[tex]\frac{3}{17}+6[/tex]
Answer (2)
Rewrite 6 as a fraction with a denominator of 17: 6 = 17 102 .
Add the two fractions: 17 3 + 17 102 = 17 3 + 102 .
Simplify the numerator: 3 + 102 = 105 .
The final result is 17 105 .
Explanation
Understanding the problem We need to evaluate the expression 17 3 + 6 .
Rewriting 6 as a fraction To add the fraction 17 3 to the whole number 6, we need to express 6 as a fraction with the same denominator as 17 3 , which is 17. We can do this by multiplying 6 by 17 17 .
6 = 6 × 17 17 = 17 6 × 17 = 17 102
Adding the fractions Now that we have both terms as fractions with the same denominator, we can add them: 17 3 + 17 102 = 17 3 + 102
Simplifying the numerator Next, we simplify the numerator by adding 3 and 102: 3 + 102 = 105 So, the fraction becomes: 17 105
Final result The final result is 17 105 . This fraction is already in its simplest form because 105 and 17 do not share any common factors other than 1.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Understanding how to add fractions is essential for accurate calculations in these situations. For example, if you need to add 17 3 of a cup of flour to 6 cups of flour, you would perform the calculation 17 3 + 6 to determine the total amount of flour needed, which is 17 105 cups.
To add 17 3 and 6, we rewrite 6 as 17 102 and then sum the fractions, resulting in 17 105 . This fraction is in its simplest form. Understanding this method of addition with fractions is essential in mathematics.
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