Improve your math knowledge using the Division of Mixed Numbers Word Problems available. Practice the different questions on dividing mixed numbers and understand how various questions are framed. We have explained the concept in detail and explained how to divide mixed fractions easily. Learn the problem-solving approach used and apply the knowledge to solve similar problems. Students can find problems on the division of mixed fractions ranging from easy to difficult ones.

Also, Refer:

- Word Problems on Addition of Mixed Fractions
- Word Problems on Subtraction of Mixed Fractions
- Worksheet on Word Problems on Multiplication of Mixed Fractions

## Word Problems on Dividing Mixed Fractions

**Example 1.
**A shopkeeper cut 30 m long cloth into 1 \(\frac {2}{ 8} \) each. Find the total number of pieces he cut?

**Solution:**

Length of the cloth=30 m

Each piece length =1\(\frac {2}{ 8} \) =\(\frac {10}{ 8} \)

The total number of pieces=30 ÷ \(\frac {10}{ 8} \)

=\(\frac {30}{ 1} \) ÷ \(\frac {10}{ 8} \)

=30 × \(\frac {8}{ 10} \)

=\(\frac {240}{ 10} \) =24

Anish cut the cloth into 24 pieces.

**Example 2.
**A board was 6 \(\frac {1}{ 5} \) feet long. It is cut into pieces 1 \(\frac {1}{ 3} \) feet long. Find how many pieces are there?

**Solution:**

The length of the board = 6 \(\frac {1}{ 5} \)

Each piece length = \(\frac {11}{ 3} \)

No. of pieces=6 \(\frac {1}{ 5} \) ÷1 \(\frac {1}{ 3} \)

=\(\frac {31}{ 5} \) ÷ \(\frac {4}{ 3} \)

=\(\frac {31}{ 5} \) × \(\frac {3}{ 4} \)

=\(\frac {93}{ 20} \) = 4 \(\frac {13}{ 20} \)

Hence, a board was cut into 4 \(\frac {13}{ 20} \) pieces.

**Example 3.
**Anusha is painting sarees. She has 1 \(\frac {1}{ 4} \) paint remaining. Each saree requires \(\frac {1}{ 10} \) of a liter of paint. How many sarees can she paint?

**Solution:**

Paint remaining=1 \(\frac {1}{ 4} \) =\(\frac {5}{ 4} \)

Each saree requires paint=\(\frac {1}{ 10} \)

No. of sarees she can paint= \(\frac {5}{ 4} \) ÷\(\frac {1}{ 10} \)

=\(\frac {5}{ 4} \) ×\(\frac {10}{ 1} \)

=\(\frac {50}{ 4} \)

=\(\frac {25}{ 2} \) = 12 \(\frac {1}{ 2} \)

Therefore, Anusha can paint 12 \(\frac {1}{ 2} \) sarees.

**Example 4.
**Charan bought 2 \(\frac {3}{ 5} \) kg chocolates and ate them in 20 days. How much did he consume each day?

**Solution:**

Charan bought chocolates= 2 \(\frac {3}{ 5} \) kg

Charan ate chocolates=20 days

Charan ate chocolates every day=2 \(\frac {3}{ 5} \) ÷ 20

=\(\frac {13}{ 5} \) ÷ 20

=\(\frac {13}{ 5} \) ×\(\frac {1}{ 20} \)

=\(\frac {13 ×1}{ 5 × 20} \)

=\(\frac {13}{ 100} \)

Therefore, Charan consumed \(\frac {13}{ 100} \) chocolates every day.

**Example 5.
**Suman reads \(\frac {1}{ 4} \) part of the book in 1 \(\frac {1}{ 6} \) hours. How much time will he need to complete the whole book?

**Solution:**

Suman reads \(\frac {1}{ 4} \) part of the book in hours= 1 \(\frac {1}{ 6} \)=\(\frac {7}{ 6} \)

The time needed to complete the whole book=\(\frac {7}{ 6} \) ×4=\(\frac {28}{ 6} \)

Suman needs \(\frac {28}{ 6} \) hours to complete the whole book.

**Example 6.
**Hasini has 1 \(\frac {3}{ 5} \) of a bag full of chips. She eats \(\frac {1}{ 4} \) of a bag for a week. How many weeks will the food last?

**Solution:**

Hasini has a bag full of chips= 1 \(\frac {3}{ 5} \)=\(\frac {8}{ 5} \)

Hasini eats chips in a bag for a week=\(\frac {1}{ 4} \)

No. of weeks will the food last=\(\frac {8}{ 5} \) ÷\(\frac {1}{ 4} \)

=\(\frac {8}{ 5} \) × \(\frac {4}{ 1} \)

=\(\frac {32}{ 5} \)

Therefore, food will last in \(\frac {32}{ 5} \) weeks.

**Example 7.
**Sarita has some cakes she wants to distribute. she is going to distribute each person \(\frac {1}{ 4} \) of a cake, and she has 4 \(\frac {2}{ 7} \) cakes to give away. How many people will get cake?

**Solution:**

Sarita will distribute cake for each person=\(\frac {1}{ 4} \)

No. of cakes Sarita has= 4 \(\frac {2}{ 7} \)

No. of people will get cake= 4 \(\frac {2}{ 7} \) ÷ \(\frac {1}{ 4} \)

=\(\frac {30}{ 7} \)÷ \(\frac {1}{ 4} \)

=\(\frac {30}{ 7} \) × \(\frac {4}{ 1} \)

=\(\frac {120}{ 7} \) =17 \(\frac {1}{ 7} \)

Therefore, Sarita will distribute the cakes to 17 \(\frac {1}{ 7} \).

**Example 8.
**The product of two numbers is 2 \(\frac {3}{ 16} \). If one of them is 1 \(\frac {7}{ 8} \).Find the other number?

**Solution:**

Product of two numbers=2 \(\frac {3}{ 16} \)=\(\frac {35}{ 16} \)

One of the number =1 \(\frac {7}{ 8} \)=\(\frac {15}{ 8} \)

Other number=\(\frac {35}{ 16} \) ÷\(\frac {15}{ 8} \)

=\(\frac {35}{ 16} \) ×\(\frac {8}{ 15} \)

=\(\frac {35 × 8}{ 16 × 15} \)

=\(\frac {280}{ 240} \)= \(\frac {7}{ 6} \)= 1\(\frac {1}{ 6} \)

Therefore, the other number is 1\(\frac {1}{ 6} \).

**Example 9.
**Harish has 1 \(\frac {7}{ 9} \) of the money. He spends \(\frac {1}{ 4} \) of the money for a week. In how many weeks will the money be spent?

**Solution:**

Harish has money=1 \(\frac {7}{ 9} \)=\(\frac {16}{ 9} \)

Harish spends money for a week=\(\frac {1}{ 4} \)

The money will be spent=\(\frac {16}{ 9} \)÷ \(\frac {1}{ 4} \)

=\(\frac {16}{ 9} \)× \(\frac {4}{ 1} \)= \(\frac {64}{ 9} \)= 7\(\frac {1}{ 9} \)

The money will be spent in 7\(\frac {1}{ 9} \) 1/9 weeks.

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