[tex]\frac{2}{7}+\frac{6}{3}=[/tex]
Answer (2)
To solve 7 2 + 3 6 , we first simplify 3 6 to get 2, and then rewrite the equation as 7 2 + 2 . Converting 2 to 7 14 allows us to add the fractions, resulting in 7 16 .
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Simplify the fraction 3 6 to 2 .
Rewrite the problem as 7 2 + 2 .
Find a common denominator and rewrite 2 as 7 14 .
Add the fractions: 7 2 + 7 14 = 7 16 .
The final answer is 7 16 .
Explanation
Simplifying the fractions We are asked to add two fractions: 7 2 and 3 6 . To do this, we need to find a common denominator. First, we can simplify the second fraction.
Simplifying 6/3 The fraction 3 6 can be simplified to 2 , since 6 ÷ 3 = 2 . So, we can rewrite the problem as 7 2 + 2 .
Rewriting the whole number To add a fraction and a whole number, we can rewrite the whole number as a fraction with a denominator of 1. So, we have 7 2 + 1 2 .
Finding a common denominator Now, we need to find a common denominator for 7 2 and 1 2 . The least common denominator (LCD) of 7 and 1 is 7. So, we need to convert 1 2 to a fraction with a denominator of 7.
Converting to a common denominator To convert 1 2 to a fraction with a denominator of 7, we multiply both the numerator and the denominator by 7: 1 2 × 7 7 = 7 14 .
Adding the fractions Now we can add the two fractions: 7 2 + 7 14 = 7 2 + 14 = 7 16 .
Final Answer The fraction 7 16 is an improper fraction, meaning the numerator is greater than the denominator. We can convert it to a mixed number by dividing 16 by 7. 16 ÷ 7 = 2 with a remainder of 2. So, 7 16 = 2 7 2 .
Result Therefore, 7 2 + 3 6 = 7 16 .
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 7 2 of a cup of flour and you want to double the recipe, you would need to add 7 2 + 7 2 to find the total amount of flour needed. Understanding how to add fractions is essential for accurately following recipes and ensuring the desired outcome. Also, when splitting a pizza or cake, you use fractions to divide it into equal parts.
