Final answer:
The equation −7/8 = −1/6 – 3 1/8 is solved by converting the mixed number to an improper fraction, finding common denominators, and then simplifying. The final solution to the equation is −1/4.
Step-by-step explanation:
Solving the equation −7/8 = −1/6 – 3 1/8 involves understanding how to work with fractions. First, let's convert the mixed number into an improper fraction so the equation has consistent terms. The mixed number 3 1/8 is converted by multiplying the whole number 3 by the denominator 8 and adding the numerator 1, yielding 25/8. Thus, the equation becomes −7/8 = −1/6 – 25/8.
Next, we need to have a common denominator to subtract the fractions. In this case, the least common denominator (LCD) for 6 and 8 is 24. We convert the fractions to have the denominator of 24, and so −1/6 becomes −4/24 and –25/8 becomes –75/24, which makes the equation: −7/8 = −4/24 – 75/24.
Now, we solve for the missing number by adding 75/24 to both sides of the equation: −7/8 + 75/24 = −4/24 – 75/24 + 75/24, simplifying to −7/8 + 75/24 = −4/24. Then we convert −7/8 to 21/24 to have a common denominator, which gives us: 21/24 + 75/24 = −4/24. Adding these two fractions, we get: 96/24 = −4/24.
Now that we have the same denominator on both sides, we can cancel the denominators and we're left with 96 = −4.
Finally, we divide both sides by 96 and find that the solution to the equation is −1/4, which is the same as −0.25 or −1/4 when stated in fraction form.
When we think about subtraction of fractions in terms of algebra, it's important to remember to find a common denominator, convert any mixed numbers into improper fractions, simplify where possible, and check if the solution is reasonable.