Multiplying fractions and whole numbers

Question

Why does multiplying numbers less than 1 with fractional parts take away from whole number term and make the operation seem like a subtraction or division

e.g
0.25*1000 = 250 // same as 1000/4 or 1000-750

A strange thing to beginner mathematicians

Answer 1

It's because it is like that $$0.25=\frac{25}{100}=\frac14$$ So$$\frac{1}{4}\cdot1000=\frac{1000}{4}=250$$ And it is $$1000-750=250$$ because we want to take $\frac14$ of something which is the same as taking the whole thing and removing $\frac34$ of it.... id est $$\frac14=1-\frac34$$ So the equation is basically both sides multiplied by $1000$

Answer 2

Hint: $\;0.25=\frac{1}{4}\,$ so $\,0.25 \cdot 1000 = \bbox[border:1px solid black]{\cfrac{1000}{4}}=\cfrac{1000\cdot (4-3)}{4}=\cfrac{4000}{4}-\cfrac{3000}{4}=\bbox[border:1px solid black]{1000-750}$