Math worksheet titled "Word Problems on Dividing Fractions" featuring four word problems that require dividing fractions to solve practical problems.

Problem 1:

Jack needs to make sandwiches for a class picnic with \(\frac{2}{9}\) of a kilogram of sugar. If each sandwich needs \(\frac{3}{18}\) of a kilogram of sugar, then how many total sandwiches can be made?

#### Solution:
To determine how many sandwiches Jack can make, we need to divide the total amount of sugar by the amount of sugar required per sandwich.

1. Total sugar available: \(\frac{2}{9}\) kg
2. Sugar needed per sandwich: \(\frac{3}{18}\) kg

First, simplify \(\frac{3}{18}\):
\[
\frac{3}{18} = \frac{1}{6}
\]

Now, divide the total sugar by the sugar needed per sandwich:
\[
\text{Number of sandwiches} = \frac{\frac{2}{9}}{\frac{1}{6}}
\]

Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{2}{9}}{\frac{1}{6}} = \frac{2}{9} \times \frac{6}{1} = \frac{2 \times 6}{9 \times 1} = \frac{12}{9}
\]

Simplify \(\frac{12}{9}\):
\[
\frac{12}{9} = \frac{4}{3}
\]

Thus, Jack can make \(\frac{4}{3}\) sandwiches, which is equivalent to \(1 \frac{1}{3}\) sandwiches.

#### Final Answer for Problem 1:
\[
\boxed{\frac{4}{3}}
\]

---

Problem 2:

John has a piece of metal rod that is \(\frac{3}{4}\) of a meter long. He needs to cut pieces from the rod that are \(\frac{5}{16}\) of a meter long. How many pieces can John cut?

#### Solution:
To determine how many pieces John can cut, we need to divide the total length of the rod by the length of each piece.

1. Total length of the rod: \(\frac{3}{4}\) meters
2. Length of each piece: \(\frac{5}{16}\) meters

Divide the total length by the length of each piece:
\[
\text{Number of pieces} = \frac{\frac{3}{4}}{\frac{5}{16}}
\]

Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{3}{4}}{\frac{5}{16}} = \frac{3}{4} \times \frac{16}{5} = \frac{3 \times 16}{4 \times 5} = \frac{48}{20}
\]

Simplify \(\frac{48}{20}\):
\[
\frac{48}{20} = \frac{12}{5} = 2 \frac{2}{5}
\]

Since John cannot cut a fraction of a piece, we take the integer part of the result. Therefore, John can cut 2 full pieces.

#### Final Answer for Problem 2:
\[
\boxed{2}
\]

---

Problem 3:

\(\frac{3}{7}\) of a 1-liter container is filled with water. If a mug can contain \(\frac{9}{84}\) of a liter, then how many mugs of water are needed to fill up the bucket?

#### Solution:
First, determine the total amount of water in the container:
\[
\text{Amount of water} = \frac{3}{7} \times 1 = \frac{3}{7} \text{ liters}
\]

Next, simplify \(\frac{9}{84}\):
\[
\frac{9}{84} = \frac{3}{28}
\]

Now, divide the total amount of water by the capacity of one mug:
\[
\text{Number of mugs} = \frac{\frac{3}{7}}{\frac{3}{28}}
\]

Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{3}{7}}{\frac{3}{28}} = \frac{3}{7} \times \frac{28}{3} = \frac{3 \times 28}{7 \times 3} = \frac{84}{21}
\]

Simplify \(\frac{84}{21}\):
\[
\frac{84}{21} = 4
\]

#### Final Answer for Problem 3:
\[
\boxed{4}
\]

---

Problem 4:

A box of table tennis balls weighs \(\frac{5}{9}\) of a kg. If each ball weighs \(\frac{15}{81}\) of a kg, then how many balls are there in the box?

#### Solution:
To determine the number of balls in the box, we need to divide the total weight of the box by the weight of each ball.

1. Total weight of the box: \(\frac{5}{9}\) kg
2. Weight of each ball: \(\frac{15}{81}\) kg

First, simplify \(\frac{15}{81}\):
\[
\frac{15}{81} = \frac{5}{27}
\]

Now, divide the total weight by the weight of each ball:
\[
\text{Number of balls} = \frac{\frac{5}{9}}{\frac{5}{27}}
\]

Dividing by a fraction is equivalent to multiplying by its reciprocal:
\[
\frac{\frac{5}{9}}{\frac{5}{27}} = \frac{5}{9} \times \frac{27}{5} = \frac{5 \times 27}{9 \times 5} = \frac{135}{45}
\]

Simplify \(\frac{135}{45}\):
\[
\frac{135}{45} = 3
\]

#### Final Answer for Problem 4:
\[
\boxed{3}
\]

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Final Answers:

1. \(\boxed{\frac{4}{3}}\)
2. \(\boxed{2}\)
3. \(\boxed{4}\)
4. \(\boxed{3}\)