The absolute value of a number is its distance from 0 on the number line.

• The absolute value of -7 is 7, because it is 7 units away from 0.
• The absolute value of 5 is 5, because it is 5 units away from 0.

A common factor of two numbers is a number that evenly divides both numbers. 

• The factors of 15 are 1, 3, 5, and 15.
• The factors of 20 are 1, 2, 4, 5, 10, and 20.

The common factors of 15 and 20 are 1 and 5.

A common multiple of two numbers is a product that results from multiplying each of the two numbers by some whole number. 

• The multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, . . . .
• The multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, . . . .

The common multiples of 3 and 5 are 15, 30, 45, 60, . . . .

The coordinate plane is one way to represent pairs of numbers. The plane is made of a horizontal number line and a vertical number line that cross at 0.

Pairs of numbers can be used to describe the location of a point in the coordinate plane.

Point \(R\) is located at \((3,\text-2)\). This means \(R\) is 3 units to the right and 2 units down from \((0,0)\).

The greatest common factor of two numbers is the largest number that evenly divides both numbers. 

• The factors of 45 are 1, 3, 5, 9, 15, and 45.
• The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

The greatest common factor of 45 and 60 is 15.

An inequality is a statement that compares two values or expressions using symbols such as “\(>\)” or “\(<\)”. 

• The symbol “\(>\)” means “is greater than.”
• The symbol “\(<\)” means “is less than.”

For example, the inequality \(\text-3 > \text-7\) tells us that -3 is greater than -7.

The least common multiple of two numbers is the smallest product that results from multiplying each of the two numbers by some whole number.

• The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, . . . .
• The multiples of 10 are 10, 20, 30, 40, 50, 60, 70, 80, . . . .

The least common multiple of 6 and 10 is 30.

A negative number is a number that is less than 0.

Two numbers are opposites if they are the same distance from 0 on the number line, but on different sides. One is negative, and the other is positive.

A positive number is a number that is greater than 0.

The coordinate plane is divided into 4 sections called quadrants. The quadrants are numbered using Roman numerals, as shown.

A rational number is a number that can be written as a positive fraction, a negative fraction, or zero.

• 8 and -8 are rational numbers because they can be written as \(\frac81\) and \(\text-\frac81\).
• 0.75 and -0.75 are rational numbers because they can be written as \(\frac{75}{100}\) and \(\text-\frac{75}{100}\).

The sign of any number other than 0 is either positive or negative.

For example, the sign of 6 is positive. The sign of -6 is negative. Zero does not have a sign, because it is not positive or negative.

A solution to an inequality is a number that can be used in place of the variable to make the inequality true.

• A solution to the inequality \(c<10\) is 5, because it is true that \(5<10\).
• Some other solutions to this inequality are 9.9, 0, and -4.