Chapter 6: Expressions and Equations

This chapter is all about math with letters and numbers together. Let's find out what you will learn!

What You Will Learn

Finding common factors and multiples. You will learn to find the biggest number that can divide evenly into two other numbers (this is called the "greatest common factor"). You will also find the smallest number that two other numbers can both divide into evenly (this is called the "least common multiple"). You will use a math rule called the distributive property to break numbers apart in a smart way. For example, 36 + 8 can be written as 4 × (9 + 2).

Writing and solving expressions with exponents. An exponent is a small number that tells you how many times to multiply a number by itself. You will learn to read, write, and solve these kinds of problems.

Writing expressions with letters. Sometimes letters stand for numbers we don't know yet. These letters are called variables. You will:

• Write math problems using letters and numbers, like writing "5 – y" for "subtract y from 5."
• Learn the special names for parts of an expression, like sum (an addition answer), term, product (a multiplication answer), factor, quotient (a division answer), and coefficient (a number in front of a letter).
• Find the value of an expression when you know what number the letter stands for.
• Use the correct order of operations—the right order to do each step in a math problem.

Making equivalent expressions. Equivalent means "equal" or "the same value." You will learn ways to rewrite expressions so they look different but mean the same thing. For example, 3(2 + x) is the same as 6 + 3x.

Checking if expressions are equal. You will learn how to check whether two expressions always give the same answer, no matter what number you use for the letter.

Understanding equations and inequalities. An equation is a math sentence that says two things are equal, like 3 + 2 = 5. You will learn to check whether a number makes an equation true. You will also use letters to stand for unknown numbers in real-life problems.

Solving equations. You will solve equations like x + p = q and px = q, where all the numbers are positive.

Writing inequalities. An inequality compares two things and shows they are not equal, using symbols like > (greater than) or < (less than). You will learn to write inequalities like x > c or x < c, and show that they can have many, many possible answers. You will draw these answers on a number line.

Important Words in This Chapter

Here are some important words you will learn, explained in easy terms:

• Numeric expression – a math phrase using only numbers, like 3 + 4.
• Equivalent expressions – two expressions that equal the same amount.
• Simplify – to make an expression shorter or easier.
• Order of operations – the correct order to solve a math problem, step by step.
• Grouping symbols – marks like ( ) and [ ] that show which parts to solve first.
• Algebraic expression – a math phrase that has at least one letter standing for a number.
• Evaluate – to find the value of an expression by plugging in a number for the letter.
• Sum – the answer when you add.
• Difference – the answer when you subtract.
• Product – the answer when you multiply.
• Quotient – the answer when you divide.
• Term – a single number or letter (or numbers and letters multiplied together) in an expression.
• Like terms – terms that have the exact same letter part, so you can combine them.
• Coefficient – the number in front of a letter, like the 3 in 3x.
• Constant – a number that never changes.
• Variable – a letter that stands for a number you don't know yet.