Just like any language, math has actually a means to communicate ideas. One algebraic expression is a compact means of describing mathematical objects using a **combination** the numbers, variables (letters), and arithmetic operationsnamely addition, subtraction, multiplication, and division.

You are watching: The product of 5 and x

In other words, the three main components of algebraic expressions room **numbers**, **variables**, and also **arithmetic operations**.

Examples:1, 6, 8, 27, 32, etc.

Variables or LettersExamples:x, y, a, h, p, etc.

Arithmetic OperationsExamples:+ (addition), - (subtraction) , \times (multiplication) , ÷ (division)

The complying with are easy instances that can help you get familiarized v the operations of addition, subtraction, multiplication,and division.

**Addition**

the sum of x and 5 → x+5

**Subtraction**

the difference of y and 3 → y-3

**Multiplication**

the product the n and also 2 → 2n

**Division**

the quotient the k and 7 → \Largek \over 7

## Writing Algebraic expression Step-by-Step examples

Let’s walk over more examples.

**Example 1:** The amount of double a number and 3

**Answer:** Let variable x it is in the unknown number. So twice a number means 2x. The amount (use to add symbol) of twice a number and 3 can be created as 2x+3.

**Example 2:** The distinction of triple a number and 5

**Answer:**Let change y it is in the unknown number. So triple a number means 3y. The** **difference** **(use minus symbol) of triple a number and also 5 need to be written as 3y - 5.

**Example 3:**The amount of the quotient that m and 2, and also the product the 4 and also n.

**Answer:**In this case, the unknown numbers space already noted as m and also n. That’s one much less thing come worry.

The key is to recognize that we room going come **add** a quotient and a product.

Therefore, the sum of the quotient and product is \Largem \over 2 + 4n.

**Example 4:** The difference of the productof 7 and w, and also the quotient the 2 and v.

**Answer:** In this case, the unknown numbers have actually been assigned with equivalent variables which room w and also v.

The vital is to identify that we space going to **subtract** the product by the quotient of some expressions.

Therefore, the difference of the product and quotient is 7w - \Large2 \over v.

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## Common native or terms to typical Addition, Subtraction, Multiplication, and also Division

Now, let’s walk over some common words or phrases that define the 4 arithmetic operations. That is vital that you knowthese words or phrases come be successful in composing or interpreting any type of given algebraic expression.

## Math Phrases into Algebraic Expressions

The vital to finding out is to examine a lot of examples!

MATH PHRASES | ALGEBRAIC EXPRESSIONS |

a number to add 9 | y + 9 |

the sum of a number and 10 | m + 10 |

total the a number and 5 | b + 5 |

a number raised by 4 | x + 4 |

h take far 2 | h − 2 |

2 take away by a number | 2 − h |

a number minus 11 | k − 11 |

11 minus a number | 11 − k |

a number decreased by 7 | y − 7 |

the difference of n and 25 | n − 25 |

the difference of 25 and also n | 25 − n |

5 less than a number | x − 5 |

x less than the number 5 | 5 − x |

the product the r and 4 | 4r |

7 time a number | 7p |

double a number | 2x |

triple a number | 3x |

a number split by 4 | w / 4 |

the quotient the w and 6 | w / 6 |

the quotient that 12 and also m | 12 / m |

a number divided by 3 | f / 3 |

t end 7 | t / 7 |

5 right into a number | a / 5 |

a number right into 5 | 5 / a |

the sum of x and 7 separated by 2 | ( x + 7 ) / 2 |

the difference of m and also 3 over 5 | ( m − 3) / 5 |

11 more than the product the 3 and y | 3y + 11 |

6 much less than the quotient that c and also 10 | ( c / 10 ) − 6 |

3 minus the product the 5 and also a number | 3 − 5x |

the sum of 5 and the quotient of z and also 7 | ( z / 7 ) + 5 |

the difference of double a number and also 3 | 2m − 3 |

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