Add and simplify your answer. Type your answer in as a fraction using the / key. [tex]\frac{5}{7}+\frac{3}{14}[/tex]
Answer (2)
Find a common denominator for the fractions, which is 14.
Rewrite 7 5 as 14 10 .
Add the fractions: 14 10 + 14 3 = 14 13 .
The simplified answer is 14 13 .
Explanation
Understanding the problem We are asked to add two fractions, 7 5 and 14 3 , and simplify the result.
Finding a common denominator To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 7 and 14 is 14.
Rewriting the first fraction Now, we rewrite the first fraction, 7 5 , with the common denominator of 14. To do this, we multiply both the numerator and the denominator by 2: 7 5 = 7 × 2 5 × 2 = 14 10 .
Adding the fractions Now that both fractions have the same denominator, we can add them: 14 10 + 14 3 = 14 10 + 3 = 14 13 .
Simplifying the result Finally, we check if the resulting fraction, 14 13 , can be simplified. Since 13 is a prime number and it does not divide 14, the fraction is already in its simplest form.
Final Answer Therefore, the sum of the two fractions, in its simplest form, is 14 13 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have 7 5 of a pizza and your friend gives you 14 3 of a pizza, you can add these fractions to find the total amount of pizza you have. In this case, you would have 14 13 of a pizza.
To add 7 5 and 14 3 , we find a common denominator of 14 and rewrite the fractions as 14 10 and 14 3 . Adding them gives 14 13 , which is already in its simplest form. Thus, the final answer is 14 13 .
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