Subtract these two fractions:
[tex]$\frac{7}{8}-\frac{1}{4}=?$[/tex]
Answer (2)
Find a common denominator for the fractions, which is 8.
Convert 4 1 to 8 2 .
Subtract the fractions: 8 7 − 8 2 = 8 5 .
The final answer is 8 5 .
Explanation
Understanding the Problem We are asked to subtract two fractions: 8 7 and 4 1 . To do this, we need to find a common denominator.
Finding a Common Denominator The least common multiple of 8 and 4 is 8. So, we will rewrite both fractions with a denominator of 8.
Converting Fractions The first fraction, 8 7 , already has the desired denominator. The second fraction, 4 1 , can be converted to a fraction with a denominator of 8 by multiplying both the numerator and the denominator by 2: 4 1 = 4 × 2 1 × 2 = 8 2
Subtracting the Fractions Now that both fractions have the same denominator, we can subtract them: 8 7 − 8 2 = 8 7 − 2 = 8 5
Final Answer The resulting fraction, 8 5 , is in its simplest form, as 5 and 8 have no common factors other than 1. Therefore, the final answer is 8 5 .
Examples
Fractions are used in everyday life, such as when cooking, measuring ingredients, or splitting a pizza. For example, if you have a pizza cut into 8 slices and you eat 1 slice, you have eaten 8 1 of the pizza. If you then eat another slice, you have eaten a total of 8 2 or 4 1 of the pizza. If you started with 8 7 of a pizza and ate 4 1 of the pizza, you would subtract 8 7 − 4 1 to find out how much pizza is left.
To subtract 8 7 − 4 1 , convert 4 1 to 8 2 to have a common denominator. Then subtract to get 8 5 . The final result is 8 5 .
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