Add. Simplify the answer and write it as a mixed number. [tex]$\frac{5}{6}+\frac{2}{9}$[/tex]
Answer (2)
Find the least common multiple (LCM) of the denominators 6 and 9, which is 18.
Convert both fractions to equivalent fractions with the common denominator: 6 5 = 18 15 and 9 2 = 18 4 .
Add the fractions: 18 15 + 18 4 = 18 19 .
Convert the improper fraction to a mixed number: 18 19 = 1 18 1 .
Explanation
Find the Common Denominator We need to add the fractions 6 5 and 9 2 . To do this, we first need to find a common denominator. The least common multiple (LCM) of 6 and 9 is 18.
Convert to Equivalent Fractions Now, we convert both fractions to have a denominator of 18. To convert 6 5 , we multiply both the numerator and denominator by 3: 6 5 = 6 × 3 5 × 3 = 18 15 To convert 9 2 , we multiply both the numerator and denominator by 2: 9 2 = 9 × 2 2 × 2 = 18 4
Add the Fractions Now that both fractions have the same denominator, we can add them: 18 15 + 18 4 = 18 15 + 4 = 18 19
Convert to Mixed Number Finally, we convert the improper fraction 18 19 to a mixed number. Since 19 divided by 18 is 1 with a remainder of 1, we have: 18 19 = 1 18 1
Examples
Fractions are used in everyday life, such as when cooking, baking, or measuring ingredients. For example, if a recipe calls for 6 5 of a cup of flour and you only have 9 2 of a cup, you need to add the two fractions to determine the total amount of flour you have. Understanding how to add fractions is essential for accurate measurements and successful cooking.
To add 6 5 and 9 2 , we first find a common denominator of 18, converting the fractions to 18 15 and 18 4 . After adding these, we get 18 19 , which simplifies to the mixed number 1 18 1 .
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