Subtract these two fractions: [tex]$\frac{9}{7}-\frac{1}{2}=?$[/tex]
Answer (2)
Find a common denominator for the fractions, which is 14.
Convert both fractions to equivalent fractions with the common denominator: 7 9 = 14 18 and 2 1 = 14 7 .
Subtract the fractions: 14 18 − 14 7 = 14 11 .
The result of the subtraction is 14 11 .
Explanation
Finding a Common Denominator We are asked to subtract two fractions: 7 9 and 2 1 . To do this, we need to find a common denominator.
Determining the LCM The least common multiple (LCM) of 7 and 2 is 14. So, we will convert both fractions to equivalent fractions with a denominator of 14.
Converting the First Fraction To convert 7 9 to a fraction with a denominator of 14, we multiply both the numerator and the denominator by 2: 7 9 = 7 × 2 9 × 2 = 14 18
Converting the Second Fraction To convert 2 1 to a fraction with a denominator of 14, we multiply both the numerator and the denominator by 7: 2 1 = 2 × 7 1 × 7 = 14 7
Subtracting the Fractions Now that both fractions have the same denominator, we can subtract them: 14 18 − 14 7 = 14 18 − 7 = 14 11
Final Answer The resulting fraction is 14 11 . This fraction is already in its simplest form, as 11 and 14 have no common factors other than 1. Therefore, the final answer is 14 11 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a bill with friends. For example, if you have 7 9 of a pizza and you eat 2 1 of the pizza, you need to subtract the fractions to find out how much pizza is left. This calculation helps you determine the remaining portion, which is 14 11 of the pizza. Understanding fraction subtraction is essential for accurate measurements and fair divisions in various real-world scenarios.
To subtract 7 9 and 2 1 , first find a common denominator, which is 14. Convert the fractions to 14 18 and 14 7 , and then subtract them to get 14 11 .
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