4.e 7.NS.A.2.A 7.NS.A.2a Math.7.NS.2a 7.NS.A.2.A 7.NR.1.6 7.NS.2.a 7.NS.2a 7.NS.2.a 4.f 7.NS.A.2.B 7.NS.A.2b Math.7.NS.2b 7.NS.A.2.B 7.NR.1.7 7.NS.2.a 7.NS.2b 7.NS.2.b 7.NS.A.2.C 7.NS.A.2c Math.7.NS.2c 7.NS.A.2.C 7.NR.1.9 7.NS.2.c 7.NS.2c 7.NS.2.c 4.g 7.NS.A.2.D 7.NS.A.2d Math.7.NS.2d 7.NS.A.2.D 7.NR.1.10 7.NS.2.d 7.NS.2d 7.NS.2.d CC.2.1.7.E.1 M07.A-N.1.1.3

Understanding Operations - Multiply/Divide 7th Grade

Alabama Course of Study Standards: 4.e
Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.
Arkansas Academic Standards: 7.NS.A.2.A
Understand that multiplication is extended from fractions to all rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, and the rules for multiplying signed numbers Interpret products of rational numbers by describing real-world contexts
Arizona - K-12 Academic Standards: 7.NS.A.2a Common Core State Standards: Math.7.NS.2a or 7.NS.A.2.A Kentucky Academic Standards (KAS): 7.NS.2.a Mississippi College- and Career-Readiness Standards: 7.NS.2a
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.
Georgia Standards of Excellence (GSE): 7.NR.1.6
Make sense of multiplication of rational numbers using realistic applications.
North Carolina - Standard Course of Study: 7.NS.2.a
Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.
Alabama Course of Study Standards: 4.f
Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a nonzero divisor) as a rational number.
Arkansas Academic Standards: 7.NS.A.2.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 (e.g., if p and q are integers, then -(p/q) = (-p)/q = p/(-q)) Interpret quotients of rational numbers by describing real-world contexts
Arizona - K-12 Academic Standards: 7.NS.A.2b Common Core State Standards: Math.7.NS.2b or 7.NS.A.2.B Kentucky Academic Standards (KAS): 7.NS.2.a Mississippi College- and Career-Readiness Standards: 7.NS.2b
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 real-world contexts.
Georgia Standards of Excellence (GSE): 7.NR.1.7
Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.
North Carolina - Standard Course of Study: 7.NS.2.b
Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.
Arkansas Academic Standards: 7.NS.A.2.C
Fluently multiply and divide rational numbers by applying properties of operations as strategies
Arizona - K-12 Academic Standards: 7.NS.A.2c Common Core State Standards: Math.7.NS.2c or 7.NS.A.2.C Kentucky Academic Standards (KAS): 7.NS.2.c Mississippi College- and Career-Readiness Standards: 7.NS.2c
Apply properties of operations as strategies to multiply and divide rational numbers.
Georgia Standards of Excellence (GSE): 7.NR.1.9
Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.
North Carolina - Standard Course of Study: 7.NS.2.c
Use division and previous understandings of fractions and decimals. Convert a fraction to a decimal using long division. Understand that the decimal form of a rational number terminates in 0s or eventually repeats.
Alabama Course of Study Standards: 4.g
Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.
Arkansas Academic Standards: 7.NS.A.2.D
Convert a fraction to a decimal using long division Know that the decimal form of a fraction terminates in 0s or eventually repeats
Arizona - K-12 Academic Standards: 7.NS.A.2d
Convert a rational number to decimal form using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.
Common Core State Standards: Math.7.NS.2d or 7.NS.A.2.D Kentucky Academic Standards (KAS): 7.NS.2.d Mississippi College- and Career-Readiness Standards: 7.NS.2d
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.
Georgia Standards of Excellence (GSE): 7.NR.1.10
Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.
North Carolina - Standard Course of Study: 7.NS.2.d
Understand that the decimal form of a rational number terminates in 0s or eventually repeats.
Pennsylvania Core Standards: CC.2.1.7.E.1
Apply and extend previous understandings of operations with fractions to operations with rational numbers.
Pennsylvania Core Standards: M07.A-N.1.1.3
Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

Subtracting a rational number is the same as adding its additive inverse. This can be used along with the distributive property to find equivalent expressions.

Distributive Property: The product of a number and a sum is equal to the sum of the number multiplied by each addend.
Additive Inverse: A number and its opposite are additive inverses.
Additive inverses have a sum of 0.

First, write the expression as one fraction.

\frac{2}{- 9} \times \frac{- 7}{- 8} = \frac{(2) (- 7)}{(- 9) (- 8)}

Then, simplify.

\begin{array}{rcl} \frac{(2) (- 7)}{(- 9) (- 8)} & = & \frac{(2) [(- 1) (7)]}{(- 9) [(- 1) (8)]} \\ = & \frac{(2) (7)}{(- 9) (8)} \end{array}

So, the expression

\frac{(2) (7)}{(- 9) (8)}

is equivalent to the expression

\frac{2}{- 9} \times \frac{- 7}{- 8}

Understanding Operations - Multiply/Divide

Alabama Course of Study Standards: 4.e

Extend strategies of multiplication to rational numbers to develop rules for multiplying signed numbers, showing that the properties of the operations are preserved.

Arkansas Academic Standards: 7.NS.A.2.A

Arizona - K-12 Academic Standards: 7.NS.A.2a

Common Core State Standards: Math.7.NS.2a or 7.NS.A.2.A

Kentucky Academic Standards (KAS): 7.NS.2.a

Mississippi College- and Career-Readiness Standards: 7.NS.2a

Georgia Standards of Excellence (GSE): 7.NR.1.6

Make sense of multiplication of rational numbers using realistic applications.

North Carolina - Standard Course of Study: 7.NS.2.a

Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor.

Alabama Course of Study Standards: 4.f

Divide integers and explain that division by zero is undefined. Interpret the quotient of integers (with a nonzero divisor) as a rational number.

Arkansas Academic Standards: 7.NS.A.2.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 (e.g., if p and q are integers, then -(p/q) = (-p)/q = p/(-q))Interpret quotients of rational numbers by describing real-world contexts

Arizona - K-12 Academic Standards: 7.NS.A.2b

Common Core State Standards: Math.7.NS.2b or 7.NS.A.2.B

Kentucky Academic Standards (KAS): 7.NS.2.a

Mississippi College- and Career-Readiness Standards: 7.NS.2b

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 real-world contexts.

Georgia Standards of Excellence (GSE): 7.NR.1.7

Show and explain that integers can be divided, assuming the divisor is not zero, and every quotient of integers is a rational number.

North Carolina - Standard Course of Study: 7.NS.2.b

Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts.

Arkansas Academic Standards: 7.NS.A.2.C

Fluently multiply and divide rational numbers by applying properties of operations as strategies

Arizona - K-12 Academic Standards: 7.NS.A.2c

Common Core State Standards: Math.7.NS.2c or 7.NS.A.2.C

Kentucky Academic Standards (KAS): 7.NS.2.c

Mississippi College- and Career-Readiness Standards: 7.NS.2c

Apply properties of operations as strategies to multiply and divide rational numbers.

Georgia Standards of Excellence (GSE): 7.NR.1.9

Apply properties of operations as strategies to solve multiplication and division problems involving rational numbers represented in an applicable scenario.

North Carolina - Standard Course of Study: 7.NS.2.c

Use division and previous understandings of fractions and decimals.Convert a fraction to a decimal using long division.Understand that the decimal form of a rational number terminates in 0s or eventually repeats.

Alabama Course of Study Standards: 4.g

Convert a rational number to a decimal using long division, explaining that the decimal form of a rational number terminates or eventually repeats.

Arkansas Academic Standards: 7.NS.A.2.D

Convert a fraction to a decimal using long divisionKnow that the decimal form of a fraction terminates in 0s or eventually repeats

Arizona - K-12 Academic Standards: 7.NS.A.2d

Convert a rational number to decimal form using long division; know that the decimal form of a rational number terminates in 0’s or eventually repeats.

Common Core State Standards: Math.7.NS.2d or 7.NS.A.2.D

Kentucky Academic Standards (KAS): 7.NS.2.d

Mississippi College- and Career-Readiness Standards: 7.NS.2d

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.

Georgia Standards of Excellence (GSE): 7.NR.1.10

Convert rational numbers between forms to include fractions, decimal numbers and percentages, using understanding of the part divided by the whole. Know that the decimal form of a rational number terminates in 0s or eventually repeats.

North Carolina - Standard Course of Study: 7.NS.2.d

Understand that the decimal form of a rational number terminates in 0s or eventually repeats.

Pennsylvania Core Standards: CC.2.1.7.E.1

Apply and extend previous understandings of operations with fractions to operations with rational numbers.

Pennsylvania Core Standards: M07.A-N.1.1.3

Apply properties of operations to multiply and divide rational numbers, including real-world contexts; demonstrate that the decimal form of a rational number terminates or eventually repeats.

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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 (e.g., if p and q are integers, then -(p/q) = (-p)/q = p/(-q))
Interpret quotients of rational numbers by describing real-world contexts

Use division and previous understandings of fractions and decimals.
Convert a fraction to a decimal using long division.
Understand that the decimal form of a rational number terminates in 0s or eventually repeats.

Convert a fraction to a decimal using long division
Know that the decimal form of a fraction terminates in 0s or eventually repeats