The Number System

7.NS.1Represent addition and subtraction on a horizontal or vertical number line diagram.7.NS.1aDescribe situations in which opposite quantities combine to make 0. Show that a number and its opposite have a sum of 0 (are additive inverses). For example, show zero-pairs with two-color counters.7.NS.1bShow 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.7.NS.1cModel subtraction of rational numbers as adding the additive inverse, p - q = p + (-q).7.NS.1dModel subtraction as the distance between two rational numbers on the number line where the distance is the absolute value of their difference.7.NS.1eApply properties of operations as strategies to add and subtract rational numbers.7.NS.2Apply and extend previous understandings of multiplication and division of positive rational numbers to multiply and divide all rational numbers.7.NS.2aDescribe how multiplication is extended from positive rational numbers to all 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.7.NS.2bExplain 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. Leading to situations such that if p and q are integers, then –(p/q) = -p/q = p/-q.7.NS.2cApply properties of operations as strategies to multiply and divide rational numbers.7.NS.2dConvert a rational number in the form of a fraction to its decimal equivalent using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.7.NS.3Solve and interpret real-world and mathematical problems involving the four operations with rational numbers. (Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
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