Fraction Sense — Practice Problems and Worked Solutions

The formulas you need here

16 worked problems

Every step is generated and checked by a computer algebra system.

1. 1.

   Evaluate and simplify the fraction.

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

   Answer: $\frac{3}{4}$

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{3}{4}$$
2. 2.

   Evaluate and simplify the fraction.

   $$\frac{5}{6}-\frac{2}{6}$$

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

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{1}{2}$$
3. 3.

   Evaluate and simplify the fraction.

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

   Answer: $\frac{3}{4}$

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{3}{4}$$
4. 4.

   Evaluate and simplify the fraction.

   $$\frac{2}{3}\cdot \frac{3}{5}$$

   Answer: $\frac{2}{5}$

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{2}{5}$$
5. 5.

   Evaluate and simplify the fraction.

   $$\frac{3}{4}÷\frac{1}{2}$$

   Answer: $\frac{3}{2}$

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{3}{2}$$
6. 6.

   Evaluate and simplify the fraction.

   $$1-\frac{2}{5}+\frac{1}{10}$$

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

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{7}{10}$$
7. 7.

   Evaluate and simplify the fraction.

   $$\frac{2}{5}+\frac{1}{5}$$

   Answer: $\frac{3}{5}$

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{3}{5}$$
8. 8.

   Evaluate and simplify the fraction.

   $$\frac{7}{8}-\frac{3}{8}$$

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

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{1}{2}$$
9. 9.

   Evaluate and simplify the fraction.

   $$\frac{1}{3}+\frac{1}{6}$$

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

   Step-by-step solution

   1. $$\text{Use a common denominator for addition or subtraction.}$$
   2. $$\text{Operate on the numerators, then simplify.}$$
   3. $$=\frac{1}{2}$$
10. 10.

    Evaluate and simplify the fraction.

    $$\frac{3}{4}\cdot \frac{2}{9}$$

    Answer: $\frac{1}{6}$

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{1}{6}$$
11. 11.

    Evaluate and simplify the fraction.

    $$\frac{2}{3}÷\frac{4}{9}$$

    Answer: $\frac{3}{2}$

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{3}{2}$$
12. 12.

    Evaluate and simplify the fraction.

    $$\frac{5}{6}+\frac{1}{3}$$

    Answer: $\frac{7}{6}$

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{7}{6}$$
13. 13.

    Evaluate and simplify the fraction.

    $$\frac{9}{10}-\frac{2}{5}$$

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

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{1}{2}$$
14. 14.

    Evaluate and simplify the fraction.

    $$\frac{1}{2}\cdot \frac{4}{7}$$

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

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{2}{7}$$
15. 15.

    Evaluate and simplify the fraction.

    $$\frac{5}{8}÷\frac{5}{4}$$

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

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{1}{2}$$
16. 16.

    Evaluate and simplify the fraction.

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

    Answer: $\frac{11}{8}$

    Step-by-step solution

    1. $$\text{Use a common denominator for addition or subtraction.}$$
    2. $$\text{Operate on the numerators, then simplify.}$$
    3. $$=\frac{11}{8}$$

More from Math Foundations

• Order of Operations
• Signed Numbers
• Ratios and Percentages
• Exponents and Roots
• Algebraic Expressions
• Linear Equations
• Polynomial Basics
• Inequalities
• Coordinate Plane
• Reading Graphs
• Function Machines
• Substitution
• Factoring Basics