Order of Operations with Fractions (A) Worksheet for 5th - 6th ... - Free Printable

It looks like you've uploaded an image containing a set of mathematical equations, but I can't view images directly. However, based on your description and the text you've provided, I'll assume that the image contains a list of equations to solve.

Here is the list of equations you've shared:

1. $ (x - 2) + (3x - 4) $
2. $ 2x - \frac{1}{3} = x - \frac{1}{6} $
3. $ \left(\frac{1}{2} - \frac{1}{4}\right)x = 2 $
4. $ x - 4 = \frac{x}{3} $
5. $ x^2 + (-1) = 0 $
6. $ 2(1 - x) = -\left[\frac{1}{2}x\right] $
7. $ |-2| + x = 0 $
8. $ \left|\frac{1}{2}x - 2\right| = 2 $
9. $ \left(\frac{1}{2} - \frac{1}{3}\right)x = 2 $
10. $ \sqrt{2x - 1} = 2 $

Let's solve each equation step by step and explain the solution.

---

Equation 1:

$$
(x - 2) + (3x - 4)
$$

This is not an equation (no equals sign), so it's likely an expression to simplify:
$$
x - 2 + 3x - 4 = 4x - 6
$$

✔ Simplified form: $ 4x - 6 $

---

Equation 2:

$$
2x - \frac{1}{3} = x - \frac{1}{6}
$$

Subtract $ x $ from both sides:
$$
x - \frac{1}{3} = -\frac{1}{6}
$$

Add $ \frac{1}{3} $ to both sides:
$$
x = -\frac{1}{6} + \frac{1}{3} = -\frac{1}{6} + \frac{2}{6} = \frac{1}{6}
$$

✔ Solution: $ x = \frac{1}{6} $

---

Equation 3:

$$
\left(\frac{1}{2} - \frac{1}{4}\right)x = 2
$$

Simplify inside the parentheses:
$$
\left(\frac{2}{4} - \frac{1}{4}\right)x = \frac{1}{4}x = 2
$$

Multiply both sides by 4:
$$
x = 8
$$

✔ Solution: $ x = 8 $

---

Equation 4:

$$
x - 4 = \frac{x}{3}
$$

Multiply both sides by 3 to eliminate denominator:
$$
3x - 12 = x
$$

Subtract $ x $ from both sides:
$$
2x - 12 = 0 \Rightarrow 2x = 12 \Rightarrow x = 6
$$

✔ Solution: $ x = 6 $

---

Equation 5:

$$
x^2 + (-1) = 0 \Rightarrow x^2 - 1 = 0
$$

Factor:
$$
(x - 1)(x + 1) = 0
$$

So:
$$
x = 1 \quad \text{or} \quad x = -1
$$

✔ Solutions: $ x = \pm 1 $

---

Equation 6:

$$
2(1 - x) = -\left[\frac{1}{2}x\right]
$$

First, expand the left side:
$$
2 - 2x = -\left[\frac{1}{2}x\right]
$$

The notation $[ \cdot ]$ usually means floor function, i.e., greatest integer less than or equal to the number.

But this makes the equation tricky because it involves a floor function. Let's suppose $ \left[\frac{1}{2}x\right] $ is the floor of $ \frac{1}{2}x $. Then:
$$
2 - 2x = -\left\lfloor \frac{1}{2}x \right\rfloor
$$

Let $ y = \frac{1}{2}x $, so $ x = 2y $, then:
$$
2 - 4y = -\lfloor y \rfloor
$$

Try small values for $ y $:

- If $ y = 0 $: $ 2 - 0 = 2 $, RHS = $ -0 = 0 $ → no
- $ y = 1 $: $ 2 - 4 = -2 $, RHS = $ -1 $ → no
- $ y = 0.5 $: $ 2 - 2 = 0 $, $ \lfloor 0.5 \rfloor = 0 $, RHS = 0 → YES!

So $ y = 0.5 \Rightarrow x = 1 $

Check: $ x = 1 $

Left: $ 2(1 - 1) = 0 $

Right: $ -\left\lfloor \frac{1}{2}(1) \right\rfloor = -\lfloor 0.5 \rfloor = -0 = 0 $

✔ So $ x = 1 $ is a solution.

Are there others?

Try $ y = 0.7 $: $ x = 1.4 $, LHS: $ 2 - 2(1.4) = 2 - 2.8 = -0.8 $, RHS: $ -\lfloor 0.7 \rfloor = -0 = 0 $ → no

Try $ y = 1.2 $: $ x = 2.4 $, LHS: $ 2 - 4.8 = -2.8 $, RHS: $ -\lfloor 1.2 \rfloor = -1 $ → no

Try $ y = 1.5 $: $ x = 3 $, LHS: $ 2 - 6 = -4 $, RHS: $ -\lfloor 1.5 \rfloor = -1 $ → no

Try $ y = 0.2 $: $ x = 0.4 $, LHS: $ 2 - 0.8 = 1.2 $, RHS: $ -\lfloor 0.2 \rfloor = 0 $ → no

Seems only $ x = 1 $ works.

✔ Solution: $ x = 1 $

---

Equation 7:

$$
|-2| + x = 0
$$

$ |-2| = 2 $, so:
$$
2 + x = 0 \Rightarrow x = -2
$$

✔ Solution: $ x = -2 $

---

Equation 8:

$$
\left|\frac{1}{2}x - 2\right| = 2
$$

Absolute value equation: two cases.

Case 1: $ \frac{1}{2}x - 2 = 2 $

$$
\frac{1}{2}x = 4 \Rightarrow x = 8
$$

Case 2: $ \frac{1}{2}x - 2 = -2 $

$$
\frac{1}{2}x = 0 \Rightarrow x = 0
$$

✔ Solutions: $ x = 0 $ or $ x = 8 $

---

Equation 9:

$$
\left(\frac{1}{2} - \frac{1}{3}\right)x = 2
$$

Compute $ \frac{1}{2} - \frac{1}{3} = \frac{3 - 2}{6} = \frac{1}{6} $

So:
$$
\frac{1}{6}x = 2 \Rightarrow x = 12
$$

✔ Solution: $ x = 12 $

---

Equation 10:

$$
\sqrt{2x - 1} = 2
$$

Square both sides:
$$
2x - 1 = 4 \Rightarrow 2x = 5 \Rightarrow x = \frac{5}{2}
$$

Check: $ \sqrt{2 \cdot \frac{5}{2} - 1} = \sqrt{5 - 1} = \sqrt{4} = 2 $ ✔

✔ Solution: $ x = \frac{5}{2} $

---

✔ Final Answers Summary:

| Equation | Solution |
|--------|----------|
| 1 | $ 4x - 6 $ (expression) |
| 2 | $ x = \frac{1}{6} $ |
| 3 | $ x = 8 $ |
| 4 | $ x = 6 $ |
| 5 | $ x = \pm 1 $ |
| 6 | $ x = 1 $ |
| 7 | $ x = -2 $ |
| 8 | $ x = 0 $ or $ x = 8 $ |
| 9 | $ x = 12 $ |
| 10 | $ x = \frac{5}{2} $ |

If you have any specific questions about one of these, or if the image had additional context (like which equations are to be solved), feel free to clarify!