Dividing Fractions: math test, Grade 6 – download the PDF

1 Computations / 4 pts

Compute and simplify.

1. \( 6 \div \dfrac{1}{3} \)
2. \( \dfrac{4}{5} \div 2 \)
3. \( \dfrac{5}{8} \div \dfrac{5}{12} \)
4. \( 2\dfrac{1}{3} \div \dfrac{7}{6} \)

2 Reciprocals / 3 pts

1. Give the reciprocal of \( \dfrac{9}{4} \).
2. Give the reciprocal of 6.
3. True or false: \( \dfrac{3}{5} \div 4 = \dfrac{12}{5} \). Justify and correct if needed.

3 Bar model / 3 pts

The bar is cut into twelfths and 10 twelfths are colored, which is \( \dfrac{5}{6} \).

1. Write the division that asks how many \( \dfrac{1}{12} \) fit in \( \dfrac{5}{6} \).
2. Give the quotient.
3. Check your answer by multiplication.

4 Soup for the class / 4 pts

1. A cook has \( 3\dfrac{1}{2} \) liters of soup. Each bowl holds \( \dfrac{1}{4} \) liter. How many bowls can she fill?
2. Then \( \dfrac{3}{4} \) liter of soup is shared equally among 3 students. How much does each student get?

5 Interpreting quotients / 3 pts

1. Is \( 7 \div \dfrac{2}{5} \) greater or less than 7? Explain.
2. Is \( \dfrac{3}{4} \div \dfrac{9}{8} \) greater or less than \( \dfrac{3}{4} \)? Explain.
3. Compute the quotient in part b.

6 Slow snail / 3 pts

A snail crawls \( \dfrac{3}{10} \) meter in \( \dfrac{1}{4} \) hour.

1. Find its speed in meters per hour.
2. How many hours would it need to crawl 3 meters at that speed?