Adding Rational Numbers in Fractional Form

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ROSE MARIE C. CALDERON

4TH YR BSED - MATH


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DEFINITION OF TERMS

RATIONAL NUMBERS

- Any number that can be made by

dividing one integer by another. Theword comes from "ratio".

- Is a number that can be in the form p/qwhere pandqare integers andqis not

equal to zero.
http://www.mathsisfun.com/whole-numbers.htmlhttp://www.mathsisfun.com/whole-numbers.html


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p q p / q =

1 1 1/1 11 2 1/2 0.5

55 100 55/100 0.55

1 1000 1/1000 0.001

253 10 253/10 25.3

7 0 7/0No! "q"can't be

zero!

Examples:


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WHATAREFRACTIONS?

Fractions are for counting PART of something

The denominator

tells us how many

pieces something

is cut into.

The numerator

tells how manyfractional pieces

there are


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BASIC FRACTIONS

A fraction is part of an entire object.

1/4 is

pink

1/2 is

pink

3/4 is

pink

4/4 orone whole

is pink


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TOADDFRACTIONSWITHTHE

SAMEDENOMINATOR

Keep the common denominatorand add the numerator.

Example: 2/5 + 1/5= 3/5

Example: 4/10 + 3/10= 7/10

Notice that the denominator doesnot change, you only add thenumerator!


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ADDING FRACTIONSWITHCOMMON

DENOMINATORS

8

4

8

3

8

7

+ =


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TRYSOME!!!

1.) 1/3 + 1/3 =

2.) 3/8 + 4/8 =

3.) 1/10 + 6/10 =

4.) 1/5 + 2/5 =

5.) 24/50 + 20/50 =

6.) 6/13 + 6/13 =

7.) 2/45 + 12/45 =

8.) 8/90 + 15/90 =

2/3

7/8

7/10

3/5

49/50

12/13

14/45

23/90


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ADDINGFRACTIONSWITHDIFFERENT

DENOMINATORSISALITTLEDIFFERENT

You must first change the

fraction before you can addfractions.

The fractions must have thesame denominators to add

them.


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ADDING FRACTIONSWITHDIFFERENT

DENOMINATORS

Problem:

You cant add fractions with differentdenominators without getting them ready first.They will be ready to add when they havecommon denominators

Solution:Turn fractions into equivalent fractions with acommon denominator that is find the LowestCommon Multiple (LCM) of the two

denominators


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FINDINGTHE

LOWEST COMMON DENOMINATOR

The lowest common multiple of two numbers is

the lowest number in BOTH lists of multiples

3

1

2

1

Multiples of 2 are 2, 4, 6, 8, 10Multiples of 3 are 3, 6, 9, 12,

What is the lowest commonmultiple?


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FINDINGTHE

LOWEST COMMON DENOMINATOR

The lowest common multiple of two numbers is

the lowest number they will BOTH divide into

3

1

2

1

2 divides into 2, 4, 6, 8..3 divides into 3, 6, 9.

What is the lowest number 2 and 3both divide into?


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+The Lowest Common Multiple of 2 and 3 is 6 so turn all fractions into sixths

6

5

6

2

6

3

2

2

3

1

3

3

2

1

You cant add fractions with

different denominators

Special form of 1

3

1

2

1


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10

9

10

4

10

5

5

2

2

1

Lowest common denominator is 10 so make all fractions tenths

11


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4

1

3

1

Turn both fractions into twelfths

12

7

12

3

12

4


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3

2

7

3

What is the lowest numberBOTH 3 and 7 divide into?

Hmmmmm??????It is 21. So that is mycommon denominator

21

?

21

?

What special formof 1 will change 7to 21. Hmmmm?

It is 3/3

So I multiply3/7 by 3/3

3

3

What specialform of 1 will

change 3 to 21.Hmmmm?

It is 7/7So I multiply2/3 by 7/7

7

7

Now 3x3=9 and 2x7=14Now I know the new

numerators

21

14

21

9

Finally the fractions are READYto add. I just have to add the

numerators 9+14=23

21

21

21

23


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ADDING MIXED

NUMBERSBasic concepts and methods

for adding mixed numbers.


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DEFINITION

Mixed Number = A mixednumber is a whole number with

a fraction attached.

Example = 3 4/5, This isread as three and four fifths.


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ADDING MIXED NUMBERS Separate the fraction and the whole number sections,

add them separately and recombine at the end

2

2

1

3

1

5

6

57

76

5

22

1

3

1

5


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Adding Rational Numbers in Fractional Form

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