Mixed Operations with Two Fractions with Unlike Denominators ... - Free Printable

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

1. $\frac{7}{2} - \frac{9}{7}$
* Find a common denominator: The least common multiple for 2 and 7 is 14.
* Convert fractions:
* $\frac{7}{2} = \frac{7 \times 7}{2 \times 7} = \frac{49}{14}$
* $\frac{9}{7} = \frac{9 \times 2}{7 \times 2} = \frac{18}{14}$
* Subtract: $\frac{49}{14} - \frac{18}{14} = \frac{31}{14}$
* Convert to mixed number: 14 goes into 31 two times ($14 \times 2 = 28$) with a remainder of 3.
* Result: $2 \frac{3}{14}$

2. $(-\frac{4}{3}) + (-\frac{6}{7})$
* Combine signs: Adding a negative is the same as subtraction: $-\frac{4}{3} - \frac{6}{7}$.
* Find a common denominator: The least common multiple for 3 and 7 is 21.
* Convert fractions:
* $-\frac{4}{3} = -\frac{28}{21}$
* $-\frac{6}{7} = -\frac{18}{21}$
* Add numerators: $-28 - 18 = -46$.
* Result: $-\frac{46}{21}$ (or $-2 \frac{4}{21}$)

3. $(-\frac{1}{2}) - (-\frac{6}{5})$
* Combine signs: Subtracting a negative becomes addition: $-\frac{1}{2} + \frac{6}{5}$.
* Find a common denominator: The least common multiple for 2 and 5 is 10.
* Convert fractions:
* $-\frac{1}{2} = -\frac{5}{10}$
* $\frac{6}{5} = \frac{12}{10}$
* Add: $-\frac{5}{10} + \frac{12}{10} = \frac{7}{10}$
* Result: $\frac{7}{10}$

4. $\frac{27}{7} \times (-\frac{2}{7})$
* Determine sign: Positive times negative equals negative.
* Multiply numerators: $27 \times 2 = 54$.
* Multiply denominators: $7 \times 7 = 49$.
* Result: $-\frac{54}{49}$ (or $-1 \frac{5}{49}$)

5. $\frac{7}{8} \div \frac{10}{9}$
* Flip and multiply: To divide by a fraction, multiply by its reciprocal (flip the second fraction).
* Equation: $\frac{7}{8} \times \frac{9}{10}$
* Multiply numerators: $7 \times 9 = 63$.
* Multiply denominators: $8 \times 10 = 80$.
* Result: $\frac{63}{80}$

6. $\frac{20}{7} - \frac{5}{2}$
* Find a common denominator: The least common multiple for 7 and 2 is 14.
* Convert fractions:
* $\frac{20}{7} = \frac{40}{14}$
* $\frac{5}{2} = \frac{35}{14}$
* Subtract: $\frac{40}{14} - \frac{35}{14} = \frac{5}{14}$
* Result: $\frac{5}{14}$

7. $(-\frac{3}{2}) \div (-\frac{7}{3})$
* Determine sign: Negative divided by negative equals positive.
* Flip and multiply: $\frac{3}{2} \times \frac{3}{7}$
* Multiply numerators: $3 \times 3 = 9$.
* Multiply denominators: $2 \times 7 = 14$.
* Result: $\frac{9}{14}$

8. $\frac{7}{3} \times (-\frac{13}{8})$
* Determine sign: Positive times negative equals negative.
* Multiply numerators: $7 \times 13 = 91$.
* Multiply denominators: $3 \times 8 = 24$.
* Result: $-\frac{91}{24}$ (or $-3 \frac{19}{24}$)

9. $(-\frac{7}{6}) \div \frac{16}{5}$
* Determine sign: Negative divided by positive equals negative.
* Flip and multiply: $-\frac{7}{6} \times \frac{5}{16}$
* Multiply numerators: $7 \times 5 = 35$.
* Multiply denominators: $6 \times 16 = 96$.
* Result: $-\frac{35}{96}$

10. $(-\frac{3}{2}) \times \frac{3}{2}$
* Determine sign: Negative times positive equals negative.
* Multiply numerators: $3 \times 3 = 9$.
* Multiply denominators: $2 \times 2 = 4$.
* Result: $-\frac{9}{4}$ (or $-2 \frac{1}{4}$)

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Final Answer:
1. $2 \frac{3}{14}$
2. $-\frac{46}{21}$
3. $\frac{7}{10}$
4. $-\frac{54}{49}$
5. $\frac{63}{80}$
6. $\frac{5}{14}$
7. $\frac{9}{14}$
8. $-\frac{91}{24}$
9. $-\frac{35}{96}$
10. $-\frac{9}{4}$