The Number System 7.NS
Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers.
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.
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.
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.
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.
d. Apply properties of operations as strategies to add and subtract
rational numbers.
2. Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
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.
Common Core State Standards for MAT HEMAT ICS
grade 7 | 49
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 realworld
contexts.
c. Apply properties of operations as strategies to multiply and
divide rational numbers.
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.
3. Solve real-world and mathematical problems involving the four
operations with rational numbers.
Apply and extend previous understandings of operations with
fractions to add, subtract, multiply, and divide rational numbers.
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.
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.
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.
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.
d. Apply properties of operations as strategies to add and subtract
rational numbers.
2. Apply and extend previous understandings of multiplication and
division and of fractions to multiply and divide rational numbers.
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.
Common Core State Standards for MAT HEMAT ICS
grade 7 | 49
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 realworld
contexts.
c. Apply properties of operations as strategies to multiply and
divide rational numbers.
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.
3. Solve real-world and mathematical problems involving the four
operations with rational numbers.