Solve the equation w−5 2/5=3 1/4.(1 point) =2 3/20w8 13/20w w=8 3/9 w 8 3/20
To solve the equation, we need to simplify the left side of the equation:
w - 5 2/5
First, let's convert the mixed number 5 2/5 into an improper fraction:
5 2/5 = (5 * 5 + 2)/5 = 27/5
Now we can substitute this value back into the equation:
w - 27/5 = 3 1/4
Next, let's convert the mixed number 3 1/4 into an improper fraction:
3 1/4 = (3 * 4 + 1)/4 = 13/4
Substituting back into the equation:
w - 27/5 = 13/4
Now let's find a common denominator for the fractions on the right:
The common denominator for 5 and 4 is 20.
Multiplying both sides of the equation by 20:
20w - 108/20 = 65/20
Next, let's simplify the fractions:
-108/20 = -27/5
65/20 = 13/4
The equation becomes:
20w - 27/5 = 13/4
To eliminate the fractions, we can multiply both sides of the equation by the least common multiple of the denominators (20 * 5 * 4 = 400):
400 * (20w - 27/5) = 400 * (13/4)
Simplifying,
400 * (20w) - 400 * (27/5) = 400 * (13/4)
8000w - 2160 = 1300
Next, let's isolate the variable w by adding 2160 to both sides:
8000w - 2160 + 2160 = 1300 + 2160
8000w = 3460
Finally, divide both sides by 8000 to solve for w:
w = 3460/8000
The fraction cannot be simplified further, so the solution to the equation is w = 3460/8000.