How to Subtract Mixed Numbers?

Subtracting mixed numbers might seem tricky at first, but with a few steps, it becomes straightforward. Let’s break it down.

Step-by-Step Guide

  1. Convert Mixed Numbers to Improper Fractions
    Mixed numbers consist of a whole number and a fraction. To subtract them, first convert each mixed number to an improper fraction. An improper fraction has a numerator larger than its denominator. For example, to convert
    $2frac{3}{4}$:

    1. Multiply the whole number by the denominator: $2 times 4 = 8$
    2. Add the numerator to the result: $8 + 3 = 11$
    3. Place the result over the original denominator: $frac{11}{4}$

  1. Find a Common Denominator
    To subtract fractions, they must have the same denominator. If the fractions already share a denominator, you can skip this step. Otherwise, find the least common denominator (LCD). For instance, if subtracting $frac{11}{4}$ and $frac{5}{6}$, the LCD of 4 and 6 is 12.

  1. Convert Fractions to Equivalent Fractions
    Convert each fraction to an equivalent fraction with the LCD as the new denominator:

    • For $frac{11}{4}$: $frac{11 times 3}{4 times 3} = frac{33}{12}$
    • For $frac{5}{6}$: $frac{5 times 2}{6 times 2} = frac{10}{12}$

  1. Subtract the Numerators
    Now that the fractions have the same denominator, subtract the numerators:
    $frac{33}{12} – frac{10}{12} = frac{23}{12}$

  1. Simplify the Result
    If the resulting fraction is improper, convert it back to a mixed number:

    • Divide the numerator by the denominator: $23 div 12 = 1$ remainder $11$
    • The quotient is the whole number, and the remainder is the new numerator: $1frac{11}{12}$

Example Problem

Let’s subtract $3frac{2}{5}$ from $5frac{3}{10}$:

  1. Convert to improper fractions:
    • $5frac{3}{10} = frac{53}{10}$
    • $3frac{2}{5} = frac{17}{5} = frac{34}{10}$
  2. Find the common denominator (which is 10 here).
  3. Convert to equivalent fractions:
    • $frac{53}{10}$ (already has the common denominator)
    • $frac{34}{10}$ (already has the common denominator)
  4. Subtract the numerators:
    • $frac{53}{10} – frac{34}{10} = frac{19}{10}$
  5. Simplify the result:
    • $frac{19}{10} = 1frac{9}{10}$

Conclusion

Subtracting mixed numbers involves converting them to improper fractions, finding a common denominator, subtracting, and simplifying the result. With practice, these steps become second nature, making the process much easier.

Citations

  1. 1. Khan Academy – Subtracting Mixed Numbers
  2. 2. Math is Fun – Mixed Numbers
  3. 3. Purplemath – Mixed Numbers

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