3 1/2+w-5 1/4=8
I'm totally confused on how to work this out!
me too
3 1/2+w-5 1/4=8
First, the fractions need to have the same denominator.
3 1/2 = 3 2/4
3 2/4 + w - 5 1/4 = 8
Subtract 3 2/4 from both sides
w - 5 1/4 = 4 2/4
Add 5 1/4 to both sides
w = 9 3/4
To solve this equation, we need to simplify the expressions on both sides and isolate the variable, "w". Let's break it down step by step:
1. Start by simplifying the mixed numbers on both sides of the equation:
The left side of the equation can be simplified as follows:
3 1/2 = 7/2 (since 3 multiplied by 2 is 6, and then adding 1 gives us 7, making the fraction 7/2)
5 1/4 = 21/4 (following the same logic, 5 multiplied by 4 is 20, and then adding 1 gives us 21, making the fraction 21/4)
Now our equation becomes: 7/2 + w - 21/4 = 8
2. Next, we need to find a common denominator for the fractions on the left side, which is 4:
Multiplying the numerator and denominator of 7/2 by 2, we get 14/4.
Our equation becomes: 14/4 + w - 21/4 = 8
3. Combine like terms by adding the fractions:
14/4 - 21/4 = -7/4
Our equation becomes: -7/4 + w = 8
4. To isolate the variable, "w", we need to move -7/4 to the other side of the equation by adding it:
-7/4 + 7/4 + w = 8 + 7/4
The -7/4 and +7/4 cancel each other out because they are additive inverses (add up to zero).
Our equation becomes: w = 8 + 7/4
5. To add the whole number and fraction, we need to find a common denominator, which is 4:
Multiplying the numerator and denominator of 8 by 4, we get 32/4.
Our equation becomes: w = 32/4 + 7/4
6. Combine the fractions by adding the numerators and keeping the denominator the same:
32/4 + 7/4 = (32 + 7)/4 = 39/4
Therefore, the solution to the equation is w = 39/4 or w = 9 3/4.