The denominator of the first fraction is 3. The denominator of the second fraction is 5. Because these two numbers are different, we need the lowest common denominator, which, in this case is 15 because 3 x 5 = 15. So we multiply:

We can do this because 5/5

1 and 3/3

1 and we know that multiplying a number by 1 doesn't change the number. Now we add:

Adding Fractions with Different Denominators

To Add Fractions with different denominators:

Find the Lowest Common Denominator (LCD) of the fractions

Add in the new numbers to the fractions to have the LCD

Add the numerators of the fractions

Simplify the Fraction

Example: Find the Sum of 2/9 and 3/12

Determine the Greatest Common Factor of 9 and 12 which is 3

Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)

OR - Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3*12=36)

Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)

The result is 8/36 + 9/36

Add the numerators and put the sum over the LCD = 17/36

Simplify the fraction if possible. In this case it is not possible

To add or subtract mixed numbers, simply convert the mixed numbers into improper fractions, then add or subtract them as fractions.

Example:

9 1/2 + 5 3/4 = ?

Converting each number to an improper fraction, we have 9 1/2

19/2 and 5 3/4

23/4.

We want to calculate 19/2 + 23/4. The LCM of 2 and 4 is 4, so

19/2 + 23/4

38/4 + 23/4

(38 + 23)/4 = 61/4.

Converting back to a mixed number, we have 61/4 = 15 1/4.

The strategy of converting numbers into fractions when adding or subtracting is often useful, even in situations where one of the numbers is whole or a fraction.

Example:

13 - 1 1/3 = ?

In this situation, we may regard 13 as a mixed number without a fractional part. To convert it into a fraction, we look at the denominator of the fraction 4/3, which is 1 1/3 expressed as an improper fraction. The denominator is 3, and 13

39/3. So 13 - 1 1/3

39/3 - 4/3

(39-4)/3

35/3, and 35/3 = 11 2/3.

Example:

5 1/8 - 2/3 = ?

This time, we may regard 2/3 as a mixed number with 0 as its whole part. Converting the first mixed number to an improper fraction, we have 5 1/8 = 41/8. The problem becomes

5 1/8 - 2/3

41/8 - 2/3

123/24 - 16/24

(123 - 16)/24

107/24.

Converting back to a mixed number, we have 107/24 = 4 11/24.

Example:

92 + 4/5 = ?

This is easy. To express this as a mixed number, just put the whole number and the fraction side by side. The answer is 92 4/5.

Google images

Subtracting fractions:

The of the first fraction is 8. The denominator of the second fraction is 3. Because these 2 numbers are different, we need , which, in this case is 24 because 3 x 8 = 24. So we multiply:

We can do this because 3/3 = 1 and 8/8 = 1 and we know that multiplying a number by 1 doesn't change the number. Now we subtract:

Subtracting Fractions with Different Denominators

To Subtract Fractions with different denominators:

Find the Lowest Common Denominator (LCD) of the fractions

Rename the fractions to have the LCD

Subtract the numerators of the fractions

The difference will be the numerator and the LCD will be the denominator of the answer.

Simplify the Fraction

Example: Find the difference between 3/12 and 2/9.

Determine the Greatest Common Factor of 12 and 9 which is 3

Either multiply the numbers and divide by the GCF (9*12=108, 108/3=36)

OR - Divide one of the numbers by the GCF and multiply the answer times the other number (12/3=4, 9*4=36)

Rename the fractions to use the Lowest Common Denominator (3/12=9/36, 2/9=8/36)

The result is 9/36 - 8/36

Subtract the numerators and put the difference over the LCD = 1/36

Simplify the fraction if possible. In this case it is not possible

## Adding Fractions:

## The denominator of the first fraction is 3. The denominator of the second fraction is 5. Because these two numbers are different, we need the lowest common denominator, which, in this case is 15 because 3 x 5 = 15. So we multiply:

## We can do this because 5/5

## 1 and 3/3

## 1 and we know that multiplying a number by 1 doesn't change the number. Now we add:

Adding Fractions with Different DenominatorsTo Add Fractions with different denominators:Find the Lowest Common Denominator (LCD) of the fractionsAdd in the new numbers to the fractions to have the LCDAdd the numerators of the fractionsSimplify the FractionExample: Find the Sum of 2/9 and 3/12Determine the Greatest Common Factor of 9 and 12 which is 3Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)OR - Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3*12=36)Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)The result is 8/36 + 9/36Add the numerators and put the sum over the LCD = 17/36Simplify the fraction if possible. In this case it is not possible## To add or subtract mixed numbers, simply convert the mixed numbers into improper fractions, then add or subtract them as fractions.

## Example:

## 9 1/2 + 5 3/4 = ?

## Converting each number to an improper fraction, we have 9 1/2

## 19/2 and 5 3/4

## 23/4.

## We want to calculate 19/2 + 23/4. The LCM of 2 and 4 is 4, so

## 19/2 + 23/4

## 38/4 + 23/4

## (38 + 23)/4 = 61/4.

## Converting back to a mixed number, we have 61/4 = 15 1/4.

## The strategy of converting numbers into fractions when adding or subtracting is often useful, even in situations where one of the numbers is whole or a fraction.

## Example:

## 13 - 1 1/3 = ?

## In this situation, we may regard 13 as a mixed number without a fractional part. To convert it into a fraction, we look at the denominator of the fraction 4/3, which is 1 1/3 expressed as an improper fraction. The denominator is 3, and 13

## 39/3. So 13 - 1 1/3

## 39/3 - 4/3

## (39-4)/3

## 35/3, and 35/3 = 11 2/3.

## Example:

## 5 1/8 - 2/3 = ?

## This time, we may regard 2/3 as a mixed number with 0 as its whole part. Converting the first mixed number to an improper fraction, we have 5 1/8 = 41/8. The problem becomes

## 5 1/8 - 2/3

## 41/8 - 2/3

## 123/24 - 16/24

## (123 - 16)/24

## 107/24.

## Converting back to a mixed number, we have 107/24 = 4 11/24.

## Example:

## 92 + 4/5 = ?

## This is easy. To express this as a mixed number, just put the whole number and the fraction side by side. The answer is 92 4/5.

## Google images

## Subtracting fractions:

## The of the first fraction is 8. The denominator of the second fraction is 3. Because these 2 numbers are different, we need , which, in this case is 24 because 3 x 8 = 24. So we multiply:

## We can do this because 3/3 = 1 and 8/8 = 1 and we know that multiplying a number by 1 doesn't change the number. Now we subtract:

Subtracting Fractions with Different DenominatorsTo Subtract Fractions with different denominators:Find the Lowest Common Denominator (LCD) of the fractionsRename the fractions to have the LCDSubtract the numerators of the fractionsThe difference will be the numerator and the LCD will be the denominator of the answer.Simplify the FractionExample: Find the difference between 3/12 and 2/9.Determine the Greatest Common Factor of 12 and 9 which is 3Either multiply the numbers and divide by the GCF (9*12=108, 108/3=36)OR - Divide one of the numbers by the GCF and multiply the answer times the other number (12/3=4, 9*4=36)Rename the fractions to use the Lowest Common Denominator (3/12=9/36, 2/9=8/36)The result is 9/36 - 8/36Subtract the numerators and put the difference over the LCD = 1/36Simplify the fraction if possible. In this case it is not possible## __

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