Lesson 54: Reducing by Grouping Factors Equal to 1 — Practice Questions

1. 1. Reduce the fraction $\frac{42}{70}$ to its simplest form by factoring the numerator and denominator. The simplified fraction is ___.

2. 2. Using the property of grouping common factors, reduce the fraction $\frac{3 \cdot 5 \cdot 5 \cdot 7}{2 \cdot 3 \cdot 5 \cdot 5}$ to its simplest form.

   • A. $\frac{7}{2}$
   • B. $\frac{2}{7}$
   • C. $\frac{35}{10}$
   • D. $\frac{21}{10}$

3. 3. To simplify $\frac{48}{60}$, which option correctly shows the fraction as a product of its prime factors?

   • A. $\frac{2 \cdot 2 \cdot 2 \cdot 2 \cdot 3}{2 \cdot 2 \cdot 3 \cdot 5}$
   • B. $\frac{4 \cdot 12}{5 \cdot 12}$
   • C. $\frac{2 \cdot 2 \cdot 2 \cdot 6}{2 \cdot 3 \cdot 10}$
   • D. $\frac{2 \cdot 2 \cdot 2 \cdot 3}{2 \cdot 3 \cdot 5}$

4. 4. Simplify the expression $\frac{2 \cdot 3 \cdot 7 \cdot 11}{3 \cdot 7 \cdot 13}$ by canceling common factors. The result is ___.

5. 5. The process of canceling common factors works because any number divided by itself is equal to what value?

   • A. 0
   • B. 1
   • C. The number itself
   • D. The simplified fraction

6. 6. Which expression is equivalent to solving $\frac{2}{5} \div \frac{3}{4}$ using the 'invert and multiply' rule?

   • A. $\frac{2}{5} \times \frac{4}{3}$
   • B. $\frac{5}{2} \times \frac{3}{4}$
   • C. $\frac{2}{5} \times \frac{3}{4}$
   • D. $\frac{5}{2} \times \frac{4}{3}$

7. 7. Solve the following division problem: $\frac{1}{3} \div \frac{2}{7} = $___

8. 8. A baker has $\frac{3}{4}$ of a jug of milk. If each batch of muffins requires $\frac{1}{8}$ of a jug, how many batches can she make? ___

9. 9. Calculate $\frac{9}{10} \div \frac{3}{5}$ and simplify the result to its lowest terms. The answer is ___.

10. 10. What is the simplified result of $\frac{4}{5} \div \frac{2}{3}$?

    • A. $\frac{6}{5}$
    • B. $\frac{8}{15}$
    • C. $\frac{5}{6}$
    • D. $\frac{15}{8}$