Divide these two fractions: [tex]$\frac{4}{5}+\frac{2}{3}=?$[/tex]
Answer (2)
Find a common denominator for the fractions 5 4 and 3 2 , which is 15.
Convert the fractions to equivalent fractions with the common denominator: 5 4 = 15 12 and 3 2 = 15 10 .
Add the equivalent fractions: 15 12 + 15 10 = 15 22 .
The final answer is 15 22 .
Explanation
Finding a Common Denominator We are asked to add two fractions: 5 4 and 3 2 . To add fractions, we need to find a common denominator.
LCM of 5 and 3 The least common multiple (LCM) of 5 and 3 is 15. So, we will use 15 as the common denominator.
Converting to Equivalent Fractions Now, we convert each fraction to an equivalent fraction with a denominator of 15. 5 4 = 5 × 3 4 × 3 = 15 12 3 2 = 3 × 5 2 × 5 = 15 10
Adding the Fractions Next, we add the two equivalent fractions: 15 12 + 15 10 = 15 12 + 10 = 15 22
Simplifying the Result The fraction 15 22 is already in its simplest form, as 22 and 15 have no common factors other than 1. Therefore, the sum of the two fractions is 15 22 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you are baking a cake and the recipe calls for 5 4 of a cup of flour and 3 2 of a cup of sugar, you need to add these fractions to know the total amount of dry ingredients. Understanding how to add fractions allows you to accurately measure the ingredients and bake a delicious cake.
To add 5 4 and 3 2 , we find a common denominator of 15. Converting the fractions, we get 15 12 and 15 10 , which sum to 15 22 . This can also be expressed as the mixed number 1 15 7 .
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