[tex]$\frac{3}{8}+\frac{1}{3}$[/tex]
Answer (2)
Find the least common denominator (LCD) of 8 and 3, which is 24.
Rewrite the fractions with the common denominator: 8 3 = 24 9 and 3 1 = 24 8 .
Add the fractions: 24 9 + 24 8 = 24 17 .
The final answer is 24 17 .
Explanation
Problem Analysis We are asked to add two fractions, 8 3 and 3 1 . To add fractions, we need to find a common denominator.
Finding the Least Common Denominator (LCD) The denominators are 8 and 3. We need to find the least common multiple (LCM) of 8 and 3. The LCM is the smallest number that is a multiple of both 8 and 3.
Determining the LCM of 8 and 3 The multiples of 8 are: 8, 16, 24, 32, ... The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, ... The least common multiple of 8 and 3 is 24. So, the least common denominator (LCD) is 24.
Rewriting Fractions with Common Denominator Now we need to rewrite both fractions with the common denominator of 24. To convert 8 3 to a fraction with denominator 24, we multiply both the numerator and denominator by 3: 8 × 3 3 × 3 = 24 9 To convert 3 1 to a fraction with denominator 24, we multiply both the numerator and denominator by 8: 3 × 8 1 × 8 = 24 8
Adding the Fractions Now we can add the two fractions with the common denominator: 24 9 + 24 8 = 24 9 + 8 = 24 17
Simplifying the Result The fraction 24 17 is in its simplest form since 17 is a prime number and does not divide 24.
Final Answer Therefore, the sum of 8 3 and 3 1 is 24 17 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have a pizza that is cut into 8 slices and you eat 3 slices, you have eaten 8 3 of the pizza. If your friend eats 3 1 of the pizza, to find out how much pizza you both ate in total, you would add the two fractions together, as we did in this problem. This helps in understanding proportions and dividing quantities.
To add 8 3 and 3 1 , we find a common denominator, which is 24. Rewriting each fraction gives us 24 9 and 24 8 . Adding these results in 24 17 .
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