# 4.2 Fraction Equivalence and Comparison

## Unit Goals

- Students generate and reason about equivalent fractions and compare and order fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.

### Section A Goals

- Make sense of fractions with denominators 2, 3, 4, 5, 6, 8, 10, and 12 through physical representations and diagrams.
- Reason about the location of fractions on the number line.

### Section B Goals

- Generate equivalent fractions with the following denominators: 2, 3, 4, 5, 6, 8, 10, 12, and 100.
- Use visual representations to reason about fraction equivalence, including using benchmarks such as $\frac{1}{2}$ and 1.

### Section C Goals

- Use visual representations or a numerical process to reason about fraction comparison.

### Glossary Entries

**common denominator**The same denominator in two or more fractions. For instance, \(\frac{1}{4}\) and \(\frac{5}{4}\) have a common denominator.**composite number**A whole number with more than 1 factor pair.**denominator**The bottom part of a fraction that tells how many equal parts the whole was partitioned into.**equivalent fractions**Fractions that have the same size and describe the same point on the number line. For example, \(\frac{1}{2}\) and \(\frac{2}{4}\) are equivalent fractions.**factor pair of a whole number**A pair of whole numbers that multiply to result in that number. For example, 5 and 4 are a factor pair of 20.**multiple of a number**The result of multiplying that number by a whole number. For example, 18 is a multiple of 3, because it is a result of multiplying 3 by 6.**numerator**The top part of a fraction that tells how many of the equal parts are being described.

**prime number**A whole number that is greater than 1 and has exactly one factor pair: the number itself and 1.