What is the difference between $1^{3 / 4}$ of $1 / 14$ and $1 / 2$?
(a) $1 / 2$
(b) $3 / 7$
(c) $3 / 8$
(d) $1 / 4$
(e) $1 / 8
Answer (2)
Calculate 1 3/4 = 1 .
Multiply the result by 1/14 : 1 × 14 1 = 14 1 .
Subtract the result from 1/2 : 14 1 − 2 1 = 14 1 − 14 7 = 14 − 6 .
Simplify the fraction: 14 − 6 = − 7 3 . The absolute difference is 7 3 .
Explanation
Understanding the Problem We need to find the difference between 1 3/4 of 1/14 and 1/2 . The word 'of' means multiplication. So we need to calculate 1 3/4 × 14 1 − 2 1 .
Calculating the Power First, we calculate 1 3/4 . Any power of 1 is 1, so 1 3/4 = 1 .
Multiplying by 1/14 Next, we multiply the result by 1/14 : 1 × 14 1 = 14 1 .
Subtracting the Fractions Now, we subtract the result from 1/2 : 14 1 − 2 1 . To subtract these fractions, we need a common denominator, which is 14. So we rewrite 1/2 as 7/14 . Then we have 14 1 − 14 7 = 14 1 − 7 = 14 − 6 .
Simplifying the Result Finally, we simplify the fraction: 14 − 6 = 7 − 3 . The difference is − 7 3 . However, the question asks for the difference between the two values, so we should take the absolute value, which is 7 3 .
Examples
Understanding fractions and their differences is crucial in everyday situations, such as splitting a bill with friends or calculating discounts while shopping. For instance, if you and a friend are sharing a pizza cut into 14 slices, and you eat 1 slice while your friend eats half the pizza, the difference in the amount you've eaten can be calculated using the same principles as in the problem. This helps in fair distribution and understanding proportions.
To find the difference, we calculated 1 3/4 which equals 1, then multiplied by 14 1 to get 14 1 . Subtracting 2 1 gives us an absolute value difference of 7 3 . The answer is (b) (\frac{3}{7}.
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