Some problems can't be solved in a single step. They're like a treasure hunt with multiple clues. You need to figure out the first part to get to the next. These are called multi-step word problems. The trick is to read carefully and look for clue words.

Let's try one. A baker makes 125 cakes every day. He sells 95 cakes and gives 5 away to charity. How many cakes does he have left after 3 days?

First, find out how many cakes are left each day. 125 cakes made - 95 cakes sold - 5 cakes given away = 25 cakes left per day.

Now, find the total for 3 days. 25 cakes/day × 3 days = 75 cakes.

See? You used subtraction first, then multiplication. You solved it one step at a time.

When you multiply big numbers, you don't need to guess. You can estimate first to get a rough idea of the answer. To estimate a product, round the numbers to their highest place value and then multiply.

For example, to estimate $4,872 × 38$:

1. Round 4,872 to the nearest thousand: 5,000
2. Round 38 to the nearest ten: 40
3. Multiply the rounded numbers: $5,000 × 40 = 200,000$.

The actual answer will be close to 200,000. This is a great way to check if your final calculation makes sense.

Now, let's do the exact calculation for $4,872 × 38$. We multiply 4,872 by 8 (the ones digit) first, then by 30 (the tens digit), and add the results.

Our estimate was 200,000, and the exact answer is 185,136. They are close, so our calculation is likely correct! Multiplication also has useful properties. For instance, $15 × 9$ is the same as $9 × 15$. The order doesn't matter.

Long division helps us divide big numbers. A simple way to remember the steps is DMSR—Divide, Multiply, Subtract, Bring Down. You repeat this cycle until you can't bring down any more numbers.

Let's divide 425 by 3.

1. Divide 4 by 3. It goes 1 time. Write 1 above the 4.
2. Multiply $1 × 3 = 3$. Write 3 below the 4.
3. Subtract $4 - 3 = 1$. Write 1 below the 3.
4. Bring Down the next digit, 2. You now have 12.

Now, repeat the cycle with 12.

1. Divide 12 by 3. It goes 4 times. Write 4 above the 2.
2. Multiply $4 × 3 = 12$. Write 12 below the 12.
3. Subtract $12 - 12 = 0$. Write 0 below.
4. Bring Down the 5. You now have 5.

Repeat again with 5.

1. Divide 5 by 3. It goes 1 time. Write 1 above the 5.
2. Multiply $1 × 3 = 3$. Write 3 below the 5.
3. Subtract $5 - 3 = 2$. Write 2 below. There are no more numbers to bring down.

The number left at the end, 2, is the remainder. So, $425 ÷ 3$ is 141 with a remainder of 2.

How can you be sure your answer is right? There's a formula for that. It's like checking your work.

Let's check our example: $425 ÷ 3 = 141$ R $2$. Here, the Dividend is 425, Divisor is 3, Quotient is 141, and Remainder is 2.

$(3 × 141) + 2 = 423 + 2 = 425$. It matches our dividend! So our division is correct.

Sometimes, you know the cost of many items and need to find the cost of just one, or a different quantity. This is where the Unitary Method comes in handy. It's a two-step process: find the value of one unit, then multiply to find the value of the units you need.

For example: If 6 notebooks cost ₹90, what is the cost of 5 notebooks?

First, find the cost of one notebook. Cost of 1 notebook = Total cost ÷ Number of notebooks ₹90 ÷ 6 = ₹15.

Now, find the cost of 5 notebooks. Cost of 5 notebooks = Cost of 1 notebook × 5 ₹15 × 5 = ₹75.

So, 5 notebooks cost ₹75.

Mastering these methods helps you solve complex problems by breaking them into smaller, manageable parts.