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Fractions: Adding and Subtracting

Adding and subtracting fractions involves finding a common denominator.

We can add or subtract fractions as long as they have the same denominator.

For example: $\dfrac{3}{14} + \dfrac{5}{14}=\dfrac{8}{14}$

Find $\dfrac{2}{8}+\dfrac{4}{8}$ and simplify

What is $\dfrac{3}{16} + \dfrac{6}{16}$ ?

Unfortunately, the denominators won't always be the same! 🤦‍♀️

If the denominators are different, then you must first make them the same by multiplying both numerator and denominator by the same number.

When the denominators are not the same, we need to find the LCM (lowest common multiple). Let's try $\dfrac{1}{2} - \dfrac{2}{7}$

We can't subtract these just yet

Notice that the denominators are different.

What is the lowest common multiple of 2 and 7?

14 is the lowest common multiple

We need to multiply both fractions to make their denominators 14. This means multiplying $\dfrac{1}{2}$ by $\dfrac{7}{7}$ , and $\dfrac{2}{7}$ by $\dfrac{2}{2}$ .

Multiply the fractions to make the denominators 14

$\dfrac{1}{2} \times \dfrac{7}{7} = \dfrac{7}{14}$ and $\dfrac{2}{7} \times \dfrac{2}{2}=\dfrac{4}{14}$

Subtract the fractions

$\dfrac{7}{14}-\dfrac{4}{14}=\dfrac{3}{14}$

Good work! 💪

The answer is $\dfrac{3}{14}$

What is $\dfrac{2}{6} + \dfrac{5}{8}$ ?