This Crash Course focuses on fractions. You can use the interactive videos, recap and practice questions to review this topic.
To follow this Crash Course, you should know some concepts in connection with fractions; know the difference between the numerator and the denominator; know the different types of fractions (mixed numbers, equivalent and improper fractions, etc.); be able to find equivalent fractions to reduce to simplified form; and be familiar with the concepts of the greatest common factor (GCF) and the lowest common multiple (LCM).
-
To multiply fractions, simply multiply the numerators together and multiply the denominators together.
-
To divide fractions, simply multiply the first fraction by the reciprocal of the second.
-
To add or subtract fractions, the fractions must have the same denominator.
-
After completing fraction calculations, always reduce the resulting fraction to its simplified form.
-
You have to respect the order of operations with fractions, as with any other number. The mnemonic trick for remembering this is BEDMAS.
-
When multiplying fractions, you can simplify before or after calculating.
Example:||\begin{align}\dfrac{7}{15}\times\dfrac{10}{7}&=\dfrac{\cancel{\color{#ec0000}{7}}}{3\times\cancel{\color{#333fb1}{5}}}\times\dfrac{2\times\cancel{\color{#333fb1}{5}}}{\cancel{\color{#ec0000}{7}}}\\[3pt]&=\dfrac{2}{3}\\\\&\text{or}\\\\\dfrac{7}{15}\times\dfrac{10}{7}&=\dfrac{7\times10}{15\times7}\\[3pt]&=\dfrac{70}{105}\begin{matrix}\div35\\^{\Large\div35}\end{matrix}\\[3pt]&=\dfrac{2}{3}\end{align}|| -
To convert a mixed number into a fraction, add the whole number and the fraction. The common denominator is then the denominator of the resultant fraction.
Example:||\begin{align}\color{#333fb1}{3}\dfrac{\color{#3a9a38}{4}}{\color{#ec0000}{5}}&=\dfrac{\color{#333fb1}{3}}{1}+\dfrac{\color{#3a9a38}{4}}{\color{#ec0000}{5}}\\[3pt]&=\dfrac{\color{#333fb1}{3}\times \color{#ec0000}{5}}{1\times\color{#ec0000}{5}}+\dfrac{\color{#3a9a38}{4}}{\color{#ec0000}{5}}\\[3pt]&=\dfrac{\color{#333fb1}{3}\times\color{#ec0000}{5}+\color{#3a9a38}{4}}{\color{#ec0000}{5}}\\[3pt]&=\dfrac{19}{\color{#ec0000}{5}}\end{align}|| -
To convert an improper fraction into a mixed number, divide the numerator by the denominator, then write the whole number quotient, the remainder and the divisor in the correct places.
Example:||\dfrac{23}{\color{#ec0000}{4}}\ \Rightarrow\ \begin{align}\begin{aligned}\\\color{#ec0000}{4}\\\\\ \end{aligned}\begin{aligned}\\[-2px]\\\big)\!\!\!\!\!\!\ \\\\\\\\\end{aligned}\begin{aligned}\ &\color{#333fb1}{5}\quad\\\hline&23\\-&20\ \\\hline&\ \,\color{#3a9a38}{3}\end{aligned}\end{align}\Rightarrow\ \color{#333fb1}{5}\dfrac{\color{#3a9a38}{3}}{\color{#ec0000}{4}}||
Coming soon.