Solve and match mixed number addition and subtraction problems on this educational worksheet.

Here are the step-by-step solutions for the "Adding & Subtracting Mixed Numbers" worksheet.

Part 1: Solving the LEFT Column

1. $2 + 3\frac{1}{2}$
* Add the whole numbers: $2 + 3 = 5$.
* Keep the fraction: $\frac{1}{2}$.
* Answer: $5\frac{1}{2}$

2. $4\frac{1}{2} - 3\frac{1}{4}$
* Find a common denominator for $\frac{1}{2}$ and $\frac{1}{4}$. It is 4.
* Change $\frac{1}{2}$ to $\frac{2}{4}$. The problem becomes $4\frac{2}{4} - 3\frac{1}{4}$.
* Subtract whole numbers: $4 - 3 = 1$.
* Subtract fractions: $\frac{2}{4} - \frac{1}{4} = \frac{1}{4}$.
* Answer: $1\frac{1}{4}$

3. $2\frac{1}{3} + 1\frac{1}{2}$
* Find a common denominator for 3 and 2. It is 6.
* Change $\frac{1}{3}$ to $\frac{2}{6}$ and $\frac{1}{2}$ to $\frac{3}{6}$.
* The problem becomes $2\frac{2}{6} + 1\frac{3}{6}$.
* Add whole numbers: $2 + 1 = 3$.
* Add fractions: $\frac{2}{6} + \frac{3}{6} = \frac{5}{6}$.
* Answer: $3\frac{5}{6}$

4. $6\frac{5}{6} - 3\frac{1}{3}$
* Find a common denominator for 6 and 3. It is 6.
* Change $\frac{1}{3}$ to $\frac{2}{6}$.
* The problem becomes $6\frac{5}{6} - 3\frac{2}{6}$.
* Subtract whole numbers: $6 - 3 = 3$.
* Subtract fractions: $\frac{5}{6} - \frac{2}{6} = \frac{3}{6}$.
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$.
* Answer: $3\frac{1}{2}$

5. $1\frac{1}{4} + 1\frac{1}{2}$
* Find a common denominator for 4 and 2. It is 4.
* Change $\frac{1}{2}$ to $\frac{2}{4}$.
* The problem becomes $1\frac{1}{4} + 1\frac{2}{4}$.
* Add whole numbers: $1 + 1 = 2$.
* Add fractions: $\frac{1}{4} + \frac{2}{4} = \frac{3}{4}$.
* Answer: $2\frac{3}{4}$

6. $4\frac{1}{3} - 2$
* Subtract the whole numbers: $4 - 2 = 2$.
* Keep the fraction: $\frac{1}{3}$.
* Answer: $2\frac{1}{3}$

7. $2\frac{2}{5} + 1\frac{1}{2}$
* Find a common denominator for 5 and 2. It is 10.
* Change $\frac{2}{5}$ to $\frac{4}{10}$ and $\frac{1}{2}$ to $\frac{5}{10}$.
* The problem becomes $2\frac{4}{10} + 1\frac{5}{10}$.
* Add whole numbers: $2 + 1 = 3$.
* Add fractions: $\frac{4}{10} + \frac{5}{10} = \frac{9}{10}$.
* Answer: $3\frac{9}{10}$

8. $3\frac{7}{10} - 1\frac{1}{5}$
* Find a common denominator for 10 and 5. It is 10.
* Change $\frac{1}{5}$ to $\frac{2}{10}$.
* The problem becomes $3\frac{7}{10} - 1\frac{2}{10}$.
* Subtract whole numbers: $3 - 1 = 2$.
* Subtract fractions: $\frac{7}{10} - \frac{2}{10} = \frac{5}{10}$.
* Simplify $\frac{5}{10}$ to $\frac{1}{2}$.
* Answer: $2\frac{1}{2}$

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Part 2: Solving the RIGHT Column

A. $4 - 1\frac{1}{4}$
* Think of 4 as $3\frac{4}{4}$.
* The problem becomes $3\frac{4}{4} - 1\frac{1}{4}$.
* Subtract whole numbers: $3 - 1 = 2$.
* Subtract fractions: $\frac{4}{4} - \frac{1}{4} = \frac{3}{4}$.
* Answer: $2\frac{3}{4}$

B. $1\frac{3}{4} + \frac{3}{4}$
* Add the fractions first: $\frac{3}{4} + \frac{3}{4} = \frac{6}{4}$.
* $\frac{6}{4}$ is equal to $1\frac{2}{4}$, which simplifies to $1\frac{1}{2}$.
* Add this to the whole number 1: $1 + 1\frac{1}{2} = 2\frac{1}{2}$.
* Answer: $2\frac{1}{2}$

C. $7\frac{1}{2} - 2$
* Subtract whole numbers: $7 - 2 = 5$.
* Keep the fraction: $\frac{1}{2}$.
* Answer: $5\frac{1}{2}$

D. $1\frac{3}{4} - \frac{1}{2}$
* Find a common denominator (4). Change $\frac{1}{2}$ to $\frac{2}{4}$.
* The problem becomes $1\frac{3}{4} - \frac{2}{4}$.
* Subtract fractions: $\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$.
* Keep the whole number 1.
* Answer: $1\frac{1}{4}$

E. $3\frac{1}{5} + \frac{7}{10}$
* Find a common denominator (10). Change $\frac{1}{5}$ to $\frac{2}{10}$.
* The problem becomes $3\frac{2}{10} + \frac{7}{10}$.
* Add fractions: $\frac{2}{10} + \frac{7}{10} = \frac{9}{10}$.
* Keep the whole number 3.
* Answer: $3\frac{9}{10}$

F. $1\frac{1}{6} + 1\frac{1}{6}$
* Add whole numbers: $1 + 1 = 2$.
* Add fractions: $\frac{1}{6} + \frac{1}{6} = \frac{2}{6}$.
* Simplify $\frac{2}{6}$ to $\frac{1}{3}$.
* Answer: $2\frac{1}{3}$

G. $1\frac{1}{6} + 2\frac{2}{3}$
* Find a common denominator (6). Change $\frac{2}{3}$ to $\frac{4}{6}$.
* The problem becomes $1\frac{1}{6} + 2\frac{4}{6}$.
* Add whole numbers: $1 + 2 = 3$.
* Add fractions: $\frac{1}{6} + \frac{4}{6} = \frac{5}{6}$.
* Answer: $3\frac{5}{6}$

H. $5\frac{2}{3} - 2\frac{1}{6}$
* Find a common denominator (6). Change $\frac{2}{3}$ to $\frac{4}{6}$.
* The problem becomes $5\frac{4}{6} - 2\frac{1}{6}$.
* Subtract whole numbers: $5 - 2 = 3$.
* Subtract fractions: $\frac{4}{6} - \frac{1}{6} = \frac{3}{6}$.
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$.
* Answer: $3\frac{1}{2}$

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Part 3: Matching Answers

Now we match the answers from the Left side to the Right side:

1. Left #1 ($5\frac{1}{2}$) matches Right C ($5\frac{1}{2}$)
2. Left #2 ($1\frac{1}{4}$) matches Right D ($1\frac{1}{4}$)
3. Left #3 ($3\frac{5}{6}$) matches Right G ($3\frac{5}{6}$)
4. Left #4 ($3\frac{1}{2}$) matches Right H ($3\frac{1}{2}$)
5. Left #5 ($2\frac{3}{4}$) matches Right A ($2\frac{3}{4}$)
6. Left #6 ($2\frac{1}{3}$) matches Right F ($2\frac{1}{3}$)
7. Left #7 ($3\frac{9}{10}$) matches Right E ($3\frac{9}{10}$)
8. Left #8 ($2\frac{1}{2}$) matches Right B ($2\frac{1}{2}$)

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Part 4: Triple Match Challenge

Pattern: $\frac{1}{4}, \frac{1}{2}, \frac{3}{4}, 1, \_\_\_$

To find the pattern, let's make all the numbers have a denominator of 4:
* $\frac{1}{4}$
* $\frac{1}{2} = \frac{2}{4}$
* $\frac{3}{4}$
* $1 = \frac{4}{4}$

The numerators are counting up by 1: 1, 2, 3, 4...
The next number should be $\frac{5}{4}$.
$\frac{5}{4}$ is the same as $1\frac{1}{4}$.

Looking at our matched answers above, the answer $1\frac{1}{4}$ appears in:
* Left #2
* Right D

Final Answer:
Matches:
1-C, 2-D, 3-G, 4-H, 5-A, 6-F, 7-E, 8-B

Triple Match Challenge:
Next number: $1\frac{1}{4}$
Matching answers to circle: Left #2 and Right D