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.
The Number System
Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
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Apply properties of operations as strategies to add and subtract rational numbers.
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.
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.
Describe situations in which opposite quantities combine to make 0.
Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
Fluently divide multi-digit numbers using the standard algorithm.
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.
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.
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.
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.
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.
