Solve and simplify. Express the answer in lowest terms.
$\frac{1}{5} + \frac{4}{7} = ?$
Answer (2)
Find a common denominator for the fractions, which is 35.
Rewrite the fractions with the common denominator: 1/5 = 7/35 and 4/7 = 20/35 .
Add the fractions: 7/35 + 20/35 = 27/35 .
The simplified answer is 35 27 .
Explanation
Understanding the problem We are asked to solve and simplify the expression 1/5 + 4/7 and express the answer in lowest terms.
Finding a common denominator To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 5 and 7 is 35.
Rewriting fractions Now, we rewrite each fraction with the common denominator of 35:
1/5 = ( 1 × 7 ) / ( 5 × 7 ) = 7/35
4/7 = ( 4 × 5 ) / ( 7 × 5 ) = 20/35
Adding the fractions Now that the fractions have the same denominator, we can add them:
7/35 + 20/35 = ( 7 + 20 ) /35 = 27/35
Simplifying the result The fraction 27/35 is already in its simplest form because 27 and 35 have no common factors other than 1. Therefore, the answer is 27/35 .
Final Answer The result of adding the two fractions and simplifying is 35 27 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you are making a recipe that calls for 1/5 of a cup of sugar and you want to double the recipe, you would need to calculate 1/5 + 1/5 . Similarly, if you and a friend are sharing a pizza and you eat 4/7 of the pizza, you might want to know how much pizza is left for your friend. Understanding how to add and subtract fractions is essential for many practical situations.
To add the fractions 5 1 and 7 4 , we first find a common denominator of 35. After rewriting both fractions, we add them to get 35 27 , which is already in its simplest form.
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