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A mixed number is a combination of two numbers: a whole number and a proper fraction (A proper fraction is a fraction which has a denominator that is greater than the numerator, i.e., \(\frac{3}{9}\), \(\frac{7}{19}\), etc.). Moreover, a mixed number can be converted into a fraction and it always lies between two whole numbers.

For example, let’s take the mixed number \(3 \frac{1}{6}\). This mixed number comprises two parts: a whole number which is 3 and a proper fraction which is \(\frac{1}{6}\). If we convert this mixed number into an improper fraction, which is \(\frac{19}{6}\), we find that it lies between the two whole numbers 3 and 4. Some other examples of a mixed number are \(2 \frac{1}{3}\), \(3 \frac{1}{3}\), \(4 \frac{1}{3}\), etc.

Parts of a Mixed Number

A mixed number consists of three distinct parts: a whole number, a numerator, and a denominator. Here, the numerator and the denominator are parts of the proper fraction.

How to Convert Improper Fractions to Mixed Fractions

  1. First, we need to divide the numerator of the fraction by the denominator.
  2. Next, we need to write down the quotient as the whole number of the mixed fraction.
  3. Now, the remainder becomes the numerator and the divisor becomes the denominator of the improper part.

For example, let’s take the improper fraction \(\frac{7}{2}\). When we divide 7 by 2, the quotient is 3. The remainder is 1, and the divisor is 2. So, the mixed number is \(3 \frac{1}{2}\).

Steps to Subtract Mixed Numbers

  1. First, subtract the whole parts separately and the fractional parts separately.
  2. Next, simplify your answer and write it in the lowest terms.

For example, let’s subtract \(4 \frac{1}{3} – 2 \frac{1}{5}\). So, now the subtraction is like \( \left(4 – 2\right) + \left(\frac{1}{3} – \frac{1}{5}\right) = 2 + \left(\frac{1 \cdot 5 – 1 \cdot 3}{3 \cdot 5}\right) = 2 + \frac{5 – 3}{15} = 2 + \frac{2}{15} = 2 \frac{2}{15}\).

Exercises for Subtracting Mixed Numbers

  1. \( 8 \frac{6}{8} – 7 \frac{2}{5} = \)
  2. \( 5 \frac{3}{4} – 4 \frac{2}{3} = \)
  3. \( 7 \frac{6}{7} – 5 \frac{5}{8} = \)
  4. \( 6 \frac{5}{8} – 1 \frac{1}{3} = \)
  5. \( 10 \frac{3}{10} – 2 \frac{3}{7} = \)
  6. \( 6 \frac{3}{5} – 5 \frac{1}{2} = \)
  7. \( 5 \frac{6}{7} – 2 \frac{2}{5} = \)
  8. \( 6 \frac{4}{3} – 3 = \)
  9. \( 7 \frac{5}{6} – 2 \frac{5}{8} = \)
  10. \( 8 \frac{3}{4} – 3 \frac{3}{5} = \)

Answers

  1. \(8 \frac{6}{8} – 7 \frac{2}{5} = (8 – 7) + \frac{6 \times 5 – 2 \times 8}{8 \times 5} = 1 + \frac{14}{40} = 1 + \frac{7}{20}\)

    Solution:

    Rewrite the equation with parts separated:

    \(8 + \frac{6}{8} – 7 + \frac{2}{5}\)

    Solve the whole number parts:

    \(8 – 7 = 1\)

    Then solve the fraction parts:

    \(\frac{6}{8} – \frac{2}{5} = \frac{6 \times 5 – 2 \times 8}{8 \times 5} = \frac{14}{40} = \frac{7}{20}\)

    Now, combine the whole and fraction parts:

    \(1 + \frac{7}{20}\)

  2. \(5 \frac{3}{4} – 4 \frac{2}{3} = (5 – 4) + \frac{3 \times 3 – 2 \times 4}{4 \times 3} = 1 + \frac{1}{12}\)

    Solution:

    Rewrite the equation with parts separated:

    \(5 + \frac{3}{4} – 4 + \frac{2}{3}\)

    Solve the whole number parts:

    \(5 – 4 = 1\)

    Then solve the fraction parts:

    \(\frac{3}{4} – \frac{2}{3} = \frac{3 \times 3 – 2 \times 4}{4 \times 3} = \frac{1}{12}\)

    Now, combine the whole and fraction parts:

    \(1 + \frac{1}{12}\)

  3. \(7 \frac{6}{7} – 5 \frac{5}{8} = (7 – 5) + \frac{6 \times 8 – 5 \times 7}{7 \times 8} = 2 + \frac{13}{56}\)

    Solution:

    Rewrite the equation with parts separated:

    \(7 + \frac{6}{7} – 5 + \frac{5}{8}\)

    Solve the whole number parts:

    \(7 – 5 = 2\)

    Then solve the fraction parts:

    \(\frac{6}{7} – \frac{5}{8} = \frac{6 \times 8 – 5 \times 7}{7 \times 8} = \frac{13}{56}\)

    Now, combine the whole and fraction parts:

    \(2 + \frac{13}{56}\)

  4. \(6 \frac{5}{8} – 1 \frac{1}{3} = (6 – 1) + \frac{5 \times 3 – 1 \times 8}{8 \times 3} = 5 + \frac{7}{24}\)

    Solution:

    Rewrite the equation with parts separated:

    \(6 + \frac{5}{8} – 1 + \frac{1}{3}\)

    Solve the whole number parts:

    \(6 – 1 = 5\)

    Then solve the fraction parts:

    \(\frac{5}{8} – \frac{1}{3} = \frac{5 \times 3 – 1 \times 8}{8 \times 3} = \frac{7}{24}\)

    Now, combine the whole and fraction parts:

    \(5 + \frac{7}{24}\)

  5. \(10 \frac{3}{7} – 2 \frac{3}{7} = (10 – 2) + \frac{3 \times 7 – 3 \times 7}{7 \times 7} = 8 + \frac{0}{49} = 8\)

    Solution:

    Rewrite the equation with parts separated:

    \(10 + \frac{3}{7} – 2 + \frac{3}{7}\)

    Solve the whole number parts:

    \(10 – 2 = 8\)

    Then solve the fraction parts:

    \(\frac{3}{7} – \frac{3}{7} = \frac{3 \times 7 – 3 \times 7}{7 \times 7} = \frac{0}{49} = 0\)

    Now, combine the whole and fraction parts:

    \(8\)

  6. \(6 \frac{3}{5} – 5 \frac{1}{2} = (6 – 5) + \frac{3 \times 2 – 1 \times 5}{5 \times 2} = 1 \frac{1}{10}\)

    Solution:

    Rewrite the equation with parts separated, \(6 + \frac{3}{5} – 5 + \frac{1}{2}\)

    Solve the whole number parts \(6 – 5 = 1\), then solve the fraction parts, \(\frac{3}{5} – \frac{1}{2} = \frac{3 \times 2 – 1 \times 5}{5 \times 2} = \frac{6 – 5}{10} = \frac{1}{10}\)

    Now, combine the whole and fraction parts, \(1 + \frac{1}{10} = 1 \frac{1}{10}\)

  7. \(5 \frac{6}{7} – 2 \frac{8}{28} = (5 – 2) + \frac{6 \times 8 – 2 \times 7}{7 \times 8} = 3 \frac{34}{56} = 3 \frac{17}{28}\)

    **GCF(34,56) = 2**

    Solution:

    Rewrite the equation with parts separated, \(5 + \frac{6}{7} – 2 + \frac{8}{28}\)

    Solve the whole number parts \(5 – 2 = 3\), then solve the fraction parts, \(\frac{6}{7} – \frac{2}{28} = \frac{6 \times 8 – 2 \times 7}{7 \times 8} = \frac{48 – 14}{56} = \frac{34}{56} = \frac{17}{28}\)

    Now, combine the whole and fraction parts, \(3 + \frac{17}{28} = 3 \frac{17}{28}\)

  8. \(6 \frac{3}{6} – 3 \frac{3}{8} = (6 – 3) + \frac{3 \times 8 – 3 \times 6}{8 \times 6} = 3 \frac{6}{24} = 3 \frac{1}{4}\)

    **GCF(6,24) = 6**

    Solution:

    Rewrite the equation with parts separated, \(6 + \frac{3}{6} – 3 + \frac{3}{8}\)

    Solve the whole number parts \(6 – 3 = 3\), then solve the fraction parts, \(\frac{3}{6} – \frac{3}{8} = \frac{3 \times 8 – 3 \times 6}{8 \times 6} = \frac{24 – 18}{48} = \frac{6}{48} = \frac{1}{8}\)

    Now, combine the whole and fraction parts, \(3 + \frac{1}{8} = 3 \frac{1}{8}\)

  9. \(7 \frac{5}{6} – 2 \frac{5}{8} = (7 – 2) + \left( \frac{5 \times 8 – 5 \times 6}{6 \times 8} \right) = 5 + \frac{10}{48} = 5 + \frac{5}{24}\)

    Solution:

    Rewrite the equation with parts separated, \(7 + \frac{5}{6} – 2 + \frac{5}{8}\)

    Solve the whole number parts \(7 – 2 = 5\), then solve the fraction parts, \(\frac{5}{6} – \frac{5}{8} = \frac{5 \times 8 – 5 \times 6}{6 \times 8} = \frac{10}{48} = \frac{5}{24}\)

    Now, combine the whole and fraction parts, \(5 + \frac{5}{24} = 5 \frac{5}{24}\)

  10. \(8 \frac{3}{4} – 3 \frac{3}{5} = (8 – 3) + \left( \frac{3 \times 5 – 3 \times 4}{4 \times 5} \right) = 5 + \frac{3}{20}\)

    Solution:

    Rewrite the equation with parts separated, \(8 + \frac{3}{4} – 3 + \frac{3}{5}\)

    Solve the whole number parts \(8 – 3 = 5\), then solve the fraction parts, \(\frac{3}{4} – \frac{3}{5} = \frac{3 \times 5 – 3 \times 4}{4 \times 5} = \frac{3}{20}\)

    Now, combine the whole and fraction parts, \(5 + \frac{3}{20} = 5 \frac{3}{20}\)