Fractions: Basic Operations

Fractions might look tricky, but they’re just numbers that represent parts of a whole. When we work with fractions, there are four main operations to master: addition, subtraction, multiplication, and division.

Adding and Subtracting Fractions

To add or subtract fractions, you need a common denominator. Here’s how to do it step-by-step!

Adding Fractions

1. Find a Common Denominator: Both fractions need the same denominator to add them. If they don't, find the Least Common Denominator (LCD).
2. Adjust the Fractions: Change each fraction so they have this common denominator. This can be done by multiplying the numerator and denominator by the same number so the denominator becomes the least common denominator
3. Add the Numerators: Keep the denominator the same, and just add the top numbers (numerators).
4. Simplify if possible.

Example: $\frac{2}{5} + \frac{1}{3}$

1. Common denominator: $15$
2. Adjust fractions
   • $\frac{2}{5} = \frac{6}{15}$
   • $\frac{1}{3} = \frac{5}{15}$
3. Add numerators: $$\frac{6 + 5}{15} = \frac{11}{15}$$

Answer: $$\frac{2}{5} + \frac{1}{3} = \frac{11}{15}$$

 

 

 

 

 

Subtracting Fractions

The process is the same as for addition, but you subtract the numerators instead.

Example: $\frac{3}{4} - \frac{1}{6}$

1. Common denominator: $12$
2. Adjust fractions:
   • $\frac{3}{4} = \frac{9}{12}$
   • $\frac{1}{6} = \frac{2}{12}$
3. Subtract numerators: $$\frac{9 - 2}{12} = \frac{7}{12}$$

Answer: $$\frac{3}{4} - \frac{1}{6} = \frac{7}{12}$$

 

 

 

 

Multiplying Fractions

Multiplying fractions is simpler because you don’t need a common denominator.

1. Multiply the Numerators: Top times top.
2. Multiply the Denominators: Bottom times bottom.
3. Simplify if possible.

Example: $\frac{2}{3} \times \frac{4}{5}$

1. Multiply the numerators: $2 \times 4 = 8$
2. Multiply the denominators: $2 \times 4 = 8$

Answer: $$\frac{2}{3} \times \frac{4}{5} = \frac{8}{15}$$

 

 

 

Dividing Fractions

Dividing fractions involves flipping the second fraction and then multiplying.

1. Flip the Second Fraction: Turn it upside down (this is called the reciprocal).
2. Multiply the fractions as normal.
3. Simplify if possible.

Example: $\frac{3}{5} \div \frac{2}{7}$

1. Flip the second fraction: $\frac{7}{2}$
2. Multiply:
   • Numerators: $3 \times 7 = 21$
   • Denominators: $5 \times 2 = 10$

Answer: $$\frac{3}{5} \div \frac{2}{7} = \frac{21}{10} \text{ or } 2 \frac{1}{10}$$