MA19.7A.8

Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

Students know:

a number and its opposite have a sum of 0.
A number and its opposite are called additive inverses.
properties of operations.
Absolute value represents distance on a number line, therefore it is always non-negative.
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).
The decimal form of a rational number terminates in 0s or eventually repeats.

Students are able to:

add rational numbers.
Subtract rational numbers.
Represent addition and subtraction on a number line diagram.
Describe situations in which opposite quantities combine to make 0.
Find the opposite of a number.
Interpret sums of rational numbers by describing real-world contexts.
Show that the distance between two rational numbers on the number line is the absolute value of their difference.
Use absolute value in real-world contexts involving distances.
Multiply and divide rational numbers.
Convert a rational number to a decimal using long division.

Students understand that:

p + q is the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.
Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
If a factor is multiplied by a number greater than one, the answer is larger than that factor.
If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
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.
Integers can be divided, provided that the divisor is not zero.