Page 33 - 新思维数学学生用书7 样章

2 Expressions, formulae and equations

2.1 Constructing expressions

In this section you will … Key words

• use letters to represent numbers coefficient

• use the correct order of operations in algebraic expressions constant
• write and use expressions. expression

equation
In algebra you can use a letter to represent an unknown number.
An expression contains numbers and letters, but not an equals sign. equivalent
An equation contains numbers and letters and an equals sign. expression
Example: 5n + 4 is an expression. term
5n + 4 = 19 is an equation. unknown

In the expression 5n + 4, there are two terms. 5n is one term. The other term variable
is 4.
The letter n is called the variable because it can have different values. Tip

The coefficient of n is 5 because it is the number that multiplies the variable.
In the equation 5n + 4 = 19, n is the unknown number, 5 is the coefficient of 5n + 4 means
n, and the numbers 4 and 19 are constants. A constant may also be written 5 × n + 4. Use
as a letter, such as π. π is the ratio of a circle’s circumference to its diameter. the correct
It is approximately 3.14. order of

You can use a letter to represent an unknown number to solve problems. operations.
Example: Shown is a bag of sweets. You don’t know how many sweets are in Do the
the bag. multiplication
before the
addition.

You will learn
more about π
n sweets n– 3 sweets later in your

n represents the unknown Three sweets are taken out of the bag. studies.
number of sweets in the bag. Now there are n − 3 sweets left in the bag.

Worked example 2.1

Mathew is x years old. David is 4 years older than Mathew. Adam is 2 years younger than Mathew.
Kathryn is three times Mathew’s age. Ella is half Mathew’s age.
Write down an expression for each person’s age.

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