Math & Numbers on Facts

How to add fractions with different denominators

Thu, 05 Nov 2026 00:00:00 +0000

Think of it like adding thirds of a pizza to quarters of a pizza. You can’t count them together until you cut both into slices of the same size, in this case twelfths.

How to divide fractions

Thu, 05 Nov 2026 00:00:00 +0000

Three words do all the work: keep, change, flip. Once you’ve done it twice, you won’t need to look it up again.

Example: 2/3 ÷ 4/5

Keep 2/3
Change ÷ to ×
Flip 4/5 to 5/4

2/3 × 5/4 = 10/12, which simplifies to 5/6.

How to find slope from a graph

Thu, 05 Nov 2026 00:00:00 +0000

Slope tells you how steep a line is and which way it tilts. On a graph, you can read it with nothing more than counting squares.

A worked example

Say a line passes through the points (1, 3) and (3, 7).

How to find slope from a table

Thu, 05 Nov 2026 00:00:00 +0000

A table of values is a graph with the picture taken away. Each row is a point, so finding the slope works exactly like finding slope from two points.

Worked example

x	y
0	5
1	8
2	11
3	14

Take the first two rows:

How to find slope from two points

Thu, 05 Nov 2026 00:00:00 +0000

The formula is just “rise over run” written with numbers instead of squares on a graph. If you can subtract and divide, you can do this.

Example 1: a positive slope

Find the slope between (2, 3) and (6, 11).

How to graph inequalities on a number line

Thu, 05 Nov 2026 00:00:00 +0000

An inequality like x > 3 has endless answers: 4, 3.5, 3.001, a million. A number line lets you show all of them with one circle and one arrow.

Open or closed circle?

Symbol	Meaning	Circle
<	less than	Open
>	greater than	Open
≤	less than or equal to	Closed (filled in)
≥	greater than or equal to	Closed (filled in)

A trick to remember: the “or equal to” symbols have an extra line underneath, and the closed circle has extra ink inside.

How to multiply fractions

Thu, 05 Nov 2026 00:00:00 +0000

Good news: multiplying is the easiest thing you can do with fractions. Unlike adding, you don’t need a common denominator, even when the bottoms are different.

The basic method

3/4 × 2/5

How to simplify algebraic expressions

Thu, 05 Nov 2026 00:00:00 +0000

Simplifying doesn’t change what an expression is worth. It just writes the same thing with fewer pieces, which makes the next step, often solving an equation, much easier.

What are like terms?

Like terms have the same letters raised to the same powers. Only the number in front, the coefficient, can differ.

How to simplify fractions

Thu, 05 Nov 2026 00:00:00 +0000

A simplified fraction is the same amount written with the smallest possible numbers. 18/24 and 3/4 are exactly equal; 3/4 is just easier to read.

Method 1: Divide by the greatest common factor

List the factors of both numbers.
- 18: 1, 2, 3, 6, 9, 18
- 24: 1, 2, 3, 4, 6, 8, 12, 24
The biggest number in both lists is 6.
Divide top and bottom by 6: 18 ÷ 6 = 3 and 24 ÷ 6 = 4, giving 3/4.

Method 2: Keep dividing by small numbers

If the GCF isn’t obvious, divide by any shared factor and repeat until you can’t anymore.

How to simplify rational expressions

Thu, 05 Nov 2026 00:00:00 +0000

A rational expression is just a fraction with polynomials on top and bottom. Simplifying one works exactly like simplifying an ordinary fraction: find what the top and bottom share, and divide it out.