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Represent fractions with set models

A set model represents a fraction by partitioning a collection of equal objects into equal-sized groups: the denominator names the total number of groups, and the numerator identifies how many groups are selected. This supports interpreting unit and common proper fractions, determining a fraction of a set, and recognizing equivalent representations, while excluding unequal-group interpretations and advanced fraction operations.

Detailed Explanation: Represent fractions with set models

A set model shows a fraction using a collection of equal objects.

Suppose you need to show 34\frac{3}{4} of 1212 counters.

  1. Look at the denominator, 44. It tells you to divide the counters into 4 equal groups.

  2. Divide 1212 counters equally:

12÷4=312 \div 4 = 3

So, put 33 counters in each group.

∙ ∙ ∙∙ ∙ ∙∙ ∙ ∙∙ ∙ ∙\boxed{\bullet\ \bullet\ \bullet}\quad \boxed{\bullet\ \bullet\ \bullet}\quad \boxed{\bullet\ \bullet\ \bullet}\quad \boxed{\bullet\ \bullet\ \bullet}

  1. Look at the numerator, 33. It tells you to select 3 of the 4 groups.

  2. The selected groups contain:

3+3+3=9 counters3+3+3=9\text{ counters}

So, 34\frac{3}{4} of 1212 counters is 99 counters. The denominator tells the total number of equal groups, and the numerator tells how many groups are selected.

Learn by doing: Represent fractions with set models

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