Mixed Numbers Questions with Solutions

Questions on fractions and mixed numbers are presented below. A mixed number with a whole part \( n \) and a fractional part \( \frac{a}{b} \) is written as \( n \frac{a}{b} \), which means \( n + \frac{a}{b} \).

Add mixed numbers calculator is available for your reference.

Question 1

Write the improper fraction \( \dfrac{21}{5} \) as a mixed number.

  1. \( 1 \frac{1}{5} \)
  2. \( 2 \frac{1}{5} \)
  3. \( 4 \frac{1}{5} \)
  4. \( 4 \frac{1}{4} \)
  5. \( \frac{5}{21} \)
Show Detailed Solution

Divide 21 by 5. \( 21 \div 5 = 4 \) with a remainder of \( 1 \). Thus, \( \frac{21}{5} = 4 \frac{1}{5} \). Answer: C

Question 2

Write the mixed number \( 4 \frac{1}{3} \) as an improper fraction.

  1. \( \frac{4}{3} \)
  2. \( \frac{13}{3} \)
  3. \( \frac{5}{3} \)
  4. \( \frac{3}{13} \)
  5. \( \frac{1}{3} \)
Show Detailed Solution

\( 4 \frac{1}{3} = 4 + \frac{1}{3} = \frac{4 \times 3}{3} + \frac{1}{3} = \frac{12}{3} + \frac{1}{3} = \frac{13}{3} \). Answer: B

Question 3

Add the mixed numbers and simplify: \( 3 \frac{2}{5} + 1 \frac{3}{5} \)

  1. 4
  2. 1
  3. \( 4 \frac{2}{5} \)
  4. \( 4 \frac{3}{5} \)
  5. 5
Show Detailed Solution

Add whole parts: \( 3+1=4 \). Add fractions: \( \frac{2}{5} + \frac{3}{5} = \frac{5}{5} = 1 \). \( 4 + 1 = 5 \). Answer: E

Question 4

Simplify: \( 5 \frac{2}{3} + 6 \frac{3}{4} \)

  1. \( 12 \frac{5}{12} \)
  2. 12
  3. \( 11 \frac{5}{12} \)
  4. 11
  5. \( \frac{17}{12} \)
Show Detailed Solution

\( (5+6) + (\frac{2}{3} + \frac{3}{4}) = 11 + (\frac{8}{12} + \frac{9}{12}) = 11 + \frac{17}{12} = 11 + 1 \frac{5}{12} = 12 \frac{5}{12} \). Answer: A

Question 5

Subtract the mixed numbers and simplify: \( 7 \frac{2}{3} - 4 \frac{1}{5} \)

  1. 3
  2. \( 3 \frac{1}{2} \)
  3. \( 3 \frac{7}{15} \)
  4. \( - 3 \frac{7}{15} \)
  5. 4
Show Detailed Solution

\( (7-4) + (\frac{2}{3} - \frac{1}{5}) = 3 + (\frac{10}{15} - \frac{3}{15}) = 3 \frac{7}{15} \). Answer: C

Question 6

Simplify: \( 9 \frac{1}{4} - 5 \frac{3}{4} \)

  1. \( 4 \frac{1}{2} \)
  2. 4
  3. \( 2 \frac{1}{2} \)
  4. \( 3 \frac{1}{2} \)
  5. 4
Show Detailed Solution

\( (9-5) + (\frac{1}{4} - \frac{3}{4}) = 4 - \frac{2}{4} = 4 - \frac{1}{2} = 3 \frac{1}{2} \). Answer: D

Question 7

Multiply the mixed numbers and simplify: \( (1 \frac{1}{3}) \times (2 \frac{2}{3}) \)

  1. \( 3 \frac{5}{9} \)
  2. \( 2 \frac{2}{9} \)
  3. \( \frac{8}{9} \)
  4. \( \frac{2}{9} \)
  5. 2
Show Detailed Solution

\( \frac{4}{3} \times \frac{8}{3} = \frac{32}{9} = 3 \frac{5}{9} \). Answer: A

Question 8

Divide the mixed numbers and simplify: \( (3 \frac{1}{2}) \div (2 \frac{1}{2}) \)

  1. \( \frac{3}{2} \)
  2. \( \frac{2}{3} \)
  3. \( \frac{2}{5} \)
  4. \( 3 \frac{2}{5} \)
  5. \( 1 \frac{2}{5} \)
Show Detailed Solution

\( \frac{7}{2} \div \frac{5}{2} = \frac{7}{2} \times \frac{2}{5} = \frac{7}{5} = 1 \frac{2}{5} \). Answer: E

Question 9

What number should be added to \( 1 \frac{1}{3} - 2 \frac{1}{2} \) to obtain 2?

  1. 3
  2. \( 2 \frac{1}{2} \)
  3. \( 3 \frac{1}{6} \)
  4. \( 1 \frac{1}{3} \)
  5. \( 1 \frac{1}{2} \)
Show Detailed Solution

\( (1 \frac{1}{3} - 2 \frac{1}{2}) + x = 2 \implies x = 2 - 1 \frac{1}{3} + 2 \frac{1}{2} = (2 - 1 + 2) + (-\frac{1}{3} + \frac{1}{2}) = 3 - \frac{2}{6} + \frac{3}{6} = 3 \frac{1}{6} \). Answer: C

Question 10

What number should be subtracted from \( 2 \frac{1}{5} + 5 \frac{1}{3} \) to obtain 0?

  1. \( 7 \frac{1}{5} \)
  2. \( 7 \frac{1}{3} \)
  3. 7
  4. \( 7 \frac{8}{15} \)
  5. \( 6 \frac{8}{15} \)
Show Detailed Solution

\( (2 \frac{1}{5} + 5 \frac{1}{3}) - x = 0 \implies x = 2 \frac{1}{5} + 5 \frac{1}{3} = (2+5) + (\frac{3}{15} + \frac{5}{15}) = 7 \frac{8}{15} \). Answer: D

Question 11

What is the reciprocal of the mixed number \( 2 \frac{1}{8} \)?

  1. \( \frac{8}{17} \)
  2. \( 2 \frac{8}{17} \)
  3. \( \frac{1}{2} \)
  4. \( \frac{4}{5} \)
  5. \( \frac{8}{21} \)
Show Detailed Solution

\( 2 \frac{1}{8} = \frac{17}{8} \). Reciprocal is \( \frac{8}{17} \). Answer: A