📐 Math Help Center

Learn how to solve common math problems step-by-step

➕ Basic Operations

Addition

Addition is combining two or more numbers to find their total or sum.

a + b = c

Example: 23 + 45

Line up the numbers by place value (ones under ones, tens under tens)

Add the ones column: 3 + 5 = 8

Add the tens column: 2 + 4 = 6

Answer: 68

When adding large numbers, start from the rightmost digit (ones place) and work left. If a column adds up to 10 or more, carry the extra to the next column.

Subtraction

Subtraction is taking one number away from another to find the difference.

a - b = c

Example: 85 - 37

Line up the numbers by place value

Subtract the ones: 5 - 7 can't be done, so borrow from tens

Make 15 - 7 = 8 in the ones place

Subtract the tens: 7 - 3 = 4 (after borrowing)

Answer: 48

If you can't subtract because the top number is smaller, "borrow" 10 from the next column to the left.

Multiplication

Multiplication is repeated addition or combining equal groups.

a × b = c

Example: 12 × 8

Break it down: 12 × 8 = (10 × 8) + (2 × 8)

10 × 8 = 80

2 × 8 = 16

80 + 16 = 96

Answer: 96

Memorize times tables up to 12 × 12. For larger numbers, break them into smaller parts or use the distributive property.

Division

Division is splitting a number into equal parts or finding how many times one number fits into another.

a ÷ b = c

Example: 144 ÷ 12

How many 12s fit into 144?

Try 10: 12 × 10 = 120 (too small)

Try 12: 12 × 12 = 144 (perfect!)

Answer: 12

Division is the opposite of multiplication. If you know 12 × 12 = 144, then 144 ÷ 12 = 12.

🔢 Solving for x (Simple Equations)

One-Step Equations

To solve for x, you need to get x by itself on one side of the equation. Do the opposite operation to both sides.

Example 1: x + 5 = 12

We need to remove the +5 from the left side

Subtract 5 from both sides: x + 5 - 5 = 12 - 5

Simplify: x = 7

Check: 7 + 5 = 12 ✓

Example 2: x - 8 = 15

We need to remove the -8 from the left side

Add 8 to both sides: x - 8 + 8 = 15 + 8

Simplify: x = 23

Check: 23 - 8 = 15 ✓

Example 3: 3x = 21

x is being multiplied by 3

Divide both sides by 3: 3x ÷ 3 = 21 ÷ 3

Simplify: x = 7

Check: 3 × 7 = 21 ✓

Example 4: x/4 = 6

x is being divided by 4

Multiply both sides by 4: (x/4) × 4 = 6 × 4

Simplify: x = 24

Check: 24 ÷ 4 = 6 ✓

Remember: Whatever you do to one side of the equation, you MUST do to the other side!

Two-Step (Multi-Step) Equations

These equations require more than one operation to solve. Use the order of operations in reverse: undo addition/subtraction first, then multiplication/division.

Example 1: 2x + 5 = 13

Step 1: Remove the +5 by subtracting 5 from both sides

2x + 5 - 5 = 13 - 5

2x = 8

Step 2: Remove the ×2 by dividing both sides by 2

2x ÷ 2 = 8 ÷ 2

x = 4

Check: 2(4) + 5 = 8 + 5 = 13 ✓

Example 2: 3x - 7 = 20

Step 1: Remove the -7 by adding 7 to both sides

3x - 7 + 7 = 20 + 7

3x = 27

Step 2: Divide both sides by 3

3x ÷ 3 = 27 ÷ 3

x = 9

Check: 3(9) - 7 = 27 - 7 = 20 ✓

Example 3: (x/2) + 3 = 8

Step 1: Subtract 3 from both sides

(x/2) + 3 - 3 = 8 - 3

x/2 = 5

Step 2: Multiply both sides by 2

(x/2) × 2 = 5 × 2

x = 10

Check: (10/2) + 3 = 5 + 3 = 8 ✓

Example 4: 5x + 3 - 2x = 18

Step 1: Combine like terms (5x - 2x = 3x)

3x + 3 = 18

Step 2: Subtract 3 from both sides

3x = 15

Step 3: Divide both sides by 3

x = 5

Check: 5(5) + 3 - 2(5) = 25 + 3 - 10 = 18 ✓

For multi-step equations: 1) Simplify both sides if needed, 2) Undo addition/subtraction, 3) Undo multiplication/division, 4) Always check your answer!

🎯 Practice Problems (Try These!)

1. x + 12 = 25 (Answer: x = 13)

2. 4x = 32 (Answer: x = 8)

3. 2x + 7 = 19 (Answer: x = 6)

4. 3x - 5 = 16 (Answer: x = 7)

5. (x/3) + 4 = 9 (Answer: x = 15)