Math worksheet practicing order of operations with fractions, including coloring instructions.

Explanation:
We are given 12 expressions involving fractions and the order of operations (PEMDAS/BODMAS): Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Each expression uses only multiplication and addition/subtraction — no parentheses or exponents — so we do multiplication first, then addition/subtraction.

Let’s solve each one carefully:

1) $ \frac{1}{2} \times \frac{2}{3} + \frac{1}{6} $
→ Multiply first: $ \frac{1}{2} \times \frac{2}{3} = \frac{2}{6} = \frac{1}{3} $
→ Then add: $ \frac{1}{3} + \frac{1}{6} = \frac{2}{6} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2} $

2) $ \frac{3}{4} \times \frac{2}{5} + \frac{1}{10} $
→ Multiply: $ \frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10} $
→ Add: $ \frac{3}{10} + \frac{1}{10} = \frac{4}{10} = \frac{2}{5} $

3) $ \frac{1}{3} + \frac{1}{2} \times \frac{1}{4} $
→ Multiply first: $ \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} $
→ Add: $ \frac{1}{3} + \frac{1}{8} = \frac{8}{24} + \frac{3}{24} = \frac{11}{24} $

4) $ \frac{1}{2} \times \frac{1}{3} - \frac{1}{6} $
→ Multiply: $ \frac{1}{2} \times \frac{1}{3} = \frac{1}{6} $
→ Subtract: $ \frac{1}{6} - \frac{1}{6} = 0 $

5) $ \frac{2}{5} \times \frac{1}{4} + \frac{3}{10} $
→ Multiply: $ \frac{2}{5} \times \frac{1}{4} = \frac{2}{20} = \frac{1}{10} $
→ Add: $ \frac{1}{10} + \frac{3}{10} = \frac{4}{10} = \frac{2}{5} $

6) $ \left( \frac{2}{3} + \frac{1}{6} \right) \times \frac{1}{2} $
→ Parentheses first: $ \frac{2}{3} + \frac{1}{6} = \frac{4}{6} + \frac{1}{6} = \frac{5}{6} $
→ Multiply: $ \frac{5}{6} \times \frac{1}{2} = \frac{5}{12} $

7) $ \frac{1}{4} \times \frac{2}{3} + \frac{1}{6} $
→ Multiply: $ \frac{1}{4} \times \frac{2}{3} = \frac{2}{12} = \frac{1}{6} $
→ Add: $ \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} $

8) $ \frac{3}{4} + \frac{1}{2} \times \frac{1}{2} $
→ Multiply: $ \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} $
→ Add: $ \frac{3}{4} + \frac{1}{4} = 1 $

9) $ \frac{1}{2} - \frac{1}{3} \times \frac{1}{2} $
→ Multiply: $ \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} $
→ Subtract: $ \frac{1}{2} - \frac{1}{6} = \frac{3}{6} - \frac{1}{6} = \frac{2}{6} = \frac{1}{3} $

10) $ \frac{1}{3} + \frac{1}{2} \times \frac{1}{6} $
→ Multiply: $ \frac{1}{2} \times \frac{1}{6} = \frac{1}{12} $
→ Add: $ \frac{1}{3} + \frac{1}{12} = \frac{4}{12} + \frac{1}{12} = \frac{5}{12} $

11) $ \frac{1}{2} \times \frac{1}{4} + \frac{1}{8} $
→ Multiply: $ \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} $
→ Add: $ \frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4} $

12) $ \frac{1}{3} \times \frac{1}{2} + \frac{1}{6} $
→ Multiply: $ \frac{1}{3} \times \frac{1}{2} = \frac{1}{6} $
→ Add: $ \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} $

Now match each result to a color (as per instructions — though colors aren’t specified in text, the problem likely expects us to compute values; since the user only asked to “solve the problem accurately”, and the core math is evaluating the expressions, we provide the simplified results).

But the instruction says: *“Evaluate each expression using the order of operations. Color the answer on the color sheet…”* — however, since we can’t color, and the user wants the correct answers, we list the final simplified fraction for each.

Let me double-check each:

1) 1/2 ✔
2) 2/5 ✔
3) 11/24 ✔
4) 0 ✔
5) 2/5 ✔
6) 5/12 ✔
7) 1/3 ✔
8) 1 ✔
9) 1/3 ✔
10) 5/12 ✔
11) 1/4 ✔
12) 1/3 ✔

All correct.

Final Answer:
1) $\frac{1}{2}$
2) $\frac{2}{5}$
3) $\frac{11}{24}$
4) $0$
5) $\frac{2}{5}$
6) $\frac{5}{12}$
7) $\frac{1}{3}$
8) $1$
9) $\frac{1}{3}$
10) $\frac{5}{12}$
11) $\frac{1}{4}$
12) $\frac{1}{3}$