Adding or subtracting fractions with the same denominator

To add or subtract fractions with the same denominator you simply add or subtract the numerator. Example 1:

Adding or subtracting mixed fractions with the same denominator

When adding or subtracting mixed fractions with the same denominator you can add the whole number first then the fraction part. Example : 2

Adding or subtracting mixed fractions with different denominators

To add or subtract fractions with different denominator you must first make the denominators the same by finding the lowest common denominator (LCD). Example :

Multiplying Fractions

When multiplying fraction it is the first numerator times the second numerator divided by the first denominator times the second denominator. Example :

Multiplying Mixed Fractions

When multiplying mixed fractions you must first change the mixed fractions into improper fractions. Example : 3

Dividing Fractions

When dividing fractions, there are two methods that can be used. Mehtod 1 that will be explained later is the most frequently used. In this method our first step is to invert the divisor then change our division sign to multiplication.

final answer. It is the numerators which give us our final answer.

Espacially in example 1, you can see that there is no need to invert one of the fractions and change the sign to multiplication.

# Fractions

Adding or subtracting fractions with the same denominator

To add or subtract fractions with the same denominator you simply add or subtract the numerator. Example 1:

^{2}⁄_{7}+^{3}⁄_{7}=^{5}⁄_{7}Example 2:^{4}⁄_{5}+^{3}⁄_{5}=^{7}⁄_{5}= 1^{2}⁄_{5}Example 3:^{8}⁄_{9}-^{2}⁄_{9}=^{6}⁄_{9}=^{2}⁄_{3}Adding or subtracting mixed fractions with the same denominator

When adding or subtracting mixed fractions with the same denominator you can add the whole number first then the fraction part. Example : 2

^{4}⁄_{11}+ 1^{3}⁄_{11}= (2 + 1) +^{5}⁄_{11}+^{3}⁄_{11}= 3^{8}⁄_{11}Adding or subtracting mixed fractions with different denominators

To add or subtract fractions with different denominator you must first make the denominators the same by finding the lowest common denominator (LCD). Example :

^{3}⁄_{8}+^{1}⁄_{3}(The LCD for 8 and 3 is 24). Therefore, the answer becomes^{9}⁄_{24}+^{8}⁄_{24}=^{17}⁄_{24}Multiplying Fractions

When multiplying fraction it is the first numerator times the second numerator divided by the first denominator times the second denominator. Example :

^{4}⁄_{5}×^{3}⁄_{7}=^{12}⁄_{35}Multiplying Mixed Fractions

When multiplying mixed fractions you must first change the mixed fractions into improper fractions. Example : 3

^{2}⁄_{5}×^{3}⁄_{8}=^{17}⁄_{5}×^{3}⁄_{8}=^{51}⁄_{40}= 1^{11}⁄_{40}Dividing Fractions

When dividing fractions, there are two methods that can be used. Mehtod 1 that will be explained later is the most frequently used. In this method our first step is to invert the divisor then change our division sign to multiplication.

**Method 1:****Invert the divisor then multiply.**Example 1:^{17}⁄_{28}÷^{19}⁄_{28}=^{17}⁄_{28}×^{28}⁄_{19}=^{17}⁄_{19}Example 2:^{2}⁄_{3}÷^{7}⁄_{8}=^{2}⁄_{3}×^{8}⁄_{7}= 16⁄_{21}As you might have noticed, this method is like a trick that gives the correct answer, but it is based on the principle of the same denominator.**Method 2:****When dividing fractions we can make the denominators the same by finding the LCD.**Example 1:^{17}⁄_{28}÷^{19}⁄_{28}=^{17}⁄_{19}(We get our answer just by read across the numerators.) Example 2:^{2}⁄_{3}÷^{7}⁄_{8}(the LCD is 24. Now treat it as if you are adding or subtracting fractions.) So, this becomes^{16}⁄_{24}÷^{21}⁄_{24}=^{16}⁄_{21}(We get our answer just by read across the numerators.) Unlike adding and subtraction of fractions, we do not write back the denominator as part of ourfinal answer. It is the numerators which give us our final answer.

Espacially in example 1, you can see that there is no need to invert one of the fractions and change the sign to multiplication.

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