Solve Division Problem: 3,000 Books ÷ 120 Libraries Distribution

Q: How do I know which number to divide by which?

Remember the pattern: Total ÷ Groups = Amount per group. Since we want books per library, divide total books (3,000) by number of libraries (120).

Q: Can I simplify 3000 ÷ 120 before calculating?

Yes! Both numbers end in zero, so you can cancel: $ 3000 ÷ 120 = 300 ÷ 12 = 25 $. This makes the math easier.

Q: How do I check if 25 is the right answer?

Multiply your answer by the number of libraries: $ 25 \times 120 = 3000 $. If you get back to the original total, you're correct!

Q: Why can't the answer be 41 or 36?

Test them! $ 41 \times 120 = 4920 $ (too many books) and $ 36 \times 120 = 4320 $ (still too many). Only 25 gives exactly 3000 books.

Division Problems with Large Numbers

A government purchases 3,000 mathematics books and distributes them to 120 libraries.

How many books does each library receive?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:04 Let's start by dividing the leftmost digit by the divisor

00:08 3 is less than 120, so we'll add the next digit, and then divide

00:12 30 is also less than 120, so we'll add the next digit, and then divide

00:18 Write the result without the remainder above, paying attention to the position

00:22 Now multiply the result by the divisor

00:25 Subtract the product from the number

00:30 Now bring down the next digit and use the same steps

00:34 Divide

00:37 Write the result without the remainder above, paying attention to the position

00:41 Multiply the result and subtract

00:46 We got a remainder of 0

00:50 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A government purchases 3,000 mathematics books and distributes them to 120 libraries.

How many books does each library receive?

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Apply the division formula.
Step 3: Perform the division calculation.

Now, let's work through each step:
Step 1: The problem gives us the total number of books, $3,000$ , and the number of libraries, $120$ .
Step 2: We'll use the formula: $\text{Books per library} = \frac{3000}{120}$ .
Step 3: Perform the calculation: $3000 \div 120 = 25$ .

Therefore, the solution to the problem is $25$ , which means each library receives 25 books.

Final Answer

$25$

Key Points to Remember

Essential concepts to master this topic

Formula: Books per library equals total books divided by libraries
Technique: Calculate $3000 \div 120 = 25$ using long division
Check: Multiply answer back: $25 \times 120 = 3000$ ✓

Common Mistakes

Avoid these frequent errors

Confusing which number goes first in division
Don't divide 120 by 3,000 = 0.04 books per library! This gives an impossible fractional result. Always divide the total amount by the number of groups: total books ÷ number of libraries.

Practice Quiz

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FAQ

Everything you need to know about this question

How do I know which number to divide by which?

Remember the pattern: Total ÷ Groups = Amount per group. Since we want books per library, divide total books (3,000) by number of libraries (120).

What if the division doesn't come out evenly?

In real-world problems like this, you might get a remainder. This could mean some libraries get one extra book, or books are distributed as evenly as possible with some left over.

Can I simplify 3000 ÷ 120 before calculating?

Yes! Both numbers end in zero, so you can cancel: $3000 ÷ 120 = 300 ÷ 12 = 25$ . This makes the math easier.

How do I check if 25 is the right answer?

Multiply your answer by the number of libraries: $25 \times 120 = 3000$ . If you get back to the original total, you're correct!

Why can't the answer be 41 or 36?

Test them! $41 \times 120 = 4920$ (too many books) and $36 \times 120 = 4320$ (still too many). Only 25 gives exactly 3000 books.

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