Welcome to adding & subtracting fractions basics

$Page 1: Welcome to adding & subtracting fractions basics$
Welcome to adding & subtracting fractions basics

By: Mr. Garcia

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Adding and Subtracting Fractions with a common denominator.

Simplifying Fractions

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Adding and Subtracting Fractions with a different denominators.

Changing Improper Fractions to Mixed Numbers.

Finding a common denominator.

End Show

Adding and Subtracting FractionsStep 1: Check your fractions to see if they have a common (same) denominator (bottom number).

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Step 2: If both denominators are the same, then add the two numerators (top number) together.

Adding and Subtracting Fractions


Step 3: After adding the two numerators together, that answer will be your new numerator. Your denominator will stay the same.



Final Step: You always have to check if you can simplify your answer.


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Step 1: Check your fractions to see if they have a common (same) denominator (bottom number).

Adding and Subtracting Fractions with Uncommon Denominators


Step 2: Because these fractions do not have the same denominator you must find a common denominator for them before you can add or subtract.



One strategy you can use, to find a common denominator, is to list the multiples of the denominators until you find one common to both numbers.

8- 8 x 1= 8 8 x 2=16 8 x 3=24 8 x 4=32 8 x 5=40 8 x 6=48

10- 10 x 1 = 10 10 x 2=2010 x 3=30 10 x 4= 40



Change both fractions to new fractions with this common denominator. To do this, multiply the denominator by the factor that will equal the common denominator.

€

910× 4

= 940

€

78×5

= 740

€

940+ 740=



Whatever changes you make to the denominator, you must make the same to the numerator.

€

3640+ 3540=

€

9× 410× 4

= 3640

€

7×58×5

= 3540



Now add the two numerators together and the denominator will stay the same.

€

36+3540

= 7140



Finally you need to simplify your answer. In this example the answer is improper therefore to simplify it, we need to change it to a mixed number. After you change it to a mixed number you still need to check if you can simplify the fraction. If you forgot how to change an improper fraction to a mixed number go to that section of the presentation.


€

7140=13140


Because these fractions do not have the same denominator you must find a common denominator for them before you can add or subtract.

Finding a Common Denominator


One strategy you can use, to find a common denominator, is to list the multiples of the denominators until you find one common to both numbers.

8- 8 x 1= 8 8 x 2=16 8 x 3=24 8 x 4=32 8 x 5=40 8 x 6=48

10- 10 x 1 = 10 10 x 2=2010 x 3=30 10 x 4= 40



Change both fractions to new fractions with this common denominator. To do this, multiply the denominator by the factor that will equal the common denominator.

€

910× 4

= 940

€

78×5

= 740

€

940+ 740=




€

3640+ 3540=

€

9× 410× 4

= 3640

€

7×58×5

= 3540


That is how you find a common denominator. Now add and simplify.Click here for next slide.

A second strategy to finding a common denominator is to is to multiply the two fractions by the opposite denominator.



You will multiply the first denominator by 8 and the second denominator by 10.

€

980+ 780=


€

910×8

= 980

€

78×10

= 780




That is how you find a common denominator. Now add and simplify.

€

9×810×8

= 7280

€

7×108×10

= 7080

€

7280+ 7080=



€

7280

When you add, subtract, multiply, or divide fractions you always have to check if you can simplify your final answer. To simplify your final answer you have to find a common factor that you can divide the numerator and denominator by.



€

72−1, 2,3, 4, 6, 8, 9,12,18, 24,36, 7280−1, 2, 4, 5, 8,10,16, 20, 40, 80

To find the common factor you should list all the factors of the numerator and denominator.



€

72−1, 2,3, 4, 6, 8, 9,12,18, 24,36, 7280−1, 2, 4, 5, 8,10,16, 20, 40, 80

All of the factors that are the same in both lists are common factors.



€

72−1, 2,3, 4, 6, 8, 9,12,18, 24,36, 7280−1, 2, 4, 5, 8,10,16, 20, 40, 80

You can divide the fraction by any one of these common factors. To get the fraction in simplest form you should divide by the greatest common factor. In this example the greatest common factor is 8. Therefore divide by 8.



€

72 ÷880 ÷8

= 910

After you divide by 8 the answer you get is your answer in simplest form.


Changing Improper Fractions to Mixed Numbers

€

127



€

127

The first thing you need to do is divide the numerator by the denominator.

€

7 12)Click here for next slide.


Seven goes into 12, 1 time.

€

7 121

)Click here for next slide.


You use the Quotient, Divisor, & Remainder to make your mixed number.

€

7 121

)- 7 5

Quotient

Divisor

RemainderClick here for next slide.


The quotient becomes the whole number. The Divisor was the denominator and remains the denominator. The remainder is your numerator.

Quotient

Divisor

Remainder

€

7 12−7

1)

5

€

157

Numerator

Whole Number

Denominator



€

157

The final thing you need to check is can the fraction be simplified. In this example it can not therefore you are finished.


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Welcome to adding & subtracting fractions basics