Adding and Subtracting Fractions

• Adding and subtracting fractions involves combining or finding the difference between parts of a whole.
• Simplifying fractions means reducing them to their simplest form.
• Mixed numbers combine whole numbers and fractions.
• Word problems apply these concepts to real-life situations.

Adding Fractions

• Fractions can only be added if they have a common denominator.
• A common denominator is a number that is a multiple of all the denominators in the problem.
• If fractions don't have a common denominator, find the Least Common Multiple (LCM) of the denominators.
• The LCM will be the new common denominator.
• Once a common denominator is found, convert each fraction, without changing the fraction's value.
• To convert a fraction, determine what number the original denominator must be multiplied by to equal the new common denominator.
• Multiply both the numerator and denominator of the original fraction by this number.
• Add the numerators and keep the denominator the same.
• Simplify the resulting fraction, if possible.
• Example: 1/3 + 1/4. The LCM of 3 and 4 is 12. Convert 1/3 to 4/12 (multiply numerator and denominator by 4). Convert 1/4 to 3/12 (multiply numerator and denominator by 3).
• Now add: 4/12 + 3/12 = 7/12.

Subtracting Fractions

• Subtracting fractions also requires a common denominator.
• Find the LCM of the denominators, if needed, and convert the fractions.
• Subtract the numerators and keep the denominator the same.
• Simplify the resulting fraction, if possible.
• Example: 3/5 - 1/5 = (3-1)/5 = 2/5.
• Example: 1/2 - 1/3. The LCM of 2 and 3 is 6. Convert 1/2 to 3/6. Convert 1/3 to 2/6.
• Now subtract: 3/6 - 2/6 = 1/6.

Simplifying Fractions

• Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1.
• Find the Greatest Common Factor (GCF) of the numerator and denominator.
• The GCF is the largest number that divides evenly into both the numerator and denominator.
• Divide both the numerator and denominator by the GCF.
• The resulting fraction is the simplified form.
• Example: Simplify 4/8. The GCF of 4 and 8 is 4. Divide both by 4: 4/4 = 1, 8/4 = 2. Simplified fraction: 1/2.
• A fraction is in simplest form when the GCF of the numerator and denominator is 1.

Mixed Numbers

• A mixed number is a combination of a whole number and a fraction (e.g., 1 1/2).
• To add or subtract mixed numbers, you can either convert them to improper fractions or work with the whole numbers and fractions separately.
• An improper fraction has a numerator that is greater than or equal to the denominator e.g. 3/2.

Converting Mixed Numbers to Improper Fractions

• Multiply the whole number by the denominator of the fraction.
• Add the numerator to the result.
• Keep the same denominator.
• Example: Convert 2 1/3 to an improper fraction. 2 * 3 = 6. 6 + 1 = 7. Improper fraction: 7/3.

Converting Improper Fractions to Mixed Numbers

• Divide the numerator by the denominator.
• The quotient is the whole number part of the mixed number.
• The remainder is the numerator of the fractional part.
• Keep the same denominator.
• Example: Convert 11/4 to a mixed number. 11 ÷ 4 = 2 with a remainder of 3. Mixed number: 2 3/4.

Adding and Subtracting Mixed Numbers

• Method 1: Convert to Improper Fractions. Convert mixed numbers to improper fractions. Find a common denominator. Add or subtract the improper fractions. Convert the result back to a mixed number, if needed.
• Method 2: Work Separately. Add or subtract the whole numbers. Add or subtract the fractions (finding a common denominator if necessary). If the fractional part is an improper fraction, convert it to a mixed number and add the whole number part to the whole number from the first step.
• Example: 1 1/2 + 2 1/4. Convert to improper fractions: 3/2 + 9/4. Common denominator: 6/4 + 9/4 = 15/4. Convert back to mixed number: 3 3/4. Or, add whole numbers: 1 + 2 = 3. Add fractions: 1/2 + 1/4 = 2/4 + 1/4 = 3/4. Combine: 3 3/4.

Word Problems with Fractions

• Read the problem carefully to understand what is being asked.
• Identify the fractions and the operations needed (addition, subtraction).
• If necessary, convert mixed numbers to improper fractions.
• Find a common denominator if adding or subtracting fractions with unlike denominators.
• Perform the operation.
• Simplify the answer if possible.
• Write the answer in the context of the problem.
• Example: John ate 1/3 of a pizza, and Mary ate 1/4 of the same pizza. How much of the pizza did they eat in total? Add the fractions: 1/3 + 1/4. Find common denominator: 4/12 + 3/12 = 7/12. Answer: They ate 7/12 of the pizza.
• Word problems often involve real-world scenarios like cooking, measuring, or sharing.

Tips for Solving Fraction Problems

• Always look for opportunities to simplify fractions before performing operations.
• When adding or subtracting fractions, double-check that you have a common denominator.
• When working with mixed numbers, choose the method (improper fractions or working separately) that you find easiest.
• Practice regularly to improve your skills and confidence.
• Draw diagrams or use visual aids to help understand the problem.
• Check your answers to ensure they make sense in the context of the problem.