Addition and Subtraction Addition and Subtraction of Fractionsof Fractions

Addition and Subtraction Addition and Subtraction of Fractionsof Fractions

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Warm up

Convert these Mixed numbers as improper fractions

1)5 8/8 = 48/8 2)4 5/6 = 29/6 3)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

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Lets review of our last lesson

Improper Fraction

A fraction in which the numerator is greater than the denominator

A mixed number (fraction) is a number that has a part that is a whole number and a part that is a fraction

Mixed Number

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Conversion from an improper Conversion from an improper fraction fraction

in to a mixed fractionin 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

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The mixed fraction will look like

QuotientRemainder

Divisor

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Conversion from a mixed fraction Conversion from a mixed fraction in to a improper fractionin to a improper fraction

Multiply the whole number times the denominator

Add your answer to the numerator

Put your new number over the denominator

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The improper fraction will be written as

(Whole number x Denominator) + Numerator

Denominator

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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.

8 35x

+=

43 5

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Lets get Started

- 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.

Addition of Fractions

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Addition of Fractions with equal denominators

+ = ?

Example 1 8

+ 38

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+ =

Addition of Fractions with equal denominators

Example 1 8+ 3

8

The answer is (1+3) 8

Which can be simplified to 1 2

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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.

(1+3)(8+8)

Addition of Fractions with equal denominators

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2 1 35 5 5

+ =

6 7 13 3 10 10 10 10

6 9 1511 11 11

1+ = =

+ =

Examples of Addition with equal denominators

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In this case, we need to first convert them into equivalent fraction with the same denominator

Example:

An easy choice for a common denominator is 3×5 = 15

Therefore,

Addition of Fractions with different denominators

1 23 5

+

1 1 x 5 53 3 x 5 15

= =2 2 x 3 65 5 x 3 15

= =

1 2 5 6 113 5 15 15 15

+ = + =

Prime denominators

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Addition of Fractions with different denominators

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

Remember

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=

=

=

=

=

=

=

=

3 14 8+

3 x 24 x 2

6 18 8

+ 6 + 1 8

= 78

Examples of each type of denominators

3 25 7+ 3 x 7 2 x 5

5 x 7 7 x 5+ 21 10 21 + 10 31

35 35 35 35+ = =

5 46 9 + 5 x 3 4 x 2

6 x 3 9 x 2+ 15 08

18 18+ 15 + 08

18=

2318

Multiple Denominators

Prime Denominators

Common Factor

8 is multiple

of 4

5 and 7 are both

prime

Take LCM of 6 and 9

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Adding Mixed Numbers

3 15 +2 3

5= 3 + 1

5 + 2 + 3

5

=2 + 3 +1 + 3 5

= 5 + 45

= 5 45

Add the fractions together and the whole numbers together

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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

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Subtraction of Fractions with equal denominators

take away

This means to take away from

11 312 12

-

312

1112

1112

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Subtraction of Fractions with equal denominators

This means to take away from

11 312 12

-

312

1112

1112

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Subtraction of Fractions with equal denominators

Now you can see that there are only 8 pieces left,

therefore

11 312 12

-

11 3 11 - 312 12 12

=- = 812

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15 7 15 - 7 816 16 16 16

- = =

6 4 6 x 9 4 x 7 54-28 26

7 9 7 x 9 9 x 7 63 63- = - = =

Lets see some more examples

Equal Denominators

Different denominators

Do same as in AdditionMultiple Take the multipleCommon Factors Take LCMPrime Multiply the two

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Subtraction of mixed numbers

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

314

112

-314

112 =3 x 4 + 1 1 x 2 + 1

4 2-

= 13 3 4 2

- = 13 6 4 4

-

= 74

= 1 34

-

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Your Questions

1)3/8 + 5/8 1

2)2/9 + 3/5 37/45

3) 9/10 -3/4 3/20

4)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

5)8/15 – 2/5 2/15

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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

Questions galore

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Lets take a Break

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GAME

6/1/5 Dividing Integers

Click here to play a Game

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1)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

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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.

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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

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- 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.

Addition of Fractions

Lets recap what we have learned in this lesson

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Example 1 8+

38

The answer is (1+3) 8

Which can be simplified to 1 2

Addition of Fractions

With equal denominators

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Addition of Fractions with different denominators

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

Remember

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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

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11 312 12

-

11 3 11 - 312 12 12

=- = 812

Subtraction of fractions

Example:

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You had a Great Lesson Today