6th Grade Order of Operations worksheet featuring PEMDAS rules and fraction calculations.

Absolutely! Let’s solve each problem step by step using the Order of Operations (PEMDAS: Parentheses, Exponents, Multiplication/Division left to right, Addition/Subtraction left to right). Since there are no parentheses or exponents in these problems, we focus on Multiplication and Division first (left to right), then Addition and Subtraction (left to right).

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Problem 1a)

> $\frac{1}{3} + \frac{3}{4} + \frac{1}{2}$

✔ No multiplication or division, so we just add from left to right. But we need a common denominator.

- LCM of 3, 4, and 2 is 12.
- Convert:
- $\frac{1}{3} = \frac{4}{12}$
- $\frac{3}{4} = \frac{9}{12}$
- $\frac{1}{2} = \frac{6}{12}$

Now add:
> $\frac{4}{12} + \frac{9}{12} + \frac{6}{12} = \frac{19}{12} = 1\frac{7}{12}$

✔ Answer: $\boxed{1\frac{7}{12}}$

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Problem 1b)

> $\frac{5}{8} - \frac{1}{2} + \frac{3}{4}$

✔ Again, only addition/subtraction — go left to right. Common denominator = 8

- $\frac{1}{2} = \frac{4}{8}$
- $\frac{3}{4} = \frac{6}{8}$

So:
> $\frac{5}{8} - \frac{4}{8} + \frac{6}{8} = \frac{1}{8} + \frac{6}{8} = \frac{7}{8}$

✔ Answer: $\boxed{\frac{7}{8}}$

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Problem 1c)

> $3 \times \frac{1}{2} \times \frac{5}{6}$

✔ All multiplication — go left to right.

First: $3 \times \frac{1}{2} = \frac{3}{2}$

Then: $\frac{3}{2} \times \frac{5}{6} = \frac{15}{12} = \frac{5}{4} = 1\frac{1}{4}$

✔ Answer: $\boxed{1\frac{1}{4}}$

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Problem 1d)

> $\frac{3}{5} \times \frac{4}{9} \div \frac{3}{10}$

✔ Multiplication and division — left to right.

First: $\frac{3}{5} \times \frac{4}{9} = \frac{12}{45} = \frac{4}{15}$ (simplify by dividing numerator and denominator by 3)

Now: $\frac{4}{15} \div \frac{3}{10} = \frac{4}{15} \times \frac{10}{3} = \frac{40}{45} = \frac{8}{9}$ (simplify by dividing by 5)

✔ Answer: $\boxed{\frac{8}{9}}$

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Problem 1e)

> $3 - \frac{1}{3} \div 4$

✔ Division comes before subtraction!

First: $\frac{1}{3} \div 4 = \frac{1}{3} \times \frac{1}{4} = \frac{1}{12}$

Then: $3 - \frac{1}{12} = \frac{36}{12} - \frac{1}{12} = \frac{35}{12} = 2\frac{11}{12}$

✔ Answer: $\boxed{2\frac{11}{12}}$

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Problem 1f)

> $7 + 5 \times \frac{9}{10}$

✔ Multiplication before addition.

First: $5 \times \frac{9}{10} = \frac{45}{10} = \frac{9}{2} = 4\frac{1}{2}$

Then: $7 + 4\frac{1}{2} = 11\frac{1}{2}$

✔ Answer: $\boxed{11\frac{1}{2}}$

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Problem 1g)

> $4 \div \frac{2}{5} + 5 \div \frac{5}{8}$

✔ Two divisions — do them both first (left to right).

First: $4 \div \frac{2}{5} = 4 \times \frac{5}{2} = \frac{20}{2} = 10$

Second: $5 \div \frac{5}{8} = 5 \times \frac{8}{5} = \frac{40}{5} = 8$

Now add: $10 + 8 = 18$

✔ Answer: $\boxed{18}$

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Problem 1h)

> $4 \div 6 \times 6 + \frac{2}{5}$

✔ Division and multiplication left to right, then addition.

Step 1: $4 \div 6 = \frac{4}{6} = \frac{2}{3}$

Step 2: $\frac{2}{3} \times 6 = \frac{12}{3} = 4$

Step 3: $4 + \frac{2}{5} = \frac{20}{5} + \frac{2}{5} = \frac{22}{5} = 4\frac{2}{5}$

✔ Answer: $\boxed{4\frac{2}{5}}$

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## ✔ Final Answers:

a) $\boxed{1\frac{7}{12}}$
b) $\boxed{\frac{7}{8}}$
c) $\boxed{1\frac{1}{4}}$
d) $\boxed{\frac{8}{9}}$
e) $\boxed{2\frac{11}{12}}$
f) $\boxed{11\frac{1}{2}}$
g) $\boxed{18}$
h) $\boxed{4\frac{2}{5}}$

Let me know if you’d like to see any step explained further!