Addition and Subtraction of Fractions

Warm up Convert these Mixed numbers as improper fractions 5 8/8 = 48/8 5 8/8 = 48/8 4 5/6 = 29/6 3 3/5 = 18/5 4) Write 3 improper fractions with 4 as denominator 9/4 , 13/4, 23/4 5) Write a fraction for 26 minutes in an hour. Is it proper or an improper fraction? 26/60 proper fraction Confidential

A fraction in which the numerator is greater than the denominator Lets review of our last lesson Improper Fraction A fraction in which the numerator is greater than the denominator Mixed Number A mixed number (fraction) is a number that has a part that is a whole number and a part that is a fraction Confidential

Conversion from an improper fraction in to a mixed fraction Divide the numerator by the denominator The remainder you get put it over the denominator (i.e. in the numerator) The quotient in the place of the whole number Confidential

The mixed fraction will look like Remainder Quotient Divisor Confidential

Multiply the whole number times the denominator Conversion from a mixed fraction in to a improper fraction Multiply the whole number times the denominator Add your answer to the numerator Put your new number over the denominator Confidential

The improper fraction will be written as (Whole number x Denominator) + Numerator Denominator Confidential

Change this mixed number to an improper fraction Multiply the whole number times the denominator. Add your answer to the numerator. Put your new number over the denominator. + 3 43 8 = x 5 5 Confidential

Lets get Started Addition of Fractions more sets Addition means combining objects in two or more sets the objects must be of the same type, i.e. we combine bundles with bundles and sticks with sticks. in fractions, we can only combine pieces of the same size. In other words, the denominators must be the same. Confidential

Addition of Fractions with equal denominators Example 1 8 3 8 + + = ? Confidential

+ + = Addition of Fractions with equal denominators Example 1 8 3 8 The answer is (1+3) 8 Which can be simplified to 1 2 Confidential

Addition of Fractions with equal denominators (1+3) (8+8) is NOT the right answer because the denominator tells us how many pieces the whole is divided into, and in this addition problem, we have not changed the number of pieces in the whole. Therefore the denominator should still be 8. Confidential

1 Examples of Addition with equal denominators 2 1 3 5 5 5 + = 2 1 3 5 5 5 + = 6 7 13 3 10 10 10 10 + = = 1 6 9 15 11 11 11 + = Confidential

+ + = Addition of Fractions with different denominators 1 2 3 5 + Prime denominators In this case, we need to first convert them into equivalent fraction with the same denominator Example: 1 2 3 5 + An easy choice for a common denominator is 3×5 = 15 1 x 5 5 3 3 x 5 15 2 2 x 3 6 5 5 x 3 15 = = = = 1 2 5 6 11 3 5 15 15 15 + = + = Therefore, Confidential

Addition of Fractions with different denominators Remember When the denominators are co-prime, we need to multiply the two denominators to get the common denominator When the two denominators have a common factor we find the least common denominator by factoring When one denominator is a multiple of the other denominator the multiple is the denominator Confidential

Examples of each type of denominators Multiple Denominators 3 1 4 8 3 x 2 4 x 2 6 1 8 8 6 + 1 8 = = 7 8 + = = + 8 is multiple of 4 Prime Denominators 3 2 5 7 + 3 x 7 2 x 5 5 x 7 7 x 5 21 10 21 + 10 31 35 35 35 35 + + = = = = 5 and 7 are both prime Common Factor 5 4 6 9 5 x 3 4 x 2 6 x 3 9 x 2 23 18 + 15 08 18 18 + 15 + 08 18 = + = = = Take LCM of 6 and 9 Confidential

Add the fractions together and the whole numbers together Adding Mixed Numbers 1 5 3 5 1 5 3 5 + + + 3 + 2 = 3 2 1 + 3 5 =2 + 3 + 4 5 = 5 + 4 5 = 5 Add the fractions together and the whole numbers together Confidential

Subtraction of Fractions subtraction means taking objects away the objects must be of the same type, i.e. we can only take away apples from a group of apples - in fractions, we can only take away pieces of the same size. In other words, the denominators must be the same Confidential

Subtraction of Fractions with equal denominators 11 3 12 12 - 3 12 This means to take away from 11 12 11 12 take away Confidential

Subtraction of Fractions with equal denominators 11 3 12 12 - 3 12 11 12 This means to take away from 11 12 Confidential

Subtraction of Fractions with equal denominators 11 3 12 12 - Now you can see that there are only 8 pieces left, therefore 11 3 11 - 3 12 12 12 - = 8 12 = Confidential

Lets see some more examples Equal Denominators 15 7 15 - 7 8 16 16 16 16 - = = Different denominators 6 4 6 x 9 4 x 7 54-28 26 7 9 7 x 9 9 x 7 63 63 - = - = = Do same as in Addition Multiple Take the multiple Common Factors Take LCM Prime Multiply the two Confidential

Subtraction of mixed numbers 1 4 1 2 - 3 1 Example: Since 1/4 is not enough to be subtracted by 1/2, we have to convert all mixed numbers into improper fractions first then compute 1 4 1 2 3 x 4 + 1 1 x 2 + 1 4 2 - - 3 1 = 13 3 4 2 13 6 4 4 - = - = 7 4 3 4 = = 1 Confidential

Your Questions 3/8 + 5/8 1 2/9 + 3/5 37/45 9/10 -3/4 3/20 3/8 + 5/8 1 2/9 + 3/5 37/45 9/10 -3/4 3/20 To make a salad, Henry used ¾ pound of Boston lettuce and 2/3 pound of red lettuce. How much lettuce did he use in all? 17/12 pounds 8/15 – 2/5 2/15 Confidential

Questions galore 6) 7/9 - 1/6 11/18 7) 3 ¼ + 6 ½ 39/4 6) 7/9 - 1/6 11/18 7) 3 ¼ + 6 ½ 39/4 8) 11/12 - 1/3 7/12 9) 6/9 - 18/27 0 10) 28/12 – 48/24 1/3 Confidential

Lets take a Break Confidential

6/1/5 Dividing Integers GAME Click here to play a Game Confidential

Emma takes lesser time by 9/20 minutes Jason takes 11/5 minutes to walk across the park. Emma takes 7/4 minutes to do the same. Who takes less time and by what fraction? Emma takes lesser time by 9/20 minutes Confidential

2) Alice painted 2/3 of the wall space in her room 2) Alice painted 2/3 of the wall space in her room. Sabrina helped her by painting 1/3 of the wall space. How much did they paint together? They painted the complete wall. Confidential

3) Bob’s hat size is 27/4. Betty’s hat size is 57/8 3) Bob’s hat size is 27/4 .Betty’s hat size is 57/8. How much larger is Betty’s size than Bob’s? 3/8 of a size Confidential

Addition of Fractions Lets recap what we have learned in this lesson Addition means combining objects in two or more sets the objects must be of the same type, i.e. we combine bundles with bundles and sticks with sticks. in fractions, we can only combine pieces of the same size. In other words, the denominators must be the same. Confidential

Addition of Fractions + With equal denominators Example 1 8 3 8 The answer is (1+3) 8 Which can be simplified to 1 2 Confidential

Addition of Fractions with different denominators Remember When the denominators are co-prime, we need to multiply the two denominators to get the common denominator When the two denominators have a common factor we find the least common denominator by factoring When one denominator is a multiple of the other denominator the multiple is the denominator Confidential

Subtraction of Fractions subtraction means taking objects away the objects must be of the same type, i.e. we can only take away apples from a group of apples - in fractions, we can only take away pieces of the same size. In other words, the denominators must be the same Confidential

Subtraction of fractions 11 3 12 12 Example: - 11 3 11 - 3 12 12 12 - = 8 12 = Confidential

You had a Great Lesson Today Confidential