Question

1. \\(\frac{5}{12} + p = \frac{7}{12}\\)\
2. \\(-\frac{1}{3} = -\frac{5}{6} + u\\)

Explanation:

Problem 11: $\boldsymbol{\frac{5}{12} + p = \frac{7}{12}}$

Step1: Subtract $\frac{5}{12}$ from both sides

To solve for $p$, we subtract $\frac{5}{12}$ from both sides of the equation. This is based on the addition property of equality, which states that if we subtract the same number from both sides of an equation, the equality still holds.
$$\frac{5}{12} + p - \frac{5}{12} = \frac{7}{12} - \frac{5}{12}$$

Step2: Simplify both sides

On the left side, $\frac{5}{12} - \frac{5}{12} = 0$, so we are left with $p$. On the right side, we subtract the numerators since the denominators are the same: $\frac{7 - 5}{12} = \frac{2}{12}$. We can then simplify $\frac{2}{12}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So $\frac{2\div2}{12\div2} = \frac{1}{6}$.
$$p = \frac{1}{6}$$

Problem 12: $\boldsymbol{-\frac{1}{3} = -\frac{5}{6} + u}$

Step1: Add $\frac{5}{6}$ to both sides

To solve for $u$, we add $\frac{5}{6}$ to both sides of the equation. This is based on the addition property of equality, which allows us to add the same number to both sides of an equation without changing the equality.
$$-\frac{1}{3} + \frac{5}{6} = -\frac{5}{6} + u + \frac{5}{6}$$

Step2: Simplify both sides

On the right side, $-\frac{5}{6} + \frac{5}{6} = 0$, so we are left with $u$. On the left side, we need to find a common denominator to add the fractions. The common denominator of 3 and 6 is 6. So we rewrite $-\frac{1}{3}$ as $-\frac{2}{6}$. Then we add $-\frac{2}{6} + \frac{5}{6} = \frac{-2 + 5}{6} = \frac{3}{6}$. We can simplify $\frac{3}{6}$ by dividing both the numerator and the denominator by their greatest common divisor, which is 3. So $\frac{3\div3}{6\div3} = \frac{1}{2}$.
$$u = \frac{1}{2}$$

Answer:

s:
Problem 11: $p = \boldsymbol{\frac{1}{6}}$
Problem 12: $u = \boldsymbol{\frac{1}{2}}$