A student incorrectly calculated $5\frac{1}{3} \div 2\frac{1}{2}$ by computing the whole numbers and fractions separately. What is the main error in this approach?

The reciprocal of the dividend was used instead of the divisor.

The mixed numbers were not converted to improper fractions before dividing.

The whole numbers were multiplied instead of divided.

The final answer was not simplified correctly.

Which expression shows the correct step after converting the mixed numbers to improper fractions for $4\frac{1}{5} \div 2\frac{1}{3}$?

$\frac{21}{5} \times \frac{7}{3}$

$\frac{5}{21} \times \frac{3}{7}$

$\frac{21}{5} \times \frac{3}{7}$

$\frac{5}{21} \times \frac{7}{3}$

A student attempts to convert $4\frac{3}{8}$ to an improper fraction and gets $\frac{7}{8}$. What mistake did the student make?

They added the whole number to the numerator.

They multiplied the numerator by the denominator.

They forgot to include the whole number.

They inverted the fraction after converting.

Dividing Mixed Numbers Practice — Grade 6 math

Lesson 3: Dividing Mixed Numbers — Practice Questions

1. A student incorrectly calculated $5\frac{1}{3} \div 2\frac{1}{2}$ by computing the whole numbers and fractions separately. What is the main error in this approach?
- A. The reciprocal of the dividend was used instead of the divisor.
- B. The mixed numbers were not converted to improper fractions before dividing.
- C. The whole numbers were multiplied instead of divided.
- D. The final answer was not simplified correctly.
2. Calculate the value of $3\frac{1}{3} \div 1\frac{2}{3}$. Express your answer as a whole number. The value is ___.
3. Which expression shows the correct step after converting the mixed numbers to improper fractions for $4\frac{1}{5} \div 2\frac{1}{3}$?
- A. $\frac{21}{5} \times \frac{7}{3}$
- B. $\frac{5}{21} \times \frac{3}{7}$
- C. $\frac{21}{5} \times \frac{3}{7}$
- D. $\frac{5}{21} \times \frac{7}{3}$
4. A student attempts to convert $4\frac{3}{8}$ to an improper fraction and gets $\frac{7}{8}$. What mistake did the student make?
- A. They added the whole number to the numerator.
- B. They multiplied the numerator by the denominator.
- C. They forgot to include the whole number.
- D. They inverted the fraction after converting.
5. What is the result of $2\frac{2}{5} \div 1\frac{1}{2}$? Express your answer as an improper fraction in simplest form. The result is ___.
6. Calculate the result of $4\frac{1}{5} \div 1\frac{2}{5}$. \n___
7. Which expression represents the correct first step to solve $5\frac{1}{3} \div 2\frac{1}{4}$?
- A. $\frac{16}{3} \div \frac{9}{4}$
- B. $\frac{16}{3} \times \frac{9}{4}$
- C. $\frac{15}{3} \div \frac{8}{4}$
- D. $5 \div 2 + \frac{1}{3} \div \frac{1}{4}$
8. Find the value of $2\frac{2}{5} \div 1\frac{1}{2}$. Express your answer as a mixed number in simplest form. ___
9. After converting $4\frac{1}{2} \div 1\frac{1}{3}$ to improper fractions, what is the next correct step in the calculation?
- A. $\frac{9}{2} \times \frac{4}{3}$
- B. $\frac{9}{2} \times \frac{3}{4}$
- C. $\frac{2}{9} \times \frac{3}{4}$
- D. $\frac{9}{2} + \frac{4}{3}$
10. A rope is $5\frac{1}{4}$ meters long. If it is cut into equal pieces each $1\frac{3}{4}$ meters long, how many pieces can be made? ___