분수와 소수

A fraction names equal parts of a whole that equals one; from a part you can find the whole, the remaining fraction, or a fraction of a number. Learners partition equally, see a fraction as a count of unit fractions, and recover the whole from a given part. This part-whole model is the foundation of all fraction operations.

Sizes are compared by structure: same denominator favors the larger numerator, same numerator favors the smaller denominator, decimals compare highest place first, and the number line locates values between. Learners order fractions, mixed and improper forms, and decimals, often to fill an inequality blank. It builds magnitude sense across number systems.

Generate equivalent fractions by multiplying numerator and denominator by a common factor, then count or pin them down under digit, range, or difference constraints.

One number compared against a chosen base, written as a fraction, a rate or a percent. Speed, density, discount, interest and concentration are all the same move -- decide what the base is, divide by it, and read the answer as a comparison. The work in these problems is almost never the arithmetic; it is identifying which quantity is the base.