Simplify: [tex]$\frac{7}{6 x}+\frac{5}{8 x}$[/tex]
Answer (2)
Find a common denominator for the fractions, which is 24 x .
Rewrite each fraction with the common denominator: 6 x 7 = 24 x 28 and 8 x 5 = 24 x 15 .
Add the fractions: 24 x 28 + 24 x 15 = 24 x 43 .
The simplified expression is 24 x 43 .
Explanation
Finding a Common Denominator We are asked to simplify the expression 6 x 7 + 8 x 5 . To do this, we need to find a common denominator for the two fractions.
Determining the Least Common Denominator The denominators are 6 x and 8 x . The least common multiple (LCM) of 6 and 8 is 24. Therefore, the least common denominator for the two fractions is 24 x .
Rewriting the Fractions Now, we rewrite each fraction with the common denominator of 24 x . To do this, we multiply the numerator and denominator of the first fraction by 4, and the numerator and denominator of the second fraction by 3: 6 x 7 = 6 x × 4 7 × 4 = 24 x 28 8 x 5 = 8 x × 3 5 × 3 = 24 x 15
Adding the Fractions Now that the fractions have a common denominator, we can add them: 24 x 28 + 24 x 15 = 24 x 28 + 15 = 24 x 43
Final Answer The simplified expression is 24 x 43 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. Simplifying expressions with fractions, like the one in this problem, helps us to perform these tasks more efficiently. For example, if you need to combine two different amounts of a certain ingredient, you would need to add the fractions representing those amounts. Simplifying the resulting expression makes it easier to understand the total amount you have.
To simplify 6 x 7 + 8 x 5 , we find a common denominator of 24 x by rewriting the fractions as 24 x 28 and 24 x 15 . Adding these gives the result 24 x 43 . Thus, the simplified expression is 24 x 43 .
;
