Subtract 7/12 from 5/6.1/121/32/31/2If x/4 = 3/5, what is the value of x?5/1212/53/44/5Use the information given to answer question 37 – 41If X = 3a+ b and Y = a2-a+b What is the sum of X and Y?a2-3a+3ba2+2a+2b4a2+4a+2ba2-2a+2b find X-Y-a2-4a+b–a(a-4)-a2+4a+2ba2-4afind X when a=4 and b= -111121013

Let's break down and solve each part of the problem you've given:

### 1. Subtract \( \frac{7}{12} \) from \( \frac{5}{6} \):

To subtract these fractions, we first need to find a common denominator:

- The common denominator between 12 and 6 is 12.
- \( \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \)

Now, subtract:

\[
\frac{10}{12} - \frac{7}{12} = \frac{3}{12} = \frac{1}{4}
\]

### 2. Simplify the complex expression (not clear from your query). The likely interpretation: \( \frac{1}{12} \cdot \frac{1}{32} \cdot \frac{1}{31} \cdot \frac{1}{2} \):

Simplify:

\[
\frac{1}{12 \times 32 \times 31 \times 2}
\]

This simplifies to:

\[
\frac{1}{23808}
\]

### 3. Solve for \( x \) when \( \frac{x}{4} = \frac{3}{5} \):

Cross-multiply:

\[
5x = 12
\]

So:

\[
x = \frac{12}{5} = 2.4
\]

### 4. Evaluate expressions using \( X = 3a + b \) and \( Y = a^2 - a + b \) when \( a = 4 \) and \( b = -1 \):

First, calculate \( X \) and \( Y \):

- \( X = 3(4) + (-1) = 12 - 1 = 11 \)
- \( Y = (4)^2 - 4 + (-1) = 16 - 4 - 1 = 11 \)

#### Sum \( X + Y \):

\[
X + Y = 11 + 11 = 22
\]

#### Difference \( X - Y \):

\[
X - Y = 11 - 11 = 0
\]

### 5. Find \( X - Y \) in terms of \( a \) and \( b \):

Given the expression \( X = 3a + b \) and \( Y = a^2 - a + b \), the difference \( X - Y \):

\[
X - Y = (3a + b) - (a^2 - a + b) = 3a + b - a^2 + a - b = 4a - a^2
\]

### Summary of Solutions:
1. \( \frac{1}{4} \)
2. \( \frac{1}{23808} \)
3. \( x = 2.4 \)
4. \( X + Y = 22 \)
5. \( X - Y = 4a - a^2 \)

**Would you like a detailed breakdown of any part of these solutions?**

### Questions:
1. What is the next step to subtract fractions with different denominators?
2. How do you multiply fractions with multiple factors?
3. What is the importance of cross-multiplication when solving proportions?
4. How does the quadratic expression change when substituting values for variables?
5. How can you determine the value of \( X - Y \) using algebraic manipulation?

**Tip:** When dealing with fractions, always ensure that you simplify your result to its lowest terms.

Learn how to subtract fractions with different denominators and multiply fractions with multiple factors. Understand the importance of cross-multiplication in solving proportions. Suitable for students in Grades 5-8.

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