Adding and Subtracting Fractions
Adding Fractions with Like Denominators In order to add fractions the denominators must be the same If the denominators of the fractions are the same we follow these two steps: add the numerators keep the denominator the same
Example: 4 + = 5 Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark
Subtracting Fractions with Like Denominators In order to subtract fractions the denominators must be the same If the denominators of the fractions are the same we follow these two steps: subtract the numerators keep the denominator the same
Example: 5 - = Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark
Rules for Adding Fractions with Unlike Denominators You must have a common denominator, if you do not, you cannot add the fraction If the denominators are different, find the least common denominator (LCD) before you begin adding the fractions Always keep your denominator the same after adding fractions
Finding the LCD LCD stands for the least common denominator. This is the smallest common denominator of two fractions. Example: + 4
Finding the LCD + 4 multiples of are:,, 8, 4, 0, 4 multiples of 4 are: 4, 8,,, 0, 4, 8, is the least common denominator
Finding the LCD x x = = + = = x 4 4 x NEW EQUATION: +
NEW EQUATION: + Now, we add the numerators and keep the denominators the same + =
Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark
Rules for Subtracting Fractions with Unlike Denominators You must have a common denominator, if you do not, you cannot subtract the fraction If the denominators are different, find the least common denominator (LCD) before you begin subtracting the fractions Always keep your denominator the same after subtracting fractions
Example: - LCD = NEW EQUATION: - - = =
Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark
Adding Mixed Numbers When adding mixed numbers we have two options: option is more steps but if you get in the habit of doing option multiplying fractions will be easier. Option only works when you are adding or subtracting mixed numbers, it DOES NOT work when you multiply fractions
Adding Mixed Numbers Option : convert the mixed numbers into improper fractions find the LCD if denominators are different add the numerators and keep the denominators the same
Example: + Step : Convert to improper fractions 7 +
Example: + Step : Find the LCD if denominators are different 7 4 + LCD = +
Example: + Step : Add the numerators and keep the denominator the same 4 + = = 5
Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark
Adding Mixed Numbers Option : Add the whole numbers together find the LCD of the fractions if denominators are different add the numerators and keep the denominators the same combine the whole number with the fraction to get your answer
Example: + Step : Add the whole numbers together + =
Example: + Step : Find the LCD of the fractions if the denominators are different + LCD = +
Example: + Step : Add the numerators and keep the denominator the same 5 + =
Example: + 4 Step 4: Combine the whole number with the fraction to get your answer 5
Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark
Subtracting Mixed Numbers Follow the same steps as adding mixed numbers, simply subtract rather than add. Both options & will get you the same answer. Remember: - simplify your answer to lowest terms - convert from improper fractions to mixed numbers if necessary. If you do not, it could cost you a half mark