can someone help me with the steps to problem below, the fractions are throwing me off 5/8t+2/15t=17/20
do you mean
5 / (8t)
which is
5
---
8 t
or
(5/8) t
which is
5
-- * t
8
???????
the problem in the book is
5/8*t + 2/15*t = 17/20
OK, typing on here requires more parentheses than in a book where you can set up type :
5/8 = 5 / (2 * 2 * 2)
2/15 = 2 / (5*3)
17/20 = 17/2*5*2
least common denominator is 2*2*2*3 *5 = 8*15 = 120
so I multiply all terms by 120
120(5/8) t + 120(2/15) t = 120 (17/20)
75 t + 16 t = 102
91 t = 102
t = 102/91 = 1 11/91
how do u check it?
Of course! Solving equations with fractions can be a little challenging at first, but I'll break it down into steps for you to make it easier to understand.
Step 1: Clear the denominators
To eliminate the fractions, we can multiply both sides of the equation by the least common denominator (LCD) of the fractions involved. In this case, the LCD of 8, 15, and 20 is 120.
Multiply 5/8t by 15/15 to clear the denominators:
(5/8t) * (15/15) + 2/15t = 17/20 * (15/15)
This simplifies to:
75/120t + 2/15t = 255/300
Step 2: Combine like terms
Next, add the fractions together. To do this, we need a common denominator, which is 120t in this case.
Multiply 75/120t by 1/1 to keep it unchanged:
(75/120t) * (1/1) + 2/15t = 255/300
This simplifies to:
75/120t + 2/15t = 255/300
Step 3: Find a common denominator
To add the fractions together, we need a common denominator. To find the least common multiple (LCM) of 120 and 15, we can multiply them together and divide by their greatest common divisor (GCD). In this case, the LCM is 120.
Multiply both sides of the equation by 120 to clear the denominators:
120 * (75/120t) + 120 * (2/15t) = 120 * (255/300)
This simplifies to:
75t + 16t = 102t = 102 * 255/300
Step 4: Solve for t
Now, we can solve for t by simplifying the equation and isolating the variable on one side. Let's calculate the right side of the equation first.
Multiply 102 by 255 and divide it by 300:
102 * 255/300 = 8670/300 = 289/10
So the equation becomes:
75t + 16t = 289/10
Combine like terms:
91t = 289/10
Step 5: Solve for t
Finally, isolate t by dividing both sides of the equation by 91:
(91t)/(91) = (289/10)/(91)
This simplifies to:
t = (289/10)/(91)
To simplify it further, we can multiply the numerator and denominator of the fraction by 10 to get rid of the denominator in the numerator:
t = [(289/10) * 10]/(91 * 10)
This simplifies to:
t = (289/91)
Therefore, the solution to the equation 5/8t + 2/15t = 17/20 is t = 289/91.