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

In plain words: Students extend multiplication and division to negative numbers, see why (−1)(−1) = 1, and write fractions as decimals that end or repeat.

Quick picks

Common mistake: Using the addition rule for signs: saying −4 × (−3) = −12 because "two negatives make a bigger negative".
Builds on: 6.NS.A.1Dividing fractions 6.NS.B.2Multi-digit division
Leads to: 7.NS.A.3Rational number word problems 8.NS.A.1Irrational numbers

7.NS.A.2.aSigns of productsUnderstand 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.7.NS.A.2.bDividing integersUnderstand 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.7.NS.A.2.cProperties as strategiesApply properties of operations as strategies to multiply and divide rational numbers.7.NS.A.2.dFractions to decimalsConvert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Khan Academy Resources

Signs of products 7.NS.A.2.a

Multiplying negative numbers review Multiplying negative numbers Multiplying positive and negative fractions Exponents with negative fractional bases Signs of expressions challenge Signs of expressions Multiplying & dividing negative numbers word problems Why a negative times a negative makes sense Multiplying positive & negative numbers Why a negative times a negative is a positive Sign of expressions challenge problems The 0 & 1st power Even & odd numbers of negatives Interpreting multiplication & division of negative numbers Multiplying positive and negative fractions Exponents with negative bases 1 and -1 to different powers

Dividing integers 7.NS.A.2.b

Dividing negative numbers review Dividing mixed numbers with negatives Dividing negative numbers Negative signs in fractions Dividing positive and negative fractions Simplify complex fractions Dividing by zero Dividing positive and negative numbers Why dividing by zero is undefined Simplifying complex fractions Negative signs in fractions Dividing negative fractions

Properties as strategies 7.NS.A.2.c

Equivalent expressions with negative numbers (multiplication and division)Equivalent expressions with negative numbers (multiplication and division)

Fractions to decimals 7.NS.A.2.d

Converting fractions to decimals Comparing rational numbers Worked example: Converting a fraction (7/8) to a decimal Fraction to decimal with rounding Fraction to decimal: 11/25

Multiplying and dividing 7.NS.A.2

Order of operations with negative numbers Exponents with integer bases One-step equations with negatives (multiply & divide)Order of operations example Expressions with rational numbers

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7.NS.A.2: Multiplying and dividing