## Envision Math Accelerated Grade 7 Volume 1 Chapter 5 Generate Equivalent Expressions

**Question. How can properties of operations help to generate equivalent expressions that can be used in solving problems.**

We have to tell that how can properties of operations help to generate equivalent expressions that can be used in solving problems.

**We consider the below example:**

On the expression 3 (2 + x), we apply the distributive property to get the equivalent expression as 6 + 3x.

Similarly, we can apply the distributive property on 24+18y to get the equivalent expression as 6 (4x + 3y).

Thus, the properties of operations help to generate equivalent expressions which are of help in solving problems.

The properties of operations help to generate equivalent expressions such as distributive property.

The exploration of activity trackers and the data to develop models based on individual fitness goals is as follows

Fitness tracker

It helps in motivating us.

To maintain a healthy diet.

To set our goals.

Its disadvantages are Lack of accuracy and expensive.

It helps in motivating us, To maintain a healthy diet, To set our goals, Its disadvantages are Lack of accuracy and expensive.

**Question. Evaluate an expression it means that we substitute and replace some values.**

We are required to complete the given definition with an appropriate word.

The combination of variables and constants, in mathematics, is referred to as an expression.

When we solve or evaluate an expression it means that we substitute and replace some values in the place of variables, to get the required result.

To substitute a value means to replace or exchange variables with the numbers given.

Therefore, To evaluate a + 3 when a = 7, you can substitute 7 for ‘a’ in the expression.

To evaluate a + 3 when a = 7, you can substitute 7 for ‘a’ in the expression.

We are required to complete the given definition with an appropriate word.

In mathematics, a function or a particular task performed to get some desired result on numbers is called as an operation.

The digits or terms on which the operation is performed are called as operands.

There are particular ways and rules to perform an operation.

The set of rules which conveys that whether which term will go first in the problem is called as the order of operations.

Therefore, The set of rules used to determine the order in which operations are performed is called the order of operations.

The set of rules used to determine the order in which operations are performed is called the order of operations.

**Question. Evaluate an expression it means that we substitute and replace some values in the place of variables.**

We are required to complete the given definition with an appropriate word.

The combination of variables and constants, in mathematics, is referred to as an expression.

When we solve or evaluate an expression it means that we substitute and replace some values in the place of variables, to get the required result.

The expression contains two or more terms which may be either variable or constant and are separated by arithmetic signs such as + (or) −

Therefore, Each part of an expression that is separated by a plus or minus sign is a term.

Each part of an expression that is separated by a plus or minus sign is a term.

We are required to complete the given definition with an appropriate word.

The combination of variables and constants, in mathematics is referred to as an expression.

When we multiply two or more terms, the result obtained is called as a product.

The number of variables which are multiplied are called as factors.

Therefore, When two numbers are multiplied to get a product, each number is called a factor.

When two numbers are multiplied to get a product, each number is called a factor.

**Question. Evaluate the given expression which is 3(18-7) + 2.**

We are required to evaluate the given expression which is 3(18−7) + 2.

The set of rules used to determine the order in which operations are performed is called the order of operations.

In order to evaluate the expression, we will have to follow the below order of operations.

Brackets, multiplication or division, addition or subtraction.

**We will evaluate as below:
**

⇒ 3 . (18−7) + 2 = x

⇒ 3.11 + 2 = x

⇒ x = 33 + 2

⇒ x = 35

****

The result of the expression 3(18−7)+2 is obtained as 35.

**Question. Evaluate the given expression which is (13 + 2) ÷ (9 – 4).**

We are required to evaluate the given expression which is (13 + 2) ÷ (9 − 4).

The set of rules used to determine the order in which operations are performed is called the order of operations.

In order to evaluate the expression, we will have to follow the below order of operations.

Brackets, multiplication or division, addition or subtraction

**We will evaluate as below:
**

⇒ (13 + 2) ÷ (9 − 4) = x

⇒** **15 ÷ 5 = x

⇒ x = 3

The result of the expression (13 + 2) ÷ (9 − 4) is obtained as 3.

**Question. Evaluate the given expression which is 24 ÷ 4.2 – 2.**

We are required to evaluate the given expression which is 24 ÷ 4⋅2 − 2.

In order to evaluate the expression, we will have to follow the below order of operations.

Brackets, multiplication or division, addition or subtraction

**We will evaluate as below:
**

⇒ 24 ÷ 4.2 − 2 = x

⇒ 6.2 −2 = x

⇒ 12 − 2 = x

⇒ x = 10

The result of the expression 24 ÷ 4⋅2 − 2 is obtained as 10.

**Question. Evaluate the given expression which is ab by substituting the value of variables as a = -4 and b = 3.**

We are required to evaluate the given expression which is ab by substituting the value of variables as a = − 4 and b = 3.

When we solve or evaluate an expression it means that we substitute and replace some values in the place of variables, to get the required result.

To substitute a value means to replace or exchange variables with the numbers given.

We have

a = −4

b = 3

**We will evaluate as below:
**

⇒ a⋅b

⇒ (−4)⋅(3)

⇒ −12

The result of the expression ab is obtained as -12.

**Question. Evaluate the given expression which is 2a + 3b by substituting the value of variables as a = -4 and b = 3.**

We are required to evaluate the given expression which is 2a+3b by substituting the value of variables as a = -4 and b = 3.

To substitute a value means to replace or exchange variables with the numbers given.

The order of operation that will be followed is Brackets, multiplication or division, addition or subtraction

We have

a = −4

b =3

**We will evaluate as below:**

⇒ 2a + 3b

⇒ 2(−4) + 3(3)

⇒ −8 + 9

⇒ 1

The result of the expression 2a + 3b is obtained as 1.

**Question. Evaluate the given expression which is 2(a-b) by substituting the value of variables as a = -4 and b = 3.**

We are required to evaluate the given expression which is 2(a−b) by substituting the value of variables as a = -4 and b = 3.

To substitute a value means to replace or exchange variables with the numbers given.

The order of operation that will be followed is. Brackets, multiplication or division, addition or subtraction.

We have

a = −4

b = 3

**We will evaluate as below:**

⇒ 2(a−b)

⇒ 2(−4−3)

⇒ 2(−7)

⇒ −14

The result of the expression 2(a−b) is obtained as -14.