6th Grade - Mixed Fractions

Introduction

• "Fraction" represents a relation of a part(s) to the whole, where the whole is divided into equal parts. 
• Fraction = $\frac{numerator}{denominator} = \frac{whole thing}{number of parts in a whole}$
• Any whole number can be written as a fraction, such as 5 can be written as $\frac{5}{1}$ . This is helpful while adding, subtracting, multiplying, or dividing fractions.
• A Mixed Number consists of a whole number and a proper fraction, e.g. $2\frac{3}{5}$.

Changing Mixed Number to Improper Fraction and Vice Versa

• To change a mixed number to an improper fraction:

1. 1. Keep the denominator the same.
   2. For the numerator, multiply the whole number by the denominator and add the numerator.
   3. For example, Change $2\frac{3}{5} \mathrm{to} \mathrm{an} \mathrm{improper} \mathrm{fraction}.$

$= 2\frac{+3}{\times 5} =\frac{13}{5}$

• To change an improper fraction to a mixed number 

1. 1. Divide the numerator by the denominator.
   2. The quotient will be the whole number of the mixed number.
   3. Keep the denominator the same.
   4. The numerator will be the remainder of the division.

Addition and Subtraction of Mixed Numbers

• To add or subtract mixed numbers:

1. 1. Change the mixed number to an improper fraction. 
   2. Add/Subtract following the rules of addition/subtraction of fractions.
   3. Simplify to the lowest terms if possible.
   4. Change the improper fraction to a mixed number.

Multiplication and Division of Mixed Numbers

• To Multiply mixed numbers:

1. 1. Convert the mixed numbers into an improper fraction. 
   2. Multiply the numerators.
   3. Multiply the denominators.
   4. Simplify to the lowest (simplest) term.
   5. Occasionally, fractions can be simplified before multiplying.

• To Divide Mixed numbers:

1. 1. Change the mixed numbers to improper fractions.
   2. Apply the Keep, change, & flip rule.
   3. Keep, Change, & Flip rule

1. 1. 1.  Keep the first fraction of the expression the same.
      2.  Change the division sign to multiplication.
      3.  Flip the last fraction.
      4.  Follow the rules of multiplication of fractions.
      5.  If possible, change the fraction to its lowest terms.

Cheat Sheet

• Always simplify the fraction whenever needed and possible.
• Simplifying before multiplying or dividing makes the calculation easier. 

Blunder Area

• The word "of" means multiplication.

For example, Mr. Jim's house is $\frac{3}{4}$miles from the school. He walks $\frac{2}{3}$of the distance and then jogs the rest. How many miles does he walk?

        Solution: In this scenario, it's $\frac{2}{3}$of $\frac{3}{4}$miles. Therefore, $\frac{2}{3}\times \frac{3}{4}$ = $\frac{6}{12} = \frac{1}{2}$

• While multiplying two fractions, the numerator should be multiplied with the numerator and the denominator with the denominator.
• Always reduce the answer to its lowest term.