What is the error and correction in finding the difference?
3/4 - 9/2 = 3 - 9/4 - 2 = (-6/2) = -3
9 / 2 = 18 / 4
3 / 4 - 9 / 2 = 3 / 4 - 18 / 4 = - 15 / 4
The error in the calculation is in the step where you subtracted 9/2 from 3. Instead of subtracting 9/2 directly from 3, you subtracted 9/4 first, and then subtracted 2.
To correctly find the difference 3/4 - 9/2, here are the steps:
1. Convert the fractions to have a common denominator. In this case, the common denominator is 4.
2. Rewrite the fractions with the common denominator: 3/4 - 18/4.
3. Subtract the numerators: 3 - 18 = -15.
4. Write the result over the common denominator: -15/4.
So, the correct difference is -15/4 or -3.75.
The error in finding the difference lies in the incorrect step of distributing the subtraction across both terms in the second fraction. Let's go step by step to correct it:
Original Equation:
3/4 - 9/2 = 3 - 9/4 - 2
Step 1: Common Denominator
To subtract fractions, we need to find a common denominator for both fractions. In this case, the common denominator is 4.
Corrected equation:
3/4 - 9/2 = 3 - 9/4 - 8/4
Step 2: Subtracting Whole Numbers
3 minus 8 is equal to -5.
Corrected equation:
3/4 - 9/2 = -5/4 - 9/4
Step 3: Subtracting Fractions
Since the fractions now have the same denominator, we can directly subtract their numerators.
Corrected equation:
3/4 - 9/2 = (-5 - 9)/4 = -14/4
Step 4: Simplify the Fraction
-14/4 can be simplified by dividing the numerator and denominator by their greatest common divisor, which is 2.
Corrected equation:
3/4 - 9/2 = -7/2
Therefore, the correct difference is -7/2.