what is 5 divided by 1 5

2 min read 25-12-2024

Dividing by fractions can be tricky, but it's a fundamental concept in math. Let's break down how to solve 5 divided by 1/5, and then explore the underlying principles.

Understanding the Problem: 5 ÷ 1/5

The question "What is 5 divided by 1/5?" asks how many times 1/5 fits into 5. We can visualize this: imagine you have 5 whole pizzas, and you want to know how many 1/5 pizza slices are in those 5 pizzas.

Method 1: Visualizing the Problem

Imagine each of your 5 pizzas cut into 5 equal slices. Each pizza yields 5 slices (1/5 of a pizza each). Since you have 5 pizzas, you'd have a total of 5 * 5 = 25 slices. Therefore, there are 25 slices of 1/5 of a pizza in 5 whole pizzas.

Method 2: Reciprocal Method

Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of a fraction is simply flipping the numerator and the denominator.

Step 1: Find the reciprocal of 1/5. The reciprocal of 1/5 is 5/1 (or simply 5).
Step 2: Multiply 5 by the reciprocal. 5 x 5 = 25

Therefore, 5 divided by 1/5 equals 25.

Why Does This Work?

The reciprocal method works because division is the inverse operation of multiplication. When you divide by a fraction, you're essentially asking "how many times does this fraction go into the whole number?" Multiplying by the reciprocal provides the correct answer.

Real-World Examples

This concept is useful in many everyday situations:

Cooking: If a recipe calls for 1/5 cup of sugar per serving, and you want to make 5 servings, you'll need 5 x (1/5) = 1 cup of sugar.
Measurement: If you have a 5-meter long rope and you need to cut it into pieces that are 1/5 meter long, you'll have 5 x (5/1) = 25 pieces.

Practice Problems

Try these problems to solidify your understanding:

10 ÷ 1/2 = ?
3 ÷ 1/4 = ?
2 ÷ 1/10 = ?

Conclusion: Mastering Fraction Division

Understanding how to divide by fractions, like solving 5 divided by 1/5, is crucial for various mathematical applications. By visualizing the problem or using the reciprocal method, you can confidently tackle these types of calculations. Remember, 5 divided by 1/5 is always 25. Practice makes perfect!