Introduction
 "Fraction" represents a relation of a part(s) to the whole, where the whole is divided into equal parts.
 Fraction = $\frac{numerator}{denominator}=\frac{part\left(s\right)}{whole}$
 Any whole number can be written as a fraction. For example: $5=\frac{5}{1}$. This is helpful when multiplying and dividing fractions.
 $\frac{2}{3}$ is a Proper Fraction (the denominator is greater than the numerator).
 $\frac{5}{3}$ is an Improper Fraction (the numerator is greater than the denominator).
 $1\frac{2}{3}$ is a Mixed Number/Fraction (whole number + proper fraction).
Multiplication of Fractions/Mixed Numbers
 To multiply fractions/mixed numbers.

 Convert the mixed numbers into an improper fraction.
 Multiply the numerators.
 Multiply the denominators.
 Simplify to the lowest (simplest) term.
 Occasionally, fractions can be simplified before multiplying.
Example 1: solve: $\frac{3}{4}\xb7\frac{2}{5}$
Solution: $\frac{3}{4}\xb7\frac{2}{5}=\frac{3\mathit{}\times 2}{4\mathit{}\times 5}$
$=\frac{6}{20}$ (simplify the fraction to its lowest terms.)
$=\frac{6\xf72}{20\xf72}$
$=\frac{3}{10}$
Example 2: A recipe needs $2\frac{1}{3}$cups of sugar for a loaf of banana bread. Ms. Suzy wants to cut the sugar in half. How much sugar will Ms. Suzy use for the banana bread?
Solution: Convert the mixed number to a proper fraction.
$2\frac{1}{3}=2\frac{+1}{\times 3}=\frac{7}{3}$
Ms. Suzy cuts the sugar in half.
$=\frac{7}{3}\times \frac{1}{2}$
$=\frac{7}{6}$
Change improper fraction to a mixed number by dividing the numerator by the denominator.
$=1\frac{1}{6}$
Ms. Suzy uses $1\frac{1}{6}$cups of sugar to make a loaf of banana bread.
Division of Fractions/Mixed Numbers
 Fractions can be divided by changing them into multiplication.
 Each division expression can be written as a multiplication expression by applying the rule " Keep, Change & Flip." This rule works from left to right.
 Keep, Change, & Flip rule
1. Keep the first fraction of the expression the same.
2. Change the division sign to multiplication.
3. Flip the last fraction.
Example: $\frac{1}{3}\xf7\frac{2}{5}$
$=\frac{1}{3}\times \frac{5}{2}$
 To divide fractions/mixed numbers.

 Convert each mixed number into an improper fraction.
 Convert the division expression to multiplication by following the rule "Keep, Change, & flip ."
 Multiply the numerators.
 Multiply the denominators.
 Simplify to the lowest (simplest) form.
Example1: Solve $\frac{1}{2}\xf72$.
Solution: $\frac{1}{2}\xf72$
$=\frac{1}{2}\xf7\frac{2}{1}$
Change division to multiplication by applying the "Keep, Change, & Flip" rule.
$=\frac{1}{2}\times \frac{1}{2}$
Multiply across the numerators and denominators.
$=\frac{1\times 1}{2\times 2}$
$=\frac{1}{4}$
Example2: Solve $\frac{7}{8}\xf7\frac{1}{4}$.
Solution:
$\frac{7}{8}\xf7\frac{1}{4}$
Change division to multiplication by applying the "Keep, Change, & Flip" rule.
$=\frac{7}{8}\times \frac{4}{1}$
Multiply across the numerators and denominators.
$=\frac{7\times 4}{8\times 1}$
$=\frac{28}{8}$ (simplify the fraction by reducing it to its lowest terms.)
$=\frac{28\xf74}{8\xf74}$
$=\frac{7}{2}$
Convert the improper fraction to the mixed number by dividing the numerator by the denominator.
$=3\frac{1}{2}$
Cheat Sheet
 Any whole number can be written as a fraction, such as 5 can be written as $\frac{5}{1}$.
 While creating an equivalent fraction, both the numerator and the denominator of the fraction must be multiplied/divided by the same number.
 Always simplify the fraction whenever needed and possible. Sometimes a fraction can be simplified before multiplying/dividing.
 A fraction multiplied by its reciprocal equals 1.
$\frac{1}{2}\xb7\frac{2}{1}=1$
 The division is the inverse operation of multiplication; every division expression can be written as a multiplication expression by following the division rule of "keep, change, & flip."
$1\xf77=1\times \frac{1}{7}$
 The reciprocal of 3 is $\frac{1}{3}$ . The multiplication inverse of 3 is $\frac{1}{3}$.
Blunder Areas
 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.
 Fiona Wong
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