Find [tex]$3 / 8+1 / 6+1 / 4$[/tex]
Answer (2)
Find the least common multiple (LCM) of the denominators: LCM(8, 6, 4) = 24.
Rewrite each fraction with the common denominator: 8 3 = 24 9 , 6 1 = 24 4 , 4 1 = 24 6 .
Add the fractions: 24 9 + 24 4 + 24 6 = 24 19 .
The final answer is 24 19 .
Explanation
Finding a Common Denominator We need to find the sum of the fractions 8 3 , 6 1 , and 4 1 . To do this, we first need to find a common denominator for the fractions. The least common multiple (LCM) of the denominators 8, 6, and 4 will be our common denominator.
Determining the LCM The least common multiple of 8, 6, and 4 is 24. We can find this by listing the multiples of each number: Multiples of 8: 8, 16, 24, 32, ... Multiples of 6: 6, 12, 18, 24, 30, ... Multiples of 4: 4, 8, 12, 16, 20, 24, ... The smallest multiple that appears in all three lists is 24.
Rewriting Fractions Now we rewrite each fraction with the common denominator of 24: 8 3 = 8 × 3 3 × 3 = 24 9 6 1 = 6 × 4 1 × 4 = 24 4 4 1 = 4 × 6 1 × 6 = 24 6
Adding the Fractions Now that all fractions have the same denominator, we can add them: 24 9 + 24 4 + 24 6 = 24 9 + 4 + 6 = 24 19
Final Result The sum of the fractions is 24 19 . This fraction is already in its simplest form, as 19 is a prime number and does not divide 24.
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you are baking a cake and the recipe calls for 8 3 cup of flour, 6 1 cup of sugar, and 4 1 cup of butter, you need to add these fractions to determine the total amount of dry ingredients. The ability to add fractions is essential for accurate measurements and successful baking.
To add the fractions 8 3 + 6 1 + 4 1 , first find a common denominator of 24. Then, convert each fraction: 8 3 becomes 24 9 , 6 1 becomes 24 4 , and 4 1 becomes 24 6 . Adding these gives 24 19 .
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