How to Convert Mixed Numbers and Improper Fractions

Mixed numbers can be converted into improper fractions.
••• glasses and mathematics image by Alexander Potapov from

Fractions are expressed as two numbers separated by a line. The number above the line is the numerator. The number below the line is the denominator. If the numerator is less than the denominator, then the fraction is proper. Examples include 3/4, 4/5 and 7/9. If the numerator is greater than the denominator, then the fraction is improper. Examples include 4/3, 6/5 and 20/17. Mixed numbers consist of a whole number and a proper fraction, such as 4 1/2. Improper fractions can be converted into mixed numbers and vice versa.

    Pick an example problem: 4 5/7.

    Multiply the denominator, 7, by the whole number, 4. 7 x 4 = 28.

    Take that product, 28, and add that to the numerator of the fraction, 5. 28 + 5 = 33.

    Take that sum, 33, and place it over the denominator, 7. 33/7. 4 5/7 = 33/7.

    Use the procedure in reverse to convert improper fractions into mixed numbers. Take an example problem: 33/7.

    Divide the denominator, 7, into the numerator, 33. 7 goes into 33 four times. So 4 is the whole number.

    Take the remainder and place it over the denominator, 7. 33 divided by 7 is 4. 4 x 7 = 28. 33 -28 = 5. The remainder is 5. The fraction is 5/7. 33/7 = 4 5/7.


    • You can always check your work by converting the improper fraction back into a mixed number and vice versa.

Related Articles

How to Change Mixed Fractions to Improper Fractions
How to Know When One Fraction Is Larger Than Another...
How to Do Fractions on a TI-30X IIS
What Are Denominators & Numerators?
How to Divide Rational Numbers
How to: Improper Fractions Into Proper Fractions
How to Convert a Mixed Number to a Fractional Notation
How to Find a Fraction of a Number
How to Convert a Fraction to a Ratio
How to Solve for Range
How to Add Fractions with Mixed Numbers
How to Convert Pounds Per Square Foot to PSI
How to Find the X Intercept of a Function
How do I Calculate the Geometric Mean on an HP 12C?
How to Divide Fractions With Ease
How to Change 1/4 to a Decimal Form
Basic Mathematics Skills
How to Write the Remainder As a Whole Number
How to Write an Equivalent Fraction With a Given Denominator
Test Your Knowledge on Middle School Science

Dont Go!

We Have More Great Sciencing Articles!