Questions: Compute. Answer should be in lowest terms. 9. 8 2/5 + 9 3/10 10. 9 - 4 1/4 11. 7 1/2 × 9 3/10 12. 3 2/8 ÷ 1 2/7 13. (4 1/2 - 2) / (10 + 1/2)

Solution Steps

To solve these problems, we will first convert any mixed numbers into improper fractions. Then, we will perform the necessary arithmetic operations (addition, subtraction, multiplication, or division) on these fractions. Finally, we will simplify the resulting fraction to its lowest terms.

First, we convert the mixed numbers into improper fractions: \[ 8 \frac{2}{5} = \frac{42}{5}, \quad 9 \frac{3}{10} = \frac{93}{10} \] Next, we find a common denominator and add the fractions: \[ \frac{42}{5} + \frac{93}{10} = \frac{84}{10} + \frac{93}{10} = \frac{177}{10} \] The result is already in its simplest form: \[ \frac{177}{10} \]

We convert the mixed number into an improper fraction: \[ 4 \frac{1}{4} = \frac{17}{4} \] Now, we perform the subtraction: \[ 9 - \frac{17}{4} = \frac{36}{4} - \frac{17}{4} = \frac{19}{4} \] This result is also in its simplest form: \[ \frac{19}{4} \]

We convert the mixed numbers into improper fractions: \[ 7 \frac{1}{2} = \frac{15}{2}, \quad 9 \frac{3}{10} = \frac{93}{10} \] Next, we multiply the fractions: \[ \frac{15}{2} \times \frac{93}{10} = \frac{1395}{20} \] This result can be simplified to: \[ \frac{279}{4} \]

Final Answer