📚 Quick Study Guide: Adding & Subtracting Fractions
- 🔢 What is a Fraction? A fraction represents a part of a whole. It has a Numerator (the top number, how many parts you have) and a Denominator (the bottom number, how many total parts make up the whole). For example, $\frac{3}{4}$ means 3 out of 4 equal parts.
- ➕ Adding Fractions (Same Denominator): If fractions have the same denominator, simply add the numerators and keep the denominator the same. $\frac{A}{C} + \frac{B}{C} = \frac{A+B}{C}$
- ➖ Subtracting Fractions (Same Denominator): Similar to adding, if denominators are the same, subtract the numerators and keep the denominator the same. $\frac{A}{C} - \frac{B}{C} = \frac{A-B}{C}$
- ✨ Adding/Subtracting Fractions (Different Denominators): This is the key! You CANNOT add or subtract fractions unless they have the same denominator.
- 🔍 Finding a Common Denominator: To get the same denominator, find the Least Common Multiple (LCM) of the denominators. This is the smallest number that both denominators can divide into evenly.
- ✖️ Making Equivalent Fractions: Once you find the LCM, multiply the numerator and denominator of each fraction by the same number to change them into equivalent fractions with the common denominator. Remember, whatever you do to the bottom, you must do to the top!
- Simplify! After adding or subtracting, always check if you can simplify your answer by dividing both the numerator and the denominator by their greatest common factor (GCF).
🤔 Practice Quiz: Test Your Fraction Skills!
Choose the best answer for each question.
-
What is the sum of $\frac{2}{7} + \frac{3}{7}$?
- $\frac{5}{14}$
- $\frac{6}{49}$
- $\frac{5}{7}$
- $\frac{1}{7}$
-
Calculate $\frac{9}{10} - \frac{3}{10}$.
- $\frac{6}{20}$
- $\frac{6}{10}$
- $\frac{12}{10}$
- $\frac{3}{5}$
-
Add $\frac{1}{2} + \frac{1}{4}$.
- $\frac{2}{6}$
- $\frac{3}{4}$
- $\frac{2}{8}$
- $\frac{1}{3}$
-
Subtract $\frac{5}{6} - \frac{1}{3}$.
- $\frac{4}{3}$
- $\frac{3}{6}$
- $\frac{2}{3}$
- $\frac{4}{6}$
-
What is $\frac{2}{5} + \frac{1}{10}$ in simplest form?
- $\frac{3}{15}$
- $\frac{5}{10}$
- $\frac{1}{2}$
- $\frac{3}{5}$
-
Find the value of $\frac{7}{8} - \frac{1}{4}$.
- $\frac{6}{4}$
- $\frac{5}{8}$
- $\frac{6}{8}$
- $\frac{3}{4}$
-
Mia ate $\frac{1}{3}$ of a pizza, and Tom ate $\frac{1}{6}$ of the same pizza. How much pizza did they eat altogether?
- $\frac{2}{9}$
- $\frac{1}{2}$
- $\frac{2}{3}$
- $\frac{3}{6}$
Click to see Answers
1. C ($\frac{5}{7}$)
2. B ($\frac{6}{10}$ which simplifies to $\frac{3}{5}$ - but option B is the direct result)
3. B ($\frac{3}{4}$)
4. D ($\frac{4}{6}$ which simplifies to $\frac{2}{3}$)
5. C ($\frac{1}{2}$)
6. B ($\frac{5}{8}$)
7. B ($\frac{1}{2}$)