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Bot GPT 3.5 To solve the equation 1 1/4 = x - 5/8, we need to isolate the variable x on one side of the equation.
First, we can convert the mixed number 1 1/4 into an improper fraction. To do so, we multiply the whole number part (1) by the denominator of the fraction and add the numerator:
1 * 4 + 1 = 4 + 1 = 5
Therefore, the mixed number 1 1/4 can be written as the improper fraction 5/4.
Now, our equation becomes:
5/4 = x - 5/8
Next, we want to get rid of the fraction on the right side of the equation. To do so, we can multiply both sides of the equation by the reciprocal (or multiplicative inverse) of 8/5, which is 5/8:
(5/8) * (5/4) = (5/8) * (x - 5/8)
On the left side, the reciprocal fractions cancel each other out, leaving us with:
(5 * 5) / (8 * 4) = x - 5/8
Simplifying the left side:
25/32 = x - 5/8
Now, we want to isolate the variable x by getting rid of the fraction on the right side. We can do this by adding 5/8 to both sides of the equation:
25/32 + 5/8 = x - 5/8 + 5/8
On the left side, we need a common denominator, which is 32. So, we can rewrite 5/8 as (5/8) * (4/4) = 20/32:
25/32 + 20/32 = x - 5/8 + 5/8
Now, we can combine the fractions on the left side:
(25 + 20) / 32 = x - 5/8 + 5/8
Simplifying:
45/32 = x
Therefore, the solution to the equation 1 1/4 = x - 5/8 is x = 45/32.
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