Invariant Quotient
Multiplying dividend and divisor by the same number (not 0) leaves the quotient unchanged
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Multiplying dividend and divisor by the same number (not 0) leaves the quotient unchanged
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Share 6 pears into 3 plates and each plate gets 2. Now share 60 pears into 30 plates: ten times as many plates, ten times as many pears — and each plate still holds exactly 2! That is the invariant quotient: multiplying (or dividing) the dividend and the divisor by the same nonzero number leaves the quotient unchanged. This idea powers trial quotients by whole tens and simplifying ratios later on.
6÷3=2 — so what is 60÷30? Drag the slider to multiply both the dividend and divisor by 2, 5 or 10: more and more plates appear, but watch the green one — each share still holds 2. See why the quotient stays put when the total and the number of shares grow together.