How to multiply, divide, subtract and add

Think of these basic operations like tools in your math toolbox. Each one has its own job, and with a little practice, you can use them like a pro. So, let’s dive in and get comfortable with adding, subtracting, multiplying, and dividing—even when they look a bit bigger and scarier!

Adding and Subtracting: The Basics

Adding and subtracting numbers is like putting pieces together or taking them apart. When the numbers get bigger, we just have to be careful about lining them up—no magic tricks, just careful steps.

Addition – Bringing Numbers Together

When we add, we’re combining numbers to find a total. It’s like stacking blocks to see how tall a tower you can make!

1. Line up the digits by place value (units under units, tens under tens).
2. Start from the right and add each column.
3. If you end up with more than 9 in a column, carry over the extra to the next column.

Example: Add $456 + 378$ 

$$\begin{array}{r} 456 \\ + 378 \\ \hline 834 \\ \end{array}$$

• First, add the units:  $6 + 8 = 14$   $\rightarrow$  Write down 4 and carry over  1.
• Next, add the tens: $5 + 7 = 12$ , and add that carry-over 1 to make 13 $\rightarrow$ Write down 3 and carry over 1.
• Finally, add the hundreds:  $4 + 3 = 7$  , and add that carry-over 1  to get  8 .

The answer is:

$$834$$

Subtraction – Taking Numbers Apart

Subtracting is all about taking away. Imagine you have a pile of sweets, and you’re sharing some with a friend—subtraction helps you figure out what’s left!

1. Line up the digits by place value.
2. Start from the right and subtract each column. If you can’t, then it’s time to borrow from the next column.

Example: Subtract $532 - 175$

$$\begin{array}{r} 532 \\ - 175 \\ \hline 357 \\ \end{array}$$

• In the units column, $2 − 5$ can’t be done, so borrow from the tens. Now it’s $12 − 5 = 7$.
• In the tens, we’ve borrowed, so it’s now  $2−7$ (again can’t do it). Borrow from the hundreds, making it $12 − 7 = 5$.
• Finally, in the hundreds, $4 − 1 = 3$.

So, the answer is:

$$357$$

Multiplication: Building Bigger Numbers

Multiplying numbers is like making copies. If you have $3 \times 4$, you’re finding out what 4 groups of 3 look like all together. Here’s how it works when the numbers are bigger.

Long Multiplication – Taking It Step by Step

Long multiplication breaks it down. You multiply each digit by each other digit, one at a time, and then add it all up at the end.

Example: Multiply $237 \times 56$

Let’s walk through it:

$$\begin{array}{r} &   & 237 \\ & \times & 56 \\ \hline &   & 1422 \\ +  &   & 11850 \\ \hline &   & 13272 \\ \end{array}$$

• First, multiply $237 \times 6=1422$.
• Next, multiply $237 \times 5=1185$, but shift one place to the left (since it’s in the tens place).
• Add both rows to get the answer.

So, the answer is:

$$13272$$

Grid Method – Breaking It Down by Place Value

The grid method is like a puzzle: you break the numbers into parts, multiply each part, and then put it all back together.

Example: Multiply $43 \times 27$

Let’s set it up like a grid:

$$\begin{array}{c|c|c} & 40 & 3 \\ \hline 20 & 800 & 60 \\ \hline 7 & 280 & 21 \\ \end{array}$$

• Multiply each box, then add everything up: $800+60+280+21=1161$.

$$1161$$

Scenario Problem

Try applying your division knowledge to this scenario based problem

Division: Breaking Things Down Evenly

Division helps you split numbers into equal parts. It’s like sharing out sweets so everyone gets the same amount.

Long Division – Splitting It Up

Long division helps when you’re working with bigger numbers. We break it down bit by bit.

Example: Divide $742 \div 3$

• Start with 3 into 7, which goes 2 times. Write 2 above.
  • Multiply: $2 \times 3=6$, then subtract: 7−6=1.
• Bring down the 4 to make 14.
  • 3 into 14 goes 4 times. Write 4 above.
  • Multiply: $4 \times 3=12$, then subtract: 14−12=2.
• Bring down the 2 to make 22.
  • 3 into 22 goes 7 times, with a remainder of 1.

The answer is: $$247 \, \text{remainder} \, 1$$