# Domain 7.NS, The Number System

## Cluster 7.NS.A, Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Major Cluster

### Standard 7.NS.A.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

19 Lessons

77 Activities

### Standard 7.NS.A.1.A

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

4 Lessons

16 Activities

### Standard 7.NS.A.1.B

Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

8 Lessons

32 Activities

### Standard 7.NS.A.1.C

Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

9 Lessons

34 Activities

### Standard 7.NS.A.1.D

Apply properties of operations as strategies to add and subtract rational numbers.

4 Lessons

13 Activities

### Standard 7.NS.A.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

16 Lessons

68 Activities

### Standard 7.NS.A.2.A

Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

5 Lessons

21 Activities

### Standard 7.NS.A.2.B

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then -(p/q) = (-p)/q = p/(-q). Interpret quotients of rational numbers by describing real-world contexts.

4 Lessons

16 Activities

### Standard 7.NS.A.2.C

Apply properties of operations as strategies to multiply and divide rational numbers.

5 Lessons

17 Activities

### Standard 7.NS.A.2.D

Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

6 Lessons

29 Activities

### Standard 7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.^1

14 Lessons

45 Activities