solve the equation w + 3 3/8 = 1 5/6

The Correct Answer and Explanation is:

Solution to the Equation

We are given the equation: w+338=156w + 3\frac{3}{8} = 1\frac{5}{6}

Step 1: Convert Mixed Numbers to Improper Fractions

First, convert both mixed numbers to improper fractions:

338=3×8+38=24+38=2783\frac{3}{8} = \frac{3 \times 8 + 3}{8} = \frac{24 + 3}{8} = \frac{27}{8}
156=1×6+56=6+56=1161\frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6}

So the equation becomes: w+278=116w + \frac{27}{8} = \frac{11}{6}

Step 2: Isolate ww

To solve for ww, subtract 278\frac{27}{8} from both sides: w=116−278w = \frac{11}{6} – \frac{27}{8}

Step 3: Find a Common Denominator

The least common denominator of 6 and 8 is 24. Convert both fractions:

116=11×46×4=4424\frac{11}{6} = \frac{11 \times 4}{6 \times 4} = \frac{44}{24}
278=27×38×3=8124\frac{27}{8} = \frac{27 \times 3}{8 \times 3} = \frac{81}{24}

Now subtract: w=4424−8124=−3724w = \frac{44}{24} – \frac{81}{24} = \frac{-37}{24}

Step 4: Convert to Mixed Number

−3724=−11324\frac{-37}{24} = -1 \frac{13}{24}

✅ Final Answer:

w=−11324w = -1 \frac{13}{24}

300-Word Explanation

To solve the equation w+338=156w + 3\frac{3}{8} = 1\frac{5}{6}, we need to isolate the variable ww, meaning we want to get ww by itself on one side of the equation. Since there’s an addition of a mixed number (3383\frac{3}{8}) to ww, we subtract that same value from both sides.

However, before doing that, it’s helpful to convert the mixed numbers into improper fractions. Mixed numbers are numbers made up of a whole number and a fraction (like 3383\frac{3}{8}). To convert to improper fractions, we multiply the whole number by the denominator and add the numerator. So, 3383\frac{3}{8} becomes 278\frac{27}{8} and 1561\frac{5}{6} becomes 116\frac{11}{6}.

With the equation now in fraction form (w+278=116w + \frac{27}{8} = \frac{11}{6}), we subtract 278\frac{27}{8} from both sides. To do this, the two fractions must have the same denominator. The least common denominator of 6 and 8 is 24. After converting both fractions to have this denominator, we subtract: 4424−8124=−3724\frac{44}{24} – \frac{81}{24} = \frac{-37}{24}.

This result is a negative improper fraction, which we then convert to a mixed number: −11324-1 \frac{13}{24}. This means ww is a little more than −1-1 but less than 0, reflecting that the total on the right-hand side is less than what was added to ww.

Hence, the final answer is: w=−11324\boxed{w = -1 \frac{13}{24}}