4.d 7.NS.A.1d Math.7.NS.1d 7.NS.A.1.D 7.NR.1.5 7.NS.1.d 7.NS.1d 7.NS.1.d 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 5 7.NS.A.3 Math.7.NS.3 7.NS.A.3 7.NR.1.11 7.NS.A.3 7.NS.3 7.NS.3 7.NS.3 7.NS.A.3 7.NS.A.3 CC.2.1.7.E.1 M07.A-N.1.1.3 7.NR.1.10 7.NR.1.11 7.NCC.6 7.NCC.9

Mixed Operations - Fractions, Decimals, Integers 7th Grade

Alabama Course of Study Standards: 4.d
Use a number line to demonstrate 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.
Arizona Academic Standards: 7.NS.A.1d Common Core State Standards: Math.7.NS.1d or 7.NS.A.1.D Kentucky Academic Standards (KAS): 7.NS.1.d Mississippi College- and Career-Readiness Standards: 7.NS.1d North Carolina - Standard Course of Study: 7.NS.1.d
Apply properties of operations as strategies to add and subtract rational numbers.
Georgia Standards of Excellence (GSE): 7.NR.1.5
Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.
Arizona 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: 5
Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.
Arizona Academic Standards: 7.NS.A.3
Solve mathematical problems and problems in real-world context involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions where a/b ÷ c/d when a,b,c, and d are all integers and b,c, and d ≠ 0.
Common Core State Standards: Math.7.NS.3 or 7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers.
Georgia Standards of Excellence (GSE): 7.NR.1.11
Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.
Massachusetts Curriculum Frameworks: 7.NS.A.3
Solve real-world and mathematical problems involving the four operations with integers and other rational numbers.24
North Carolina - Standard Course of Study: 7.NS.3
Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.
New York State Next Generation Learning Standards: 7.NS.3
Solve real-world and mathematical problems involving the four operations with rational numbers. Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions limited to a/b / c/d where a, b, c, and d are integers and b, c, and d ≠ 0.
Ohio's Learning Standards: 7.NS.3
Solve 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.
Tennessee Academic Standards: 7.NS.A.3
Solve 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.)
Wisconsin Academic Standards: 7.NS.A.3
Solve real-world and mathematical problems involving the four operations with rational numbers. (Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)
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.
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.
Georgia Standards of Excellence (GSE): 7.NR.1.11
Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.
Arkansas Academic Standards: 7.NCC.6
Apply properties of operations as strategies to fluently add, subtract, multiply, and divide rational numbers.
Arkansas Academic Standards: 7.NCC.9
Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.

Adding or subtracting a rational number can be represented by moving left (in the negative direction) or right (in the positive direction) on a horizontal number line.

The expression p + q represents the number located |q| units from p in the
positive or negative direction if q is positive or negative, respectively.

ADDITION

Adding a positive number indicates moving that many units to the right on a number line.

Adding a negative number indicates moving that many units to the left on a number line.

SUBTRACTION

Subtracting a positive number indicates moving that many units to the left on a number line.

First, draw an arrow to represent

1 \frac{1}{2}

.
Start at 0 and extend the arrow

1 \frac{1}{2}

units in the positive direction, which is to the right.

Next, draw an arrow to represent subtracting

3 \frac{1}{4}

from

1 \frac{1}{2}

.
Start at

1 \frac{1}{2}

and extend the arrow

3 \frac{1}{4}

units in the negative direction, which is to the left.

The second line ends at

- 1 \frac{3}{4}

. So,

1 \frac{1}{2} - 3 \frac{1}{4} = - 1 \frac{3}{4}

Mixed Operations - Fractions, Decimals, Integers

Alabama Course of Study Standards: 4.d

Use a number line to demonstrate 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.

Arizona Academic Standards: 7.NS.A.1d

Common Core State Standards: Math.7.NS.1d or 7.NS.A.1.D

Kentucky Academic Standards (KAS): 7.NS.1.d

Mississippi College- and Career-Readiness Standards: 7.NS.1d

North Carolina - Standard Course of Study: 7.NS.1.d

Apply properties of operations as strategies to add and subtract rational numbers.

Georgia Standards of Excellence (GSE): 7.NR.1.5

Apply properties of operations, including part-whole reasoning, as strategies to add and subtract rational numbers.

Arizona 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: 5

Solve real-world and mathematical problems involving the four operations of rational numbers, including complex fractions. Apply properties of operations as strategies where applicable.

Arizona Academic Standards: 7.NS.A.3

Solve mathematical problems and problems in real-world context involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions where a/b ÷ c/d when a,b,c, and d are all integers and b,c, and d ≠ 0.

Common Core State Standards: Math.7.NS.3 or 7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.

Georgia Standards of Excellence (GSE): 7.NR.1.11

Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

Massachusetts Curriculum Frameworks: 7.NS.A.3

Solve real-world and mathematical problems involving the four operations with integers and other rational numbers.24

North Carolina - Standard Course of Study: 7.NS.3

Solve real-world and mathematical problems involving numerical expressions with rational numbers using the four operations.

New York State Next Generation Learning Standards: 7.NS.3

Solve real-world and mathematical problems involving the four operations with rational numbers.Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions limited to a/b / c/d where a, b, c, and d are integers and b, c, and d ≠ 0.

Ohio's Learning Standards: 7.NS.3

Solve 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.

Tennessee Academic Standards: 7.NS.A.3

Solve 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.)

Wisconsin Academic Standards: 7.NS.A.3

Solve real-world and mathematical problems involving the four operations with rational numbers.(Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)

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.

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.

Georgia Standards of Excellence (GSE): 7.NR.1.11

Solve multi-step, contextual problems involving rational numbers, converting between forms as appropriate, and assessing the reasonableness of answers using mental computation and estimation strategies.

Arkansas Academic Standards: 7.NCC.6

Apply properties of operations as strategies to fluently add, subtract, multiply, and divide rational numbers.

Arkansas Academic Standards: 7.NCC.9

Apply operations with rational numbers involving the order of operations, involving nested grouping symbols.

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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.

Solve real-world and mathematical problems involving the four operations with rational numbers.
Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions limited to a/b / c/d where a, b, c, and d are integers and b, c, and d ≠ 0.

Solve real-world and mathematical problems involving the four operations with rational numbers.
(Note: Computations with rational numbers extend the rules for manipulating fractions to complex fractions.)