5 divided by 1/4

Guri Bee

2 min read

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18-10-2024

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Why is 5 divided by 1/4 equal to 20?

The question of "5 divided by 1/4" often trips people up, even those comfortable with basic arithmetic. The seemingly simple problem leads to an answer that feels counterintuitive at first. So, let's break it down to understand why 5 divided by 1/4 equals 20.

Understanding Division:

Think of division as asking "How many times does this number fit into that number?"

• In the case of 5 divided by 1/4, we're asking: "How many times does 1/4 fit into 5?"

This is where the confusion arises. It feels natural to try and divide 5 by 4, but that's not what the problem asks. We need to consider how many times a quarter fits into 5.

Visualizing the Solution:

Imagine a pizza cut into 4 equal slices. Each slice represents 1/4 of the whole pizza.

• How many of these 1/4 slices would it take to make a whole pizza (representing 5 whole pizzas)? It takes four slices.
• How many slices would it take to make 5 pizzas? It would take 20 slices (5 pizzas x 4 slices per pizza = 20 slices).

The Math:

Instead of dividing by a fraction, we can invert the fraction and multiply. This is a key rule in dividing fractions.

• 5 divided by 1/4 is the same as 5 multiplied by 4/1.
• 5 x 4/1 = 20/1 = 20.

Therefore, 5 divided by 1/4 equals 20.

Applying this Concept:

This understanding of dividing by fractions can be applied to many practical scenarios. Here are a couple of examples:

• Baking: If a recipe calls for 1/4 cup of flour, and you want to make a recipe 5 times larger, you would need 5 x 1/4 cup of flour, which is equal to 5/4 or 1 1/4 cups.
• Construction: If you need to cut a 5-meter long piece of wood into 1/4 meter sections, you can calculate the number of sections by dividing 5 by 1/4, which equals 20 sections.

Remember: When dividing by a fraction, invert the fraction and multiply. It's a powerful technique that simplifies seemingly complex calculations.

Source: This article was written by me, drawing on the concepts commonly discussed in math forums and online resources.