w/4-w/5-1/3=16/15
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GCD is 4*15 = 60
15w/60 - 12w/60 - 20/60 = 64/60
now, since all the fractions have a common denominator, we can ignore it (actually, just multiply everything by 60)
15w - 12w - 20 = 64
3w = 84
w = 28
To solve the equation: w/4 - w/5 - 1/3 = 16/15, we can start by finding a common denominator for the fractions.
The least common denominator between 4, 5, and 3 is 60.
Multiplying each term by 60, we have:
(60 * w/4) - (60 * w/5) - (60 * 1/3) = (60 * 16/15)
Simplifying each term, we get:
15w - 12w - 20 = 64
Next, combine like terms:
3w - 20 = 64
Move the constant term to the other side of the equation:
3w = 64 + 20
3w = 84
To isolate the variable, divide both sides of the equation by 3:
w = 84/3
Simplifying the right side:
w = 28
Therefore, the solution to the equation w/4 - w/5 - 1/3 = 16/15 is w = 28.
To solve the equation w/4 - w/5 - 1/3 = 16/15, we need to find the value of w.
Step 1: Find a common denominator for the fractions in the equation. In this case, the least common denominator (LCD) is 60 because it is divisible by 4, 5, and 3.
Step 2: Rewrite the fractions with the LCD of 60.
w/4 can be rewritten as (15w)/60 because 60/4 = 15.
w/5 can be rewritten as (12w)/60 because 60/5 = 12.
1/3 remains as 1/3.
The equation now becomes: (15w)/60 - (12w)/60 - 1/3 = 16/15.
Step 3: Combine the fractions on the left side of the equation.
[(15w) - (12w)]/60 - 1/3 = 16/15.
(3w)/60 - 1/3 = 16/15.
Step 4: Simplify the fractions on the left side.
(3w)/60 can be further reduced to w/20.
w/20 - 1/3 = 16/15.
Step 5: Find a common denominator for the fractions w/20 - 1/3.
The least common denominator (LCD) is 60 because it is divisible by 20 and 3.
Step 6: Multiply the fractions by the appropriate factor to have a common denominator of 60.
(w/20) * 3/3 = (3w)/60.
(1/3) * 20/20 = 20/60.
Equation becomes: (3w)/60 - 20/60 = 16/15.
Step 7: Combine the fractions on the left side.
[(3w) - 20]/60 = 16/15.
Step 8: Cross-multiply.
15[(3w) - 20] = 16 * 60.
Step 9: Simplify.
45w - 300 = 960.
Step 10: Isolate the w term by adding 300 to both sides.
45w = 960 + 300.
45w = 1260.
Step 11: Solve for w by dividing both sides by 45.
w = 1260/45.
w = 28.
Therefore, the solution to the equation w/4 - w/5 - 1/3 = 16/15 is w = 28.