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Adding and Subtracting Fractions Vocabulary - Fraction: a part of a whole consisting of a numerator and denominator Example: - 2 = ๐๐ข๐๐๐๐๐ก๐๐ ๐๐๐๐๐๐๐๐๐ก๐๐ Improper Fraction: a fraction that has a larger numerator than denominator Example: - 1 5 3 = ๐๐ข๐๐๐๐๐ก๐๐ ๐๐๐๐๐๐๐๐๐ก๐๐ Mixed Number: a whole number with a fraction 3 ๐๐ข๐๐๐๐๐ก๐๐ 4 ๐๐๐๐๐๐๐๐๐ก๐๐ 2 = ๐คโ๐๐๐ ๐๐ข๐๐๐๐ Example: How to add or subtract fractions with like denominators Step 1: If the fractions have like denominators, add or subtract the numerators and keep the same denominator. Do not add the denominators. Step 2: Once the fractions are added or subtracted, simplify the result if you can. The result may also be changed to a mixed number, if the question requires it. Note: The same steps apply to improper fractions that have like denominators. 3 2 7 7 Example 1: + Example 2: Example 3: Example 4: 5 12 7 11 13 15 + โ โ 7 9 5 5 Example 5: + = 5 12 3 11 7 15 = 5 7 = = = 10 12 4 11 6 15 16 5 ๐๐ 6 17 โ 6 9 17 ๐๐๐๐๐๐๐๐ฆ ๐๐ 3 1 5 Remember when simplifying, divide the numerator and denominator by the same number (factor). 5 ๐๐๐๐๐๐๐๐ฆ =โ 2 5 3 17 Be careful of negative fractions. Changing improper fractions to mixed numbers: - Divide the numerator by the denominator - The number of times that the denominator divides into the numerator becomes the whole number - If the denominator does not divide evenly, the number that is left over becomes the new numerator - To find the left over number, multiply the denominator by the whole number that was found and subtract that result from the original numerator. The difference becomes the new numerator - The denominator will stay the same, unless the fractional part can be simplified 5 7 2 2 Example 6: โ 2 = โ ๐๐ โ 1 2 How to add or subtract mixed numbers with like denominators Adding: Step 1: When adding mixed numbers, add the whole numbers then add the numerators. Step 2: If the numerator is larger than the denominator, divide the numerator by the denominator and add the number of times the denominator divides into the numerator to the current whole number. The number that is left over becomes the new numerator. Note: You can follow the directions on how to change an improper fraction to a mixed number. If the numerator is smaller than the denominator, leave the mixed number the way it is unless the fraction can be simplified. 3 1 4 8 8 8 5 7 12 9 9 9 Example 1: 2 +1 =3 Example 2: 5 + 6 = 11 ๐๐๐๐๐๐๐๐ฆ 3 1 2 Follow step 2. 12 3 9 Simplify 12 1 3 Subtracting: Step 1: When subtracting mixed numbers, subtract the whole numbers then subtract the numerators if the first numerator is larger than the second numerator. If the first numerator is smaller than the second numerator, before you subtract, you must borrow from the whole number. Note: To borrow from the whole number, subtract one from the whole number and add the value of the denominator to the numerator. Step 2: Simplify the fraction if necessary. Example 1: 3 1 2 8 8 8 2 โ1 =1 ๐๐๐๐๐๐๐๐ฆ 1 1 4 5 7 9 9 5 โ3 Example 2: ๐น๐๐๐๐๐ค ๐๐ก๐๐ 1 ๐ก๐ ๐โ๐๐๐๐ ๐กโ๐ ๐๐๐๐ ๐ก ๐๐๐๐๐ก๐๐๐ 4 14 9 7 7 9 9 โ3 =1 Changing a Mixed Number to an Improper Fraction - To change a mixed number to an improper fraction, multiply the denominator by the whole number and add the numerator. This result becomes the numerator and the denominator stays the same. 3 18 5 5 3 =5×3+3= Example 3: How to add or subtract fractions with unlike denominators Step 1: If the denominators are not the same, we must make them the same by finding a common denominator. This can be done by multiplying the denominators together or finding a number that both denominators can divide into evenly. Once you have found the new denominator, you must change the numerator to keep the fractions balanced. To change the numerator, multiply it by the same number you multiplied the denominator by to get the common denominator. Step 2: Once the fractions have the same denominator, follow the steps from the previous sections. 3 4 4 5 2 5 3 6 Example 1: + Example 2: โ = = 3×5 4×5 2×2 3×2 + 4×4 5×4 = 15 20 + 16 20 = 5 4 5 1 6 6 6 6 โ = โ =โ 31 20 =1 11 20 Note: The second fraction does not change because we can multiply 3 by 2 to get 6 to create a common denominator. 5 2 5×5 8 5 8×5 Example 3: 3 +2 =3 Example 4: 5 โ2 5 7 6 12 =5 +2 5×2 6×2 2×8 5×8 โ2 7 12 =3 =5 25 40 10 12 +2 โ2 16 40 7 12 =5 =3 41 40 3 12 =6 1 40 ๐๐๐๐๐๐๐๐ฆ 3 1 4