How to Rename Mixed Numbers in Simplest Form

Step-by-Step Guide

1. 1

   Step 1: Multiply the whole number of the mixed number by the denominator.

   Remember that a mixed number includes a whole number combined with a proper fraction.
   
   The whole number represents how many complete wholes you have.
   
   The fraction represents how many parts of a whole you have.
   
   The denominator is an indication of how many parts a whole something can be broken into.
   
   By multiplying the whole number by the denominator, you can determine how many pieces exist among wholes.
   
   For example, if you need to convert 51416{\displaystyle 5{\frac {14}{16}}}, you would first calculate 5×16=80{\displaystyle 5\times 16=80}.
2. 2

   Step 2: Add the original numerator.

   These are all the extra pieces that do not make a whole.
   
   Make sure you add this number to the product of the whole number and the denominator.
   
   This number will become the new numerator of your improper fraction.
   
   For example, 80+14=94{\displaystyle 80+14=94}.
   
   So, the new numerator of your improper fraction is
   94. , You do not need to make any changes to the denominator to create your improper fraction.For example, since the original denominator of the proper fraction was 16, the denominator of your improper fraction is also
   16.
   
   So, 51416=9416{\displaystyle 5{\frac {14}{16}}={\frac {94}{16}}}. , A factor will be any number that evenly divides into the numerator.
   
   If you need help finding all of the factors, you can make a factor tree.
   
   For example, the factors of 94 are 1, 2, 47, and
   94. , Follow the same process you used to find the numerator’s factors.
   
   For example, the factors of 16 are 1, 2, 4, 8, and
   16. , This is the largest factor that the numerator and denominator share.You know you can simplify if the numerator and denominator share any factors other than
   1.
   
   If the numerator and denominator do not share any other factors, the fraction is already simplified.
   
   For example, the largest factor 94 and 16 share is
   2.
   
   So, the fraction can be simplified. , This will give you the new numerator and denominator of your simplified fraction.For example, 94÷2=47{\displaystyle 94\div 2=47}, so the simplified numerator is
   47.
   
   To find the denominator, calculate 16÷2=8{\displaystyle 16\div 2=8}.
   
   So, the simplified fraction is 478{\displaystyle {\frac {47}{8}}}.
   
   Thus you can rename the mixed number 51416{\displaystyle 5{\frac {14}{16}}} as the improper fraction 478{\displaystyle {\frac {47}{8}}}. , Make sure you simplify.
   
   Multiply the whole number by the denominator: 2×6=12{\displaystyle 2\times 6=12}.
   
   Add the numerator: 12+4=16{\displaystyle 12+4=16}.
   
   Place the new numerator over the original denominator: 166{\displaystyle {\frac {16}{6}}}.
   
   Determine whether the fraction can be simplified.
   
   Since the numerator and denominator are even numbers, the fraction can be simplified, since they can both be divided by
   2.
   
   List the factors of the numerator: 1, 2, 4, 8,
   16.
   
   List the factors of the denominator: 1, 2, 3,
   6.
   
   Identify the greatest common factor.
   
   Since the largest factor the numerator and denominator share is 2, this is the GCF.
   
   Divide the numerator and denominator by the GCF: 16÷2=8{\displaystyle 16\div 2=8} and 6÷2=3{\displaystyle 6\div 2=3}, so the fraction simplifies to 83{\displaystyle {\frac {8}{3}}}. , Ava ate 1 brownie at the party.
   
   A little later, she ate three-quarters of a brownie.
   
   How many brownies did she eat all together? Identify the mixed number.
   
   Since Ava ate 1 whole brownie, and then three-quarters of a brownie, altogether she ate 134{\displaystyle 1{\frac {3}{4}}} brownies.
   
   Multiply the whole number by the denominator: 1×4=4{\displaystyle 1\times 4=4}.
   
   Add the numerator: 4+3=7{\displaystyle 4+3=7}.
   
   Place the new numerator over the original denominator: 74{\displaystyle {\frac {7}{4}}}.
   
   Determine whether the fraction can be simplified.
   
   Since 7 is a prime number, the only factor the numerator and denominator share is 1, so the fraction cannot be further simplified. , Convert each mixed number to an improper fraction first.
   
   Convert the first mixed number into an improper fraction: 1×4+1=5{\displaystyle 1\times 4+1=5}, so the improper fraction is 54{\displaystyle {\frac {5}{4}}}.
   
   Convert the second mixed number into an improper fraction: 1×4+3=7{\displaystyle 1\times 4+3=7}, so the improper fraction is 74{\displaystyle {\frac {7}{4}}}.
   
   Add the two fractions using the normal adding rules.
   
   Since these two fractions have the same denominator, you can simply add the numerators: 5+7=12{\displaystyle 5+7=12}, so 74+54=124{\displaystyle {\frac {7}{4}}+{\frac {5}{4}}={\frac {12}{4}}}.
   
   Determine whether the fraction can be simplified.
   
   Since the numerator and denominator are both even, the fraction can be simplified.
   
   Find the greatest common factor of the numerator and denominator.
   
   The greatest factor 12 and 4 share is
   4.
   
   Divide the numerator and denominator by the GCF: 12÷4=3{\displaystyle 12\div 4=3} and 4÷4=1{\displaystyle 4\div 4=1}, so the fraction becomes 31{\displaystyle {\frac {3}{1}}}, which simplifies to
   3.
3. 3

   Step 3: Place the new numerator over the original denominator.

4. 4

   Step 4: List the factors of the numerator.

5. 5

   Step 5: List the factors of the denominator.

6. 6

   Step 6: Identify the greatest common factor (GCF).

7. 7

   Step 7: Divide the numerator and the denominator by the greatest common factor.

8. 8

   Step 8: Rename 246{\displaystyle 2{\frac {4}{6}}} as an improper fraction.

9. 9

   Step 9: Rewrite the answer to the following problem as an improper fraction.

10. 10

    Step 10: Solve the following problem: 114+134{\displaystyle 1{\frac {1}{4}}+1{\frac {3}{4}}}.

Detailed Guide

About the Author