Question

solve for y. write your answer as a fraction, mixed number, or whole number.\\( y - \frac{1}{2} = \frac{3}{4} \\)

Explanation:

Step1: Add $\frac{1}{2}$ to both sides

To solve for \( y \), we add \(\frac{1}{2}\) to both sides of the equation \( y - \frac{1}{2} = \frac{3}{4} \). This gives us \( y = \frac{3}{4} + \frac{1}{2} \).

Step2: Find a common denominator and add

The common denominator of 4 and 2 is 4. So we rewrite \(\frac{1}{2}\) as \(\frac{2}{4}\). Then we add \(\frac{3}{4} + \frac{2}{4} = \frac{3 + 2}{4} = \frac{5}{4}\)? Wait, no, wait. Wait, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}=\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) multiplied by 2 over 2 is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is equal to \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, let's do it correctly. \(\frac{1}{2}\) is equivalent to \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) times 2 is 1, times 2 is 2? Wait, no, to add \(\frac{3}{4}\) and \(\frac{1}{2}\), we convert \(\frac{1}{2}\) to fourths. \(\frac{1}{2} = \frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) multiplied by 2 is 1, so \(\frac{1}{2} = \frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, 1/2 is 2/4? Wait, no, 1/2 is equal to 2/4? Wait, yes, because 1 times 2 is 2, 2 times 2 is 4. So \(\frac{1}{2} = \frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, I think I made a mistake. Wait, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is equal to \(\frac{2}{4}\)? Wait, yes, because 1 divided by 2 is 0.5, and 2 divided by 4 is 0.5. So \(\frac{1}{2} = \frac{2}{4}\). Then \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4}\)? Wait, no, wait the original equation is \( y - \frac{1}{2} = \frac{3}{4} \), so adding \(\frac{1}{2}\) to both sides: \( y = \frac{3}{4} + \frac{1}{2} \). Convert \(\frac{1}{2}\) to fourths: \(\frac{1}{2} = \frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, I think I messed up. Wait, \(\frac{1}{2}\) is equal to \(\frac{2}{4}\)? Wait, yes, because 1*2=2 and 2*2=4. So \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4}\)? Wait, no, that can't be. Wait, no, the equation is \( y - \frac{1}{2} = \frac{3}{4} \), so to solve for y, we add \(\frac{1}{2}\) to both sides. So \( y = \frac{3}{4} + \frac{1}{2} \). Now, \(\frac{1}{2}\) is \(\frac{2}{4}\), so \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4}\)? Wait, no, that's not right. Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, no, \(\frac{1}{2}\) is \(\frac{2}{4}\)? Wait, I think I made a mistake. Wait, \(\frac{1}{2}\) is equal to \(\frac{2}{4}\)? Wait, yes, because 1 divided by 2 is 0.5, and 2 divided by 4 is 0.5. So \(\frac{3}{4} + \frac{2}{4} = \frac{5}{4}\)? Wait, no, that's 1 and 1/4. But let's check the equation. If y is 5/4, then 5/4 - 1/2 = 5/4 - 2/4 = 3/4, which matches the right side. So that's correct. Wait, but let's do it again. Step 1: Add 1/2 to both sides. \( y = \frac{3}{4} + \frac{1}{2} \). Step 2: Convert 1/2 to fourths: 1/2 = 2/4. Then add: 3/4 + 2/4 = 5/4. Wait, but 5/4 is 1 and 1/4, which is a mixed number. But the problem says to write as a fraction, mixed number, or whole number. Wait, but the fraction button is selected. Wait, maybe I made a mistake in the common denominator. Wait, no, 1/2 is 2/4? Wait, no, 1/2 is 2/4? Wait, no, 1/2 is equal to 2/4? Wait, yes, because 1*2=2 and 2*2=4. So 3/4 + 2/4 = 5/4. So the fraction is 5/4, or the mixed number is 1 1/4. But let's check the equation again. If y = 5/4, then 5/4 - 1/2 = 5/4 - 2/4 = 3/4, which is correct. So the solution is y = 5/4 (as a fraction) or 1 1/4 (as a mixed number). But the fraction button is selected, so we'll present it as a fraction.

Wait, no, wait, I think I messed up the addition. Wait, \(\frac{3}{4} + \frac{1}{2}\). Let's convert to decimals to check. 3/4 is 0.75, 1/2 is 0.5. 0.75 + 0.5 = 1.25. 1.25 as a fraction is 5/4, which is 1 1/4. So that's correct. So the steps are:

Step1: Add $\frac{1}{2}$ to both sides

\( y = \frac{3}{4} + \frac{1}{2} \)

Step2: Convert to common denominator

\( \frac{1}{2} = \frac{2}{4} \), so \( y = \frac{3}{4} + \frac{2}{4} \)

Step3: Add the fractions

\( y = \frac{3 + 2}{4} = \frac{5}{4} \)

Answer:

\(\frac{5}{4}\)