Mixed operations involving multiplication and division help us solve real-world problems efficiently. These operations often require us to first find a total quantity using multiplication and then distribute or divide that total using division. Let’s explore two examples to understand how these operations work together.

Example 1: Distributing Pencils to Students

Problem:
There are 6 boxes with 4 pencils in each box. If each student needs 3 pencils, how many students can get pencils?

Solution:

1. Find the total number of pencils using multiplication:
   • Number of boxes = 6
   • Pencils per box = 4
   • Total pencils = 6 × 4 = 24 pencils
2. Divide the total pencils by the number needed per student:
   • Pencils per student = 3
   • Number of students = 24 ÷ 3 = 8 students

Answer:
8 students can get pencils.

Example 2: Sharing Cookie Boxes Among Friends

Problem:
A baker makes 36 cookies and packs them into boxes of 6 cookies each. If he wants to give each of 4 friends an equal number of boxes, how many boxes does each friend get?

Solution:

1. Find the total number of boxes using division:
   • Total cookies = 36
   • Cookies per box = 6
   • Total boxes = 36 ÷ 6 = 6 boxes
2. Divide the boxes equally among friends:
   • Number of friends = 4
   • Boxes per friend = 6 ÷ 4 = 1 box per friend (with 2 boxes remaining)

Answer:
Each friend gets 1 box, and there are 2 boxes left over.

Example 3: Making Bouquets from Garden Flowers

Problem:
In a garden, there are 8 rows of flowers, with 5 flowers in each row. If each bouquet needs 10 flowers, how many bouquets can be made?

Solution:

1. Find the total number of flowers using multiplication:
   • Number of rows = 8
   • Flowers per row = 5
   • Total flowers = 8 × 5 = 40 flowers
2. Divide the total flowers by the number needed per bouquet:
   • Flowers per bouquet = 10
   • Number of bouquets = 40 ÷ 10 = 4 bouquets

Answer:
4 bouquets can be made.

Example 4: Distributing Toy Cars to Stores

Problem:
A toy store has 48 toy cars. If they want to:

1. Place them into 8 equal-sized bins,
2. Then distribute the bins equally among 6 stores,
   how many toy cars will each store receive?

Solution:

1. Divide the total toy cars into bins:
   • Total toy cars = 48
   • Number of bins = 8
   • Toy cars per bin = 48 ÷ 8 = 6 cars per bin
2. Distribute the bins equally among stores:
   • Number of stores = 6
   • Since each bin has 6 cars, and there are 8 bins, but only 6 stores, we need to see how many cars each store gets.
   • Alternative Approach:
     • Total cars = 48
     • Number of stores = 6
     • Cars per store = 48 ÷ 6 = 8 cars per store