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Transformation Of Phrase Into Expression (multiple Operations)

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 : 

\(2x+2\)

Illustration Questions

"\(3\) 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: 

\((x+6) - 9\)  

Illustration Questions

"\(11\) 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:

 \(5x-3\)

Illustration Questions

"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: 

\(\Rightarrow \dfrac{x}{3}+7\)

Illustration Questions

"\(4\) 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,

\(\dfrac{x}{2}-1\)

Illustration Questions

"\(10\) 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,

\(\dfrac{10x}{18}\)

Illustration Questions

"\(20\) 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

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