# 4.3 Extending Operations to Fractions

## Unit Goals

- Students learn that a fraction $\frac{a}{b}$ is a product of a whole number $a$ and a unit fraction $\frac{1}{b}$, or $\frac{a}{b} = a \times \frac{1}{b}$, and that $n \times \frac{a}{b} = \frac{(n \space \times \space a)}{b}$. Students learn to add and subtract fractions with like denominators, and to add and subtract tenths and hundredths.

### Section A Goals

- Recognize that $n \times \frac{a}{b} = \frac{(n \space \times \space a)}{b}$.
- Represent and explain that a fraction $\frac{a}{b}$ is a multiple of $\frac{1}{b}$, namely $a \times \frac{1}{b}$.
- Represent and solve problems involving multiplication of a fraction by a whole number.

### Section B Goals

- Create and analyze line plots that display measurement data in fractions of a unit ($\frac18, \frac14, \frac12$).
- Represent and solve problems that involve the addition and subtraction of fractions and mixed numbers, including measurements presented in line plots.
- Use various strategies to add and subtract fractions and mixed numbers with like denominators.

### Section C Goals

- Reason about equivalence to add tenths and hundredths.
- Reason about equivalence to solve problems involving addition and subtraction of fractions and mixed numbers.

### 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.**mixed number**A number expressed as a whole number and a fraction less than 1.**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.