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# Transformation of Phrase into Expression involving  Addition and Multiplication

• Different operations can be performed when variables are involved.
• To write an expression for a given statement, follow three steps:

(i) Identify the number.

(ii) Identify the operations involved.

(iii) Identify the variable.

Important phrases for addition: Increased, sum, altogether, more than, plus.

Important phrases for multiplication: Product, times, of, groups.

For example: "$$2$$ more than the twice of a number."

(i) $$2$$ is a number.

(ii) 'more than' means addition and 'twice' means multiplication by $$2$$ .

(iii) A number which is unknown, let it be $$x.$$

• The statement says,

twice of a number means $$2$$ times a number $$=2x$$

• Two more than $$2x$$ is :

$$2x+2$$

#### "$$3$$ times a number and $$4$$ more."  Which option represents the correct expression for the given statement?

A $$4x-3$$

B $$4x+3$$

C $$3x+4$$

D $$3x-4$$

×

Given statement is:

"$$3$$ times a number and $$4$$ more."

(i) Here $$3$$ and $$4$$ are numbers.

(ii) 'times' means multiply and 'more' means addition.

(iii) A number which is unknown, let it be $$x.$$

$$3$$ times a number $$=3x$$,

$$3x$$ and $$4$$ more means,

$$3x+4$$

This is the required expression.

Hence option (C) is correct.

### "$$3$$ times a number and $$4$$ more."  Which option represents the correct expression for the given statement?

A

$$4x-3$$

.

B

$$4x+3$$

C

$$3x+4$$

D

$$3x-4$$

Option C is Correct

# Transformation of Phrase into Expression Involving Addition and Subtraction

• Different operations can be performed when variables are involved.
• To write an expression for a given statement, follow three steps-

(i) Identify the number.

(ii) Identify the operations involved.

(iii) Identify the variable.

Important phrases for addition: increased, sum, altogether, more than and plus.

Important phrases for subtraction: difference, take away, less than, subtraction, decreases.

For example: $$9$$ less than the sum of $$6$$ and $$x$$.

• Here $$9$$ and $$6$$ are the numbers.
• 'Sum' and 'less than' words represent two operations, addition and subtraction respectively.
• $$x$$ is the variable.
• The statement says,

sum of $$6$$ and $$x$$

$$\Rightarrow \; x+6$$

$$9$$ less than $$x+6$$ is:

$$(x+6) - 9$$

#### "$$11$$ subtracted from the sum of $$x$$ and $$7$$."  Which option correctly represents the given statement?

A $$11-(x+7)$$

B $$(x+7)-11$$

C $$7x+11$$

D $$11x+7$$

×

Given statement is,

"$$11$$ subtracted from the sum of $$x$$ and $$7$$."

(i) Here the numbers are $$11$$ and $$7$$

(ii) "Sum" and "subtracted" words represent addition and subtraction respectively.

(iii) Here $$x$$ is a variable.

According to the statement,

Sum of $$x$$ and $$7 = x+7$$

$$11$$ subtracted from $$x+7$$

$$\Rightarrow (x+7)-11$$

This is the required expression.

Hence, option (B) is correct.

### "$$11$$ subtracted from the sum of $$x$$ and $$7$$."  Which option correctly represents the given statement?

A

$$11-(x+7)$$

.

B

$$(x+7)-11$$

C

$$7x+11$$

D

$$11x+7$$

Option B is Correct

# Transformation of Phrase into Expression involving Subtraction and Multiplication

• Different operations can be performed when variables are involved.
• To write an expression for a given statement, follow three steps:

(i) Identify the number.

(ii) Identify the operations involved.

(iii) Identify the variable.

For example:

"$$5$$ times a number and $$3$$ less."

(i) $$5$$ and $$3$$ are the two numbers which are known.

(ii) 'times' means multiplication and 'less' means subtraction.

(iii) A number which is unknown, let it be $$x.$$

• The statement says

$$5$$ times a number $$=5x$$

$$5x$$ and $$3$$ less is:

$$5x-3$$

#### "Subtract $$4$$ from the product of $$7$$ and a number." Which option correctly represents the given statement?

A $$4x-7$$

B $$7x-4$$

C $$7x+4$$

D $$\dfrac{x}{7}+4$$

×

Given statement is,

"Subtract $$4$$ from the product of $$7$$ and a number".

(i) Here $$4$$ and $$7$$ are the two numbers which are known.

(ii) 'Subtract' means subtraction and 'product' means multiplication.

(iii) A number which is unknown, let it be $$x.$$

According to the statement,

product of $$7$$ and a number $$=7x$$

Subtract $$4$$ from $$7x$$ is

$$7x-4$$

This is the required expression.

Hence option (B) is correct.

### "Subtract $$4$$ from the product of $$7$$ and a number." Which option correctly represents the given statement?

A

$$4x-7$$

.

B

$$7x-4$$

C

$$7x+4$$

D

$$\dfrac{x}{7}+4$$

Option B is Correct

# Transformation of Phrase into Expression involving Addition and Division

• Different operations can be performed when variables are involved.
• To write an expression for a given statement, follow three steps:

(i) Identify the number.

(ii) Identify the operations involved.

(iii) Identify the variable.

Important phrases for addition: increased, sum, altogether, more than, plus.

Important phrases for division: quotient, split up, divided.

For example:

"$$7$$ more than the quotient of a number and $$3$$ ."

(i) $$7$$ and $$3$$ are the two numbers which are known.

(ii) 'more than' means addition and 'quotient' means division.

(iii) A number which is unknown, let it be $$x.$$

• The statement says,

quotient of a number and $$3,$$

$$\Rightarrow\;\dfrac{x}{3}$$

• $$7$$ more than $$\dfrac{x}{3}$$ is:

$$\Rightarrow \dfrac{x}{3}+7$$

#### "$$4$$ divided by a number and $$6$$ more."  Which option correctly represents the given statement?

A $$3x+6$$

B $$4x+6$$

C $$4x-6$$

D $$\dfrac{4}{x}+6$$

×

Given statement is,

"$$4$$ divided by a number and $$6$$ more."

(i) $$4$$ and $$6$$ are the two numbers which are known.

(ii) 'divided' means division and 'more' means addition.

(iii) A number which is unknown, let it be $$x.$$

$$4$$ divided by a number $$=\dfrac{4}{x}$$

$$\dfrac{4}{x}$$ and $$6$$ more means,

$$\dfrac{4}{x}+6$$

This is the required expression.

Hence, option (D) is correct.

### "$$4$$ divided by a number and $$6$$ more."  Which option correctly represents the given statement?

A

$$3x+6$$

.

B

$$4x+6$$

C

$$4x-6$$

D

$$\dfrac{4}{x}+6$$

Option D is Correct

# Transformation of Phrase into Expression involving Subtraction and Division

• Different operations can be performed when variables are involved.
• To write an expression for a given statement, follow three steps:

(i) Identify the number.

(ii) Identify the operations involved.

(iii) Identify the variable.

For example:

"Take away $$1$$ from the quotient of a number and $$2$$ ."

(i) Here, $$1$$ and $$2$$ are the two numbers which are known.

(ii) 'Take away' means subtraction and 'quotient' means division.

(iii) A number which is unknown, let it be $$x.$$

• The statement says,

quotient of a number and $$2=\dfrac{x}{2}$$

Take away $$1$$ from $$\dfrac{x}{2}$$ is,

$$\dfrac{x}{2}-1$$

#### "$$10$$ less than the quotient of $$15$$ and a number."  Which expression correctly represents the given statement?

A $$10-\dfrac{x}{15}$$

B $$15x-10$$

C $$10-\dfrac{15}{x}$$

D $$\dfrac{15}{x}-10$$

×

Given statement is,

"$$10$$ less than the quotient of $$15$$ and a number."

(i) $$15$$ and $$10$$ are the two numbers which are known.

(ii) 'quotient' means division and 'less' means subtraction.

(iii) A number which is unknown, let it be $$x.$$

According to the statement,

Quotient of $$15$$ and a number $$=\dfrac{15}{x}$$

$$10$$ less than $$\dfrac{15}{x}$$ is,

$$\dfrac{15}{x}-10$$

This is the required expression.

Hence option (D) is correct.

### "$$10$$ less than the quotient of $$15$$ and a number."  Which expression correctly represents the given statement?

A

$$10-\dfrac{x}{15}$$

.

B

$$15x-10$$

C

$$10-\dfrac{15}{x}$$

D

$$\dfrac{15}{x}-10$$

Option D is Correct

# Transformation of Phrase into Expression involving Multiplication and Division

• Different operations can be performed when variables are involved.
• To write an expression for a given statement, follow three steps:

(i) Identify the number.

(ii) Identify the operations involved.

(iii) Identify the variable.

For example:

"$$10$$ times a number divided by $$18$$ ."

(i) $$10$$ and $$18$$ are the two numbers which are known.

(ii) 'times' means multiplication and 'divided' means division.

(iii) A number which is unknown, let it be $$x.$$

The statement says,

$$10$$ times a number $$=10x$$

$$10x$$ divided by $$18$$ is,

$$\dfrac{10x}{18}$$

#### "$$20$$ times the quotient of a number and $$21$$." Which option correctly represents the given statement?

A $$20x+21$$

B $$20x-21$$

C $$\dfrac{x}{21}$$

D $$\dfrac{20x}{21}$$

×

Given statement is,

"$$20$$ times the quotient of a number and $$21$$ ."

(i) $$20$$ and $$21$$ are the two numbers which are known.

(ii) 'times' means multiplication and 'quotient' means division.

(iii) A number which is unknown, let it be $$x.$$

According to the statement,

the quotient of a number and $$21=\dfrac{x}{21}$$

$$20$$ times $$\dfrac{x}{21}$$ is

$$20\left(\dfrac{x}{21}\right)=\dfrac{20x}{21}$$

This is the required expression.

Hence option (D) is correct.

### "$$20$$ times the quotient of a number and $$21$$." Which option correctly represents the given statement?

A

$$20x+21$$

.

B

$$20x-21$$

C

$$\dfrac{x}{21}$$

D

$$\dfrac{20x}{21}$$

Option D is Correct