Sure! Here's a simple guide on how to work with fractions :
What is a Fraction?
A fraction represents a part of a whole. It has two parts:
- Numerator (top number): How many parts you have.
- Denominator (bottom number): How many equal parts the whole is divided into.
Example:
34\frac{3}{4}43 means 3 parts out of 4 equal parts.
Basic Operations with Fractions
1. Adding Fractions
- If denominators are the same , add the numerators and keep the denominator.
25+15=2+15=35\frac{2}{5}+\frac{1}{5}=\frac{2+1}{5}=\frac{3}{5}52+51=52+1=53
- If denominators are different , find a common denominator (usually the least common multiple), convert fractions, then add.
13+14=412+312=712\frac{1}{3}+\frac{1}{4}=\frac{4}{12}+\frac{3}{12}=\frac{7}{12}31+41=124+123=127
2. Subtracting Fractions
- Similar to addition: make denominators the same, then subtract numerators.
56−16=46=23\frac{5}{6}-\frac{1}{6}=\frac{4}{6}=\frac{2}{3}65−61=64=32
3. Multiplying Fractions
- Multiply the numerators and multiply the denominators.
23×45=2×43×5=815\frac{2}{3}\times \frac{4}{5}=\frac{2\times 4}{3\times 5}=\frac{8}{15}32×54=3×52×4=158
4. Dividing Fractions
- Flip the second fraction (take the reciprocal) and multiply.
34÷25=34×52=158\frac{3}{4}\div \frac{2}{5}=\frac{3}{4}\times \frac{5}{2}=\frac{15}{8}43÷52=43×25=815
Simplifying Fractions
- Find the greatest common divisor (GCD) of numerator and denominator.
- Divide both by the GCD.
Example:
812→GCD of 8 and 12 is 4\frac{8}{12}\rightarrow \text{GCD of 8 and 12 is 4}128→GCD of 8 and 12 is 4
8÷412÷4=23\frac{8\div 4}{12\div 4}=\frac{2}{3}12÷48÷4=32
Converting Between Mixed Numbers and Improper Fractions
- Mixed number to improper fraction :
213=2×3+13=732\frac{1}{3}=\frac{2\times 3+1}{3}=\frac{7}{3}231=32×3+1=37
- Improper fraction to mixed number :
73=213\frac{7}{3}=2\frac{1}{3}37=231
If you want, I can help with examples or practice problems! Just ask. 😊
