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

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.

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.

Processing Request...

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.)