Problem
A mixed number cannot be cancelled while it is still split into a whole part and a fraction, so write it as a single improper fraction first.
One fraction is easier to cancel than two pieces.
6.NS.A.1Identify SubproblemsDividing by 11 is multiplying by 1/11, and the 11 on top cancels it. Every part of the expression is now gone except a single quarter of the blank.
The whole expression is just the blank over 4.
6.NS.A.1Identify SubproblemsThe whole expression is just the blank divided by .
is eleven quarters, and sharing eleven quarters equally among eleven leaves one quarter each, because dividing undoes the multiplying that made eleven of them in the first place.
Multiplying that one quarter by the blank takes that many copies of it, so the result is the blank quarters.
A fraction with denominator 4 is a whole number exactly when the numerator is a multiple of 4, so the blank has to be 4, 8, 12, and so on.
Multiples of 4, and nothing else.
6.NS.B.4Look For A PatternThe results for those blanks are 1, 2, 3, and so on, so the smallest whole-number result comes from the smallest multiple of 4.
The blank is 4 and the result is 1.
6.NS.A.1Work BackwardsCancel everything you can first -- what is left over is usually a much smaller question.