 3/11 to an improper fraction:
    (2 * 11) + 3 = 25
    So, 2 3/11 = 25/11

  2. Find a Common Denominator: If the fractions have different denominators, find the least common multiple (LCM) of the denominators. This will be the new common denominator.

  3. Make Equivalent Fractions: Convert each fraction to an equivalent fraction with the common denominator. Do this by multiplying both the numerator and denominator of each fraction by the factor needed to get the common denominator.

  4. Add or Subtract the Numerators: Add or subtract the numerators, keeping the common denominator.

  5. Simplify the Result: If the resulting fraction is improper, convert it back to a mixed fraction. Simplify the fraction if possible by dividing both the numerator and denominator by their greatest common factor (GCF).

Example (Addition): 2 3/11 + 1 1/2

  1. Convert to improper fractions: 2 3/11 = 25/11 and 1 1/2 = 3/2
  2. Find the common denominator: The LCM of 11 and 2 is 22.
  3. Make equivalent fractions: 25/11 = 50/22 and 3/2 = 33/22
  4. Add numerators: 50/22 + 33/22 = 83/22
  5. Simplify: 83/22 = 3 17/22

Example (Subtraction): 5 1/4 - 2 2/3

  1. Convert to improper fractions: 5 1/4 = 21/4 and 2 2/3 = 8/3
  2. Find the common denominator: The LCM of 4 and 3 is 12.
  3. Make equivalent fractions: 21/4 = 63/12 and 8/3 = 32/12
  4. Subtract numerators: 63/12 - 32/12 = 31/12
  5. Simplify: 31/12 = 2 7/12

Multiplication and Division

  1. Convert Mixed Fractions to Improper Fractions: As with addition and subtraction, begin by converting mixed fractions to improper fractions.

  2. Multiply (or Divide) the Fractions:

    • Multiplication: Multiply the numerators together and the denominators together.
    • Division: Invert the second fraction (the divisor) and multiply. This is the same as multiplying by the reciprocal.

  3. Simplify the Result: Convert the resulting improper fraction back to a mixed fraction and simplify if possible.

Example (Multiplication): 1 1/2 * 2 2/3

  1. Convert to improper fractions: 1 1/2 = 3/2 and 2 2/3 = 8/3
  2. Multiply: (3/2) * (8/3) = 24/6
  3. Simplify: 24/6 = 4

Example (Division): 3 1/2 ÷ 1 3/4

  1. Convert to improper fractions: 3 1/2 = 7/2 and 1 3/4 = 7/4
  2. Invert and Multiply: (7/2) ÷ (7/4) = (7/2) * (4/7) = 28/14
  3. Simplify: 28/14 = 2

Related Articles