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Mixed numbers and improper fractions

Convert mixed numbers to improper fractions and back.

Practice + answer key · 3 pages

Worksheet settings12 questions · 2 columns · A4
Fraction denominators

Bounds control the fractional denominator; whole-number parts are fixed to the range 1–5.

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Mixed numbers and improper fractionsMixed numbers and improper fractions. Practice. Convert the mixed number 3 7/8 to an improper fraction in simplest form. Convert 18/5 to a mixed number with the fraction part in simplest form. Convert the mixed number 3 4/8 to an improper fraction in simplest form. Convert 8/3 to a mixed number with the fraction part in simplest form. Convert the mixed number 2 2/8 to an improper fraction in simplest form. Convert 7/3 to a mixed number with the fraction part in simplest form. Convert the mixed number 2 2/7 to an improper fraction in simplest form. Convert 28/6 to a mixed number with the fraction part in simplest form. Convert the mixed number 2 2/3 to an improper fraction in simplest form. Convert 19/8 to a mixed number with the fraction part in simplest form.Name __________________________Date _______________Mixed numbers and improper fractionsConvert as requested. Simplify the fraction or fractional part.Worked exampleConvert 2 3/4 to an improper fraction. → 11/4Two wholes contain 2 × 4 = 8 quarters.1.Convert the mixed number 3 7/8 toan improper fraction in simplestform.2.Convert 18/5 to a mixed numberwith the fraction part insimplest form.3.Convert the mixed number 3 4/8 toan improper fraction in simplestform.4.Convert 8/3 to a mixed numberwith the fraction part insimplest form.5.Convert the mixed number 2 2/8 toan improper fraction in simplestform.6.Convert 7/3 to a mixed numberwith the fraction part insimplest form.7.Convert the mixed number 2 2/7 toan improper fraction in simplestform.8.Convert 28/6 to a mixed numberwith the fraction part insimplest form.9.Convert the mixed number 2 2/3 toan improper fraction in simplestform.10.Convert 19/8 to a mixed numberwith the fraction part insimplest form.MathSprig · mathsprig.site · support@mathsprig.sitePage 1 of 2mathsprig-1 · mathsprig-v1 · 708133a9
Mixed numbers and improper fractionsMixed numbers and improper fractions. Practice. Convert the mixed number 3 1/4 to an improper fraction in simplest form. Convert 23/6 to a mixed number with the fraction part in simplest form.Name __________________________Date _______________Mixed numbers and improper fractionsConvert as requested. Simplify the fraction or fractional part.11.Convert the mixed number 3 1/4 toan improper fraction in simplestform.12.Convert 23/6 to a mixed numberwith the fraction part insimplest form.MathSprig · mathsprig.site · support@mathsprig.sitePage 2 of 2mathsprig-1 · mathsprig-v1 · 708133a9
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Practice + answer key · 3 pages

Fractions

What you’ll practice

Convert mixed and improper forms and simplify the fractional result.

A mixed number and an improper fraction can describe the same amount. Count the fractional parts in each whole, or divide them back into wholes and a remainder.

How this skill works

To change a mixed number into an improper fraction, multiply the whole part by the denominator and add the numerator. Keep the denominator.

To change an improper fraction into a mixed number, divide the numerator by the denominator. The quotient is the whole part and the remainder supplies the fraction numerator.

Worked example

Convert 2 3/4 to an improper fraction.
  1. Two wholes contain 2 × 4 = 8 quarters.
  2. Add the remaining 3 quarters: 8 + 3 = 11.
  3. The improper fraction is 11/4.

Answer: 11/4

Teaching notes

  • A mixed number uses addition between its whole part and fractional part, not multiplication.
  • Simplify the remaining fractional part after converting from an improper fraction.
Practice questions
  1. Convert the mixed number 3 7/8 to an improper fraction in simplest form.
  2. Convert 18/5 to a mixed number with the fraction part in simplest form.
  3. Convert the mixed number 3 4/8 to an improper fraction in simplest form.
  4. Convert 8/3 to a mixed number with the fraction part in simplest form.
  5. Convert the mixed number 2 2/8 to an improper fraction in simplest form.
  6. Convert 7/3 to a mixed number with the fraction part in simplest form.
  7. Convert the mixed number 2 2/7 to an improper fraction in simplest form.
  8. Convert 28/6 to a mixed number with the fraction part in simplest form.
  9. Convert the mixed number 2 2/3 to an improper fraction in simplest form.
  10. Convert 19/8 to a mixed number with the fraction part in simplest form.
  11. Convert the mixed number 3 1/4 to an improper fraction in simplest form.
  12. Convert 23/6 to a mixed number with the fraction part in simplest form.
Answers and steps
  1. 31/8
    1. Split each whole into 8 equal parts: 3 × 8 + 7 = 31, so the fraction is 31/8.
    2. The greatest common factor of 31 and 8 is 1. Divide both by 1: 31/8 = 31/8.
  2. 3 3/5
    1. Divide: 18 = 3 × 5 + 3. The whole part is 3; the remaining fraction is 3/5.
    2. The greatest common factor of 3 and 5 is 1. Divide both by 1: 3/5 = 3/5.
    3. After simplifying the fraction part, the mixed number is 3 3/5.
  3. 7/2
    1. Split each whole into 8 equal parts: 3 × 8 + 4 = 28, so the fraction is 28/8.
    2. The greatest common factor of 28 and 8 is 4. Divide both by 4: 28/8 = 7/2.
  4. 2 2/3
    1. Divide: 8 = 2 × 3 + 2. The whole part is 2; the remaining fraction is 2/3.
    2. The greatest common factor of 2 and 3 is 1. Divide both by 1: 2/3 = 2/3.
    3. After simplifying the fraction part, the mixed number is 2 2/3.
  5. 9/4
    1. Split each whole into 8 equal parts: 2 × 8 + 2 = 18, so the fraction is 18/8.
    2. The greatest common factor of 18 and 8 is 2. Divide both by 2: 18/8 = 9/4.
  6. 2 1/3
    1. Divide: 7 = 2 × 3 + 1. The whole part is 2; the remaining fraction is 1/3.
    2. The greatest common factor of 1 and 3 is 1. Divide both by 1: 1/3 = 1/3.
    3. After simplifying the fraction part, the mixed number is 2 1/3.
  7. 16/7
    1. Split each whole into 7 equal parts: 2 × 7 + 2 = 16, so the fraction is 16/7.
    2. The greatest common factor of 16 and 7 is 1. Divide both by 1: 16/7 = 16/7.
  8. 4 2/3
    1. Divide: 28 = 4 × 6 + 4. The whole part is 4; the remaining fraction is 4/6.
    2. The greatest common factor of 4 and 6 is 2. Divide both by 2: 4/6 = 2/3.
    3. After simplifying the fraction part, the mixed number is 4 2/3.
  9. 8/3
    1. Split each whole into 3 equal parts: 2 × 3 + 2 = 8, so the fraction is 8/3.
    2. The greatest common factor of 8 and 3 is 1. Divide both by 1: 8/3 = 8/3.
  10. 2 3/8
    1. Divide: 19 = 2 × 8 + 3. The whole part is 2; the remaining fraction is 3/8.
    2. The greatest common factor of 3 and 8 is 1. Divide both by 1: 3/8 = 3/8.
    3. After simplifying the fraction part, the mixed number is 2 3/8.
  11. 13/4
    1. Split each whole into 4 equal parts: 3 × 4 + 1 = 13, so the fraction is 13/4.
    2. The greatest common factor of 13 and 4 is 1. Divide both by 1: 13/4 = 13/4.
  12. 3 5/6
    1. Divide: 23 = 3 × 6 + 5. The whole part is 3; the remaining fraction is 5/6.
    2. The greatest common factor of 5 and 6 is 1. Divide both by 1: 5/6 = 5/6.
    3. After simplifying the fraction part, the mixed number is 3 5/6.