Add these two fractions: [tex]$\frac{3}{8}+\frac{1}{10}=?$[/tex]
Answer (2)
Find the least common multiple (LCM) of the denominators 8 and 10, which is 40.
Convert both fractions to equivalent fractions with a denominator of 40: 8 3 = 40 15 and 10 1 = 40 4 .
Add the numerators of the fractions with the common denominator: 40 15 + 40 4 = 40 19 .
The sum of the two fractions is 40 19 .
Explanation
Finding a Common Denominator We need to add two fractions: 8 3 and 10 1 . To do this, we first need to find a common denominator. The least common multiple (LCM) of 8 and 10 will be our common denominator.
Determining the LCM The least common multiple (LCM) of 8 and 10 is 40. We can find this by listing the multiples of each number until we find a common one:
Multiples of 8: 8, 16, 24, 32, 40, 48, ... Multiples of 10: 10, 20, 30, 40, 50, ...
The smallest multiple they have in common is 40.
Converting Fractions Now we need to convert both fractions to have a denominator of 40.
For 8 3 , we multiply both the numerator and the denominator by 5: 8 3 = 8 × 5 3 × 5 = 40 15 For 10 1 , we multiply both the numerator and the denominator by 4: 10 1 = 10 × 4 1 × 4 = 40 4
Adding the Fractions Now that both fractions have the same denominator, we can add them: 40 15 + 40 4 = 40 15 + 4 = 40 19
Final Answer The fraction 40 19 is in its simplest form because 19 is a prime number and does not divide 40. Therefore, the sum of the two fractions is 40 19 .
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 cut into 8 slices and you eat 3 slices, you've eaten 8 3 of the pizza. If your friend eats 1 out of 10 slices from another pizza, together you've eaten 8 3 + 10 1 of a pizza. Understanding how to add fractions helps you determine the total amount you and your friend consumed.
To add 8 3 and 10 1 , we find a common denominator, which is 40 . The fractions convert to 40 15 and 40 4 , and their sum is 40 19 .
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