Solved multi-step division word problems with step-by-step solutions

📚 What is Multi-Step Division?

Multi-step division problems involve dividing a number multiple times, often within the context of a word problem. These problems require you to identify the different steps needed to arrive at the final answer, combining division with other operations like addition, subtraction, or multiplication.

• ➗ Definition: Multi-step division involves performing two or more division operations to solve a problem.
• 🧠 Why it Matters: These skills are crucial for real-world problem-solving, from splitting costs to calculating quantities.
• 🪜 Key Steps: Understanding the problem, identifying the operations, and executing them in the correct order.

📜 A Brief History

The concept of division has been around since ancient times, with early civilizations using various methods to divide resources and quantities. Multi-step division, as we understand it today, evolved as mathematical notation and understanding became more sophisticated. Solving word problems that involve multiple calculations has always been a practical need, driving the development of these techniques.

🔑 Key Principles of Multi-Step Division

Several key principles underpin the ability to solve these types of problems effectively.

• 🧮 Order of Operations: Follow the correct order of operations (PEMDAS/BODMAS) if the problem includes other operations.
• ✍️ Break It Down: Decompose the problem into smaller, manageable steps.
• 🧐 Read Carefully: Understand what the problem is asking before attempting to solve it.
• ✅ Check Your Work: Verify that your answer makes sense in the context of the original problem.

🌍 Real-World Examples

Let's look at some examples of multi-step division problems and how to solve them.

Example 1: Sharing Pizza

A pizza restaurant made 72 pizzas. They equally distributed the pizzas into 6 boxes. Then, 4 friends decided to share the pizzas from one box equally. How many pizzas does each friend get?

Solution:

1. First, divide the total number of pizzas (72) by the number of boxes (6): $72 \div 6 = 12$ pizzas per box.
2. Then, divide the number of pizzas in one box (12) by the number of friends (4): $12 \div 4 = 3$ pizzas per friend.

Therefore, each friend gets 3 pizzas.

Example 2: Organizing Books

A librarian has 144 books to arrange on shelves. She wants to put the books on 4 shelves. Each shelf has 3 sections. How many books go in each section?

Solution:

1. First, divide the total number of books (144) by the number of shelves (4): $144 \div 4 = 36$ books per shelf.
2. Then, divide the number of books per shelf (36) by the number of sections (3): $36 \div 3 = 12$ books per section.

Therefore, each section has 12 books.

Example 3: Distributing Supplies

A teacher has 96 pencils to give to her students. She first divides the pencils equally among 3 groups. Then, each group divides their pencils among 8 students. How many pencils does each student get?

Solution:

1. First, divide the total number of pencils (96) by the number of groups (3): $96 \div 3 = 32$ pencils per group.
2. Then, divide the number of pencils per group (32) by the number of students (8): $32 \div 8 = 4$ pencils per student.

Therefore, each student gets 4 pencils.

Example 4: Packing Cookies

A baker made 120 cookies. They packed the cookies into 5 boxes. Each box has 6 rows of cookies. How many cookies are in each row?

Solution:

1. First, divide the total number of cookies (120) by the number of boxes (5): $120 \div 5 = 24$ cookies per box.
2. Then, divide the number of cookies per box (24) by the number of rows (6): $24 \div 6 = 4$ cookies per row.

Therefore, each row has 4 cookies.

Example 5: Arranging Flowers

A florist has 84 flowers to arrange into bouquets. They want to make 7 bouquets. Each bouquet will have 3 types of flowers. If each type has the same number of flowers, how many of each type will be in each bouquet?

Solution:

1. First, divide the total number of flowers (84) by the number of bouquets (7): $84 \div 7 = 12$ flowers per bouquet.
2. Then, divide the number of flowers per bouquet (12) by the number of flower types (3): $12 \div 3 = 4$ flowers of each type.

Therefore, each bouquet has 4 flowers of each type.

Example 6: Sharing Stickers

Sarah has 108 stickers. She divides them equally among 9 friends. Each friend then divides their stickers between themselves and 2 siblings. How many stickers does each person receive?

Solution:

1. First, divide the total number of stickers (108) by the number of friends (9): $108 \div 9 = 12$ stickers per friend.
2. Then, divide the number of stickers per friend (12) by the total number of people sharing (1 friend + 2 siblings = 3 people): $12 \div 3 = 4$ stickers per person.

Therefore, each person receives 4 stickers.

Example 7: Organizing Toys

A toy store has 150 toys to organize. They put the toys onto 5 shelves. Each shelf has 5 sections. How many toys are in each section?

Solution:

1. First, divide the total number of toys (150) by the number of shelves (5): $150 \div 5 = 30$ toys per shelf.
2. Then, divide the number of toys per shelf (30) by the number of sections (5): $30 \div 5 = 6$ toys per section.

Therefore, each section has 6 toys.

📝 Practice Quiz

Test your understanding with these practice problems:

1. 🧮 A bakery makes 160 cupcakes. They pack them into 8 boxes. Each box has 4 rows. How many cupcakes are in each row?
2. 📏 A school has 225 students. They divide them into 9 classes. Each class is further divided into 5 groups. How many students are in each group?
3. 💡 A farmer harvests 192 apples. He puts them into 6 baskets. Each basket has 8 sections. How many apples are in each section?

✅ Conclusion

Multi-step division problems might seem complicated, but by breaking them down into smaller steps and carefully following the order of operations, you can solve them with confidence. Remember to practice regularly, and you'll master these problems in no time!