Practice adding and subtracting mixed fractions with these 5 carefully designed problems

Here are the step-by-step solutions for each problem.

1) $2 \frac{2}{3} + 4 \frac{1}{6}$

* Step 1: Add the whole numbers together: $2 + 4 = 6$.
* Step 2: Find a common denominator for the fractions $\frac{2}{3}$ and $\frac{1}{6}$. Since 3 goes into 6, we can change $\frac{2}{3}$ to sixths.
* $\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}$.
* Step 3: Add the new fractions: $\frac{4}{6} + \frac{1}{6} = \frac{5}{6}$.
* Step 4: Combine the whole number and the fraction: $6$ and $\frac{5}{6}$.

Answer: $6 \frac{5}{6}$

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2) $6 \frac{2}{5} + 2 \frac{3}{10}$

* Step 1: Add the whole numbers: $6 + 2 = 8$.
* Step 2: Find a common denominator for $\frac{2}{5}$ and $\frac{3}{10}$. Since 5 goes into 10, change $\frac{2}{5}$ to tenths.
* $\frac{2}{5} = \frac{2 \times 2}{5 \times 2} = \frac{4}{10}$.
* Step 3: Add the fractions: $\frac{4}{10} + \frac{3}{10} = \frac{7}{10}$.
* Step 4: Combine them: $8$ and $\frac{7}{10}$.

Answer: $8 \frac{7}{10}$

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3) $5 \frac{2}{7} + 4 \frac{3}{14}$

* Step 1: Add the whole numbers: $5 + 4 = 9$.
* Step 2: Find a common denominator for $\frac{2}{7}$ and $\frac{3}{14}$. Since 7 goes into 14, change $\frac{2}{7}$ to fourteenths.
* $\frac{2}{7} = \frac{2 \times 2}{7 \times 2} = \frac{4}{14}$.
* Step 3: Add the fractions: $\frac{4}{14} + \frac{3}{14} = \frac{7}{14}$.
* Step 4: Simplify the fraction $\frac{7}{14}$. Both numbers can be divided by 7.
* $\frac{7 \div 7}{14 \div 7} = \frac{1}{2}$.
* Step 5: Combine the whole number and the simplified fraction: $9$ and $\frac{1}{2}$.

Answer: $9 \frac{1}{2}$

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4) $8 \frac{3}{4} - 6 \frac{2}{12}$

* Step 1: Subtract the whole numbers: $8 - 6 = 2$.
* Step 2: Find a common denominator for $\frac{3}{4}$ and $\frac{2}{12}$. Since 4 goes into 12, change $\frac{3}{4}$ to twelfths.
* $\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.
* Step 3: Subtract the fractions: $\frac{9}{12} - \frac{2}{12} = \frac{7}{12}$.
* Step 4: The fraction $\frac{7}{12}$ cannot be simplified further (7 is a prime number).
* Step 5: Combine the results: $2$ and $\frac{7}{12}$.

Answer: $2 \frac{7}{12}$

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5) $10 \frac{4}{5} - 5 \frac{4}{15}$

* Step 1: Subtract the whole numbers: $10 - 5 = 5$.
* Step 2: Find a common denominator for $\frac{4}{5}$ and $\frac{4}{15}$. Since 5 goes into 15, change $\frac{4}{5}$ to fifteenths.
* $\frac{4}{5} = \frac{4 \times 3}{5 \times 3} = \frac{12}{15}$.
* Step 3: Subtract the fractions: $\frac{12}{15} - \frac{4}{15} = \frac{8}{15}$.
* Step 4: Check if $\frac{8}{15}$ can be simplified. It cannot (they share no common factors).
* Step 5: Combine the results: $5$ and $\frac{8}{15}$.

Answer: $5 \frac{8}{15}$

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Final Answer:
1) $6 \frac{5}{6}$
2) $8 \frac{7}{10}$
3) $9 \frac{1}{2}$
4) $2 \frac{7}{12}$
5) $5 \frac{8}{15}$