Verified Answer :

  • Identify the common denominator of 9.
  • Add the numerators: \(1 + 7 + 9 = 17\).
  • Combine the result over the common denominator: \(\frac{17}{9}\).
  • Final answer: \(\boxed{\frac{17}{9}}\).

Explanation

  1. Problem Analysis

The problem asks to simplify the sum of three fractions: \(\frac{1}{9} + \frac{7}{9} + \frac{9}{9}\). These fractions all have the same denominator, which is \(9\). When adding fractions that share a common denominator, we simply add their numerators and keep the denominator the same. The rule is given by: \(\frac{a}{d} + \frac{b}{d} + \frac{c}{d} = \frac{a+b+c}{d}\).

  1. Adding the Fractions

To find the sum, add the numerators together while keeping the denominator constant:
\[\frac{1}{9} + \frac{7}{9} + \frac{9}{9} = \frac{1 + 7 + 9}{9}\]
Calculating the sum of the numerators:
\[1 + 7 + 9 = 17\]
Thus, the sum of the fractions is:
\[\frac{17}{9}\]
This fraction is in its simplest form because \(17\) and \(9\) share no common factors other than \(1\). Alternatively, it can be expressed as a mixed number: \(17 \div 9 = 1\) with a remainder of \(8\), so \(\frac{17}{9} = 1 \frac{8}{9}\).

  1. Final Result

The simplified form of the expression is \(\frac{17}{9}\) or \(1 \frac{8}{9}\). We will express this as the improper fraction \(\boxed{\frac{17}{9}}\).

Examples

In real life, adding fractions is essential for tasks like baking or woodworking. For example, if a recipe calls for \(\frac{1}{9}\) cup of sugar, \(\frac{7}{9}\) cup of flour, and \(\frac{9}{9}\) cup of oats, you can combine these amounts to find the total volume: \(\frac{1}{9} + \frac{7}{9} + \frac{9}{9} = \frac{17}{9}\) cups, which is approximately \(1.89\) cups. This helps in measuring ingredients accurately.

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