Why does dividing by a decimal make the number bigger?

Question

And why do negative numbers exist?

EDIT: thank you all so much for answering. I actually understand now. I wish they explained it this simply in school 😭

In: 4

Answer 1

When you’re dividing, you’re really just asking, “how many of one number can fit into another number.” 4÷2 just means, “how many 2s can fit into a 4”. The answer is 2.

When you divide by a fraction, it’s the same logic. 4 ÷ (1/2) is the same as asking, “how many halves can fit into 4”. 8 halves can fit into a 4. So, 4 ÷ (1/2) = 8. Same as 4 × 2 = 8.

EDIT: And a very non-mathematician answer to the negative numbers thing is that negative and positive numbers are opposite sides of the same coin. They just represent movement on a number line in one direction or another. Positive numbers go up, negative numbers go down.