# 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.
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### 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.