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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., \(\frac{3}{4}\), \(\frac{5}{7}\), 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 \(1 \frac{3}{4}\). So, this mixed number comprises of two parts, a whole number which is 1 and a proper fraction \(\frac{3}{4}\). Now, if we convert this mixed number into an improper fraction which is \(\frac{7}{4}\), we find that it lies between the two whole numbers 1 and 2. Some other examples of a mixed number are \(2 \frac{1}{2}\), \(1 \frac{3}{4}\), \(1 \frac{4}{5}\), 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 the 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 \(\frac{5}{3}\). Now, when we divide 5 by 3, the quotient is 1. Also, the remainder is 2 and the divisor is 3. So, the mixed number is \(1 \frac{2}{3}\).

Steps to Divide Mixed Numbers

  1. Convert the mixed numbers into improper fractions, separately.
  2. Now divide these improper fractions by changing the division sign into the multiplication sign. To do this, just flip the second fraction.
  3. Write the answer in the lowest terms.

For example, let’s divide \(4 \frac{1}{3} \div 2 \frac{1}{5}\). So, the division becomes \(\left(\frac{13}{3} \div \frac{11}{5}\right) = \frac{13}{3} \times \frac{5}{11} = \frac{65}{33} = 1 \frac{32}{33}\).

Exercises for Dividing Mixed Numbers

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

Answers

  1. \( 6 \frac{5}{4} \times 2 \frac{2}{3} = \)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 6 \frac{5}{4} = \frac{29}{4} \) and \( 2 \frac{2}{3} = \frac{8}{3} \)

    Step 2: Apply the fractions rule for multiplication, \( \frac{29}{4} \times \frac{8}{3} = \frac{232}{12} = 19 \frac{4}{12} = 19 \frac{1}{3} \)

  2. \( 4 \frac{3}{4} \div 1 \frac{4}{7} = \)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 4 \frac{3}{4} = \frac{19}{4} \) and \( 1 \frac{4}{7} = \frac{11}{7} \)

    Step 2: Apply the fractions rule for division by multiplying with the reciprocal, \( \frac{19}{4} \times \frac{7}{11} = \frac{133}{44} = 3 \frac{1}{44} \)

  3. \( 7 \frac{7}{8} \div 4 \frac{3}{5} = \)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 7 \frac{7}{8} = \frac{63}{8} \) and \( 4 \frac{3}{5} = \frac{23}{5} \)

    Step 2: Apply the fractions rule for division by multiplying with the reciprocal, \( \frac{63}{8} \times \frac{5}{23} = \frac{315}{184} = 1 \frac{131}{184} \)

  4. \( 10 \frac{4}{3} \div 3 \frac{1}{2} = \)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 10 \frac{4}{3} = \frac{34}{3} \) and \( 3 \frac{1}{2} = \frac{7}{2} \)

    Step 2: Apply the fractions rule for division by multiplying with the reciprocal, \( \frac{34}{3} \times \frac{2}{7} = \frac{68}{21} \)

  5. \( 8 \frac{7}{8} \div 7 \frac{6}{8} = \)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 8 \frac{7}{8} = \frac{71}{8} \) and \( 7 \frac{6}{8} = \frac{62}{8} \)

    Step 2: Apply the fractions rule for division by multiplying with the reciprocal, \( \frac{71}{8} \times \frac{8}{62} = \frac{71}{62} = 1 \frac{9}{62} \)

  6. \( 10 \frac{7}{2} \div 7 \frac{7}{9} = \frac{(10 \times 2 + 7)}{2} \div \frac{(7 \times 9 + 7)}{9} = \frac{27}{2} \div \frac{70}{9} = \frac{27}{2} \times \frac{9}{70} = \frac{243}{140}\)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 10 \frac{7}{2} = \frac{27}{2} \) and \( 7 \frac{7}{9} = \frac{70}{9} \)

    Step 2: Apply the fractions rule for multiplication by flipping the second fraction, \( \frac{27}{2} \times \frac{9}{70} = \frac{243}{140} \)

  7. \( 7 \frac{6}{5} \div 5 \frac{4}{5} = \frac{(7 \times 5 + 6)}{5} \div \frac{(5 \times 5 + 4)}{5} = \frac{41}{5} \div \frac{29}{5} = \frac{41}{5} \times \frac{5}{29} = \frac{41}{29}\)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 7 \frac{6}{5} = \frac{41}{5} \) and \( 5 \frac{4}{5} = \frac{29}{5} \)

    Step 2: Apply the fractions rule for multiplication by flipping the second fraction, \( \frac{41}{5} \times \frac{5}{29} = \frac{41}{29} \)

  8. \( 5 \frac{3}{2} \div 2 \frac{7}{8} = \frac{(5 \times 2 + 3)}{2} \div \frac{(2 \times 8 + 7)}{8} = \frac{13}{2} \div \frac{23}{8} = \frac{13}{2} \times \frac{8}{23} = \frac{104}{46}\)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 5 \frac{3}{2} = \frac{13}{2} \) and \( 2 \frac{7}{8} = \frac{23}{8} \)

    Step 2: Apply the fractions rule for multiplication by flipping the second fraction, \( \frac{13}{2} \times \frac{8}{23} = \frac{104}{46} \)

  9. \( 10 \frac{8}{10} \div 1 \frac{7}{9} = \frac{(10 \times 10 + 8)}{10} \div \frac{(1 \times 9 + 7)}{9} = \frac{108}{10} \div \frac{16}{9} = \frac{108}{10} \times \frac{9}{16} = \frac{972}{160}\)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 10 \frac{8}{10} = \frac{108}{10} \) and \( 1 \frac{7}{9} = \frac{16}{9} \)

    Step 2: Apply the fractions rule for multiplication by flipping the second fraction, \( \frac{108}{10} \times \frac{9}{16} = \frac{972}{160} \)

  10. \( 10 \frac{8}{10} \div 2 \frac{1}{3} = \frac{(10 \times 10 + 8)}{10} \div \frac{(2 \times 3 + 1)}{3} = \frac{108}{10} \div \frac{7}{3} = \frac{108}{10} \times \frac{3}{7} = \frac{324}{70}\)Solution:

    Step 1: Convert mixed numbers to improper fractions, \( 10 \frac{8}{10} = \frac{108}{10} \) and \( 2 \frac{1}{3} = \frac{7}{3} \)

    Step 2: Apply the fractions rule for multiplication by flipping the second fraction, \( \frac{108}{10} \times \frac{3}{7} = \frac{324}{70} \)