Four Operations Fractions Worksheet (with answers) | Teaching ... - Free Printable

Here are the step-by-step solutions for each problem. I have simplified every answer to its lowest terms as requested by the challenge.

a) $\frac{2}{8} + \frac{1}{8}$
Since the bottom numbers (denominators) are the same, we just add the top numbers: $2 + 1 = 3$.
Result: $\frac{3}{8}$. This cannot be simplified further.

b) $\frac{2}{8} - \frac{1}{8}$
Subtract the top numbers: $2 - 1 = 1$. Keep the bottom number the same.
Result: $\frac{1}{8}$.

c) $\frac{1}{8} \times \frac{1}{2}$
Multiply straight across: Top times top ($1 \times 1 = 1$) and bottom times bottom ($8 \times 2 = 16$).
Result: $\frac{1}{16}$.

d) $\frac{2}{8} \div \frac{1}{8}$
To divide fractions, flip the second fraction and multiply: $\frac{2}{8} \times \frac{8}{1}$.
The 8s cancel out, leaving $\frac{2}{1}$, which is just 2.
*(Alternatively, think: how many $\frac{1}{8}$s fit into $\frac{2}{8}$? The answer is 2).*
Result: $2$.

e) $\frac{2}{6} \div 2$
First, simplify $\frac{2}{6}$ to $\frac{1}{3}$.
Now, divide $\frac{1}{3}$ by 2. This is like sharing one-third between two people. You multiply the bottom by 2.
$\frac{1}{3 \times 2} = \frac{1}{6}$.
Result: $\frac{1}{6}$.

f) $\frac{2}{8} \times 3$
Think of 3 as $\frac{3}{1}$. Multiply across: $\frac{2 \times 3}{8 \times 1} = \frac{6}{8}$.
Simplify $\frac{6}{8}$ by dividing top and bottom by 2.
Result: $\frac{3}{4}$.

g) $1 \frac{2}{8} + \frac{7}{8}$
First, simplify the mixed number part: $\frac{2}{8}$ becomes $\frac{1}{4}$. So we have $1 \frac{1}{4} + \frac{7}{8}$.
Find a common denominator for the fractions (which is 8). Convert $\frac{1}{4}$ to $\frac{2}{8}$.
Now add: $1 \frac{2}{8} + \frac{7}{8} = 1 \frac{9}{8}$.
Since $\frac{9}{8}$ is an improper fraction (it equals $1 \frac{1}{8}$), add that whole 1 to the existing 1.
$1 + 1 \frac{1}{8} = 2 \frac{1}{8}$.
Result: $2 \frac{1}{8}$.

h) $\frac{2}{8} \div \frac{3}{5}$
First, simplify $\frac{2}{8}$ to $\frac{1}{4}$.
Now divide: $\frac{1}{4} \div \frac{3}{5}$. Flip the second fraction and multiply: $\frac{1}{4} \times \frac{5}{3}$.
Top times top: $1 \times 5 = 5$.
Bottom times bottom: $4 \times 3 = 12$.
Result: $\frac{5}{12}$.

i) $3 \frac{5}{12} - \frac{1}{6}$
Find a common denominator for the fractions. The common denominator for 12 and 6 is 12.
Convert $\frac{1}{6}$ to $\frac{2}{12}$.
Now subtract: $3 \frac{5}{12} - \frac{2}{12}$.
Keep the whole number 3. Subtract the fractions: $5 - 2 = 3$.
Result: $3 \frac{3}{12}$.
Simplify the fraction part: $\frac{3}{12}$ simplifies to $\frac{1}{4}$ (divide top and bottom by 3).
Final Result: $3 \frac{1}{4}$.

j) $\frac{3}{7} \times \frac{12}{63}$
Look for numbers that can cancel out before multiplying.
Notice that 3 (top left) and 63 (bottom right) are both divisible by 3.
$3 \div 3 = 1$.
$63 \div 3 = 21$.
The problem becomes: $\frac{1}{7} \times \frac{12}{21}$.
Now look at 12 and 21. They are both divisible by 3.
$12 \div 3 = 4$.
$21 \div 3 = 7$.
The problem becomes: $\frac{1}{7} \times \frac{4}{7}$.
Multiply across: $1 \times 4 = 4$ and $7 \times 7 = 49$.
Result: $\frac{4}{49}$.

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Final Answer:
a) $\frac{3}{8}$
b) $\frac{1}{8}$
c) $\frac{1}{16}$
d) $2$
e) $\frac{1}{6}$
f) $\frac{3}{4}$
g) $2 \frac{1}{8}$
h) $\frac{5}{12}$
i) $3 \frac{1}{4}$
j) $\frac{4}{49}$