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$3 \frac{1}{4} + z = \frac{1}{2}$

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Convert, compare, add, and subtract mixed customary units

Full solution

Q.

3 \frac{1}{4} + z = \frac{1}{2}

Isolate variable z: First, we need to isolate the variable z on one side of the equation. To do this, we subtract $3 \frac{1}{4}$ from both sides of the equation. $\newline$ $3 \frac{1}{4} + z - 3 \frac{1}{4} = \frac{1}{2} - 3 \frac{1}{4}$
Perform subtraction: Now we need to perform the subtraction on the right side of the equation. We need to convert $3 \frac{1}{4}$ to an improper fraction to make the subtraction easier. $3 \frac{1}{4}$ is the same as $\frac{13}{4}$ because $3 \times 4 + 1 = 13$ . $\newline$ $\frac{1}{2} - \frac{13}{4}$
Convert to improper fraction: To subtract these fractions, they need to have a common denominator. The least common denominator for $2$ and $4$ is $4$ . We convert $\frac{1}{2}$ to $\frac{2}{4}$ to have the same denominator. $\newline$ $\frac{2}{4} - \frac{13}{4}$
Subtract fractions: Now we can subtract the fractions. $\frac{2}{4} - \frac{13}{4} = -\frac{11}{4}$
Final result: The result of the subtraction gives us the value of $z$ . $z = -\frac{11}{4}$

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