how many times can 19 fit into 108

Daniel Parker

2 min read

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25-02-2025

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This article will guide you through calculating how many times the number 19 fits into 108. We'll explore different methods, from simple division to visual representations, making this concept accessible to everyone. Understanding this basic arithmetic operation is crucial for various mathematical applications.

Understanding Division

At its core, this problem is a division problem. We want to find out how many times 19 goes into 108 without exceeding the total. This is represented mathematically as 108 ÷ 19.

Method 1: Long Division

Long division is a traditional method for solving this type of problem. Here's how it's done:

1. Set up the problem: Write 108 inside the long division symbol (⟌) and 19 outside.

2. Estimate: How many times does 19 go into 108? A good estimate is 5 (since 19 x 5 = 95).

3. Multiply: Multiply 19 by 5: 19 x 5 = 95

4. Subtract: Subtract 95 from 108: 108 - 95 = 13

5. Remainder: The result, 13, is the remainder. This means that 19 goes into 108 five times with 13 left over.

Therefore, 19 fits into 108 five times with a remainder of 13.

Method 2: Repeated Subtraction

This method is more intuitive, especially for those new to division.

1. Start with 108: This is our starting number.

2. Repeatedly subtract 19: Subtract 19 repeatedly until you get a number less than 19.

   108 - 19 = 89 89 - 19 = 70 70 - 19 = 51 51 - 19 = 32 32 - 19 = 13

3. Count the subtractions: We subtracted 19 five times before reaching a number less than 19.

4. Remainder: The final number, 13, is the remainder.

Again, we find that 19 fits into 108 five times with a remainder of 13.

Method 3: Using a Calculator

The simplest method is to use a calculator. Simply enter 108 ÷ 19. The calculator will display 5.684… The whole number part (5) represents how many times 19 fits into 108 completely. The decimal part represents the remainder as a fraction of 19.

Visual Representation

Imagine you have 108 objects. You want to group them into sets of 19. You'll be able to make five complete groups of 19, with 13 objects left over. This visual approach helps solidify the concept.

Conclusion

Regardless of the method used, we consistently find that 19 fits into 108 five times with a remainder of 13. This problem demonstrates a fundamental arithmetic operation and showcases different approaches to solving it, catering to diverse learning styles. Understanding division and remainders is essential for various mathematical problems and real-world applications.