ISEE Middle Level

Basic Operations

Q: What if I completely forget my times tables during the test?

Take a deep breath! If you forget what `7 \cdot 8` is, just use what you know. You probably know `7 \cdot 10 = 70`. Just subtract 7 twice (`70 - 14 = 56`). You can always build up to the answer!

Addition, subtraction, multiplication, and division of whole numbers — excludes fractions (see fraction-operations) and decimals (see decimal-operations)

Generate Unlimited Practice Questions

Start Free Practice

Learn This Topic

Welcome to the foundation of all math! Imagine you're running the ultimate video game empire. 🎮 Basic operations are the tools you use to manage your virtual world. Addition is like collecting gold coins, and subtraction is when you spend those coins on epic upgrades. Multiplication is your awesome power-up multiplier (like getting 5 coins at once instead of 1!), and division is how you share the loot fairly with your gaming squad. 🏆

On the ISEE, you'll see two different math sections. The Mathematics Achievement section will test your raw calculation skills—can you add, subtract, multiply, and divide carefully without making silly mistakes? Then, the Quantitative Reasoning section might ask you to be a math detective. Instead of just solving a huge math problem, you might have to compare two columns (Column A and Column B) to see which one is bigger. 🕵️‍♂️

The trick is that you don't always have to do all the math! Sometimes, a quick estimation or looking at the numbers closely saves you tons of time. Remember, the ISEE does not penalize you for guessing. So if you're ever stuck on a super long division problem and time is running out, take your best guess and keep playing the game!

Key Formula

Inverse operations undo each other! To solve for a missing number: if

a + b = c

, then

a = c - b

. If

a \cdot b = c

, then

a = \frac{c}{b}

Practice Questions

3 practice questions for ISEE Middle Level

Q1 Medium

What is the value of

10, 042 - 3, 875

A 6,167

B 6,177

C 6,267

D 7,167

Show Solution

To find the difference, line up the numbers by their place value and subtract, borrowing as necessary:
1. In the ones column: $2 - 5$ requires borrowing. Borrow from the tens column (4 becomes 3, 2 becomes 12). $12 - 5 = 7$ .
2. In the tens column: $3 - 7$ requires borrowing. Borrow across the zeros from the ten-thousands column. The 100 becomes 99, and the 3 becomes 13. $13 - 7 = 6$ .
3. In the hundreds column: $9 - 8 = 1$ .
4. In the thousands column: $9 - 3 = 6$ .

The final difference is $6, 167$ .

Answer: A

Q2 Medium

What is the product of

415

and

28

A 4,150

B 10,620

C 11,520

D 11,620

Show Solution

To find the product, multiply $415$ by $28$ using the standard algorithm.

First, multiply by the ones digit (8):
$415 \times 8 = 3, 320$
Next, multiply by the tens digit (2), which represents 20, so place a zero at the end:
$415 \times 20 = 8, 300$
Finally, add the two partial products together:
$3, 320 + 8, 300 = 11, 620$ .

Answer: D

Q3 Medium

A school library has

3, 402

books. The librarian wants to distribute them equally onto

14

empty bookshelves. How many books will be placed on each bookshelf?

A 234

B 243

C 253

D 263

Show Solution

To find the number of books on each shelf, divide the total number of books by the number of shelves: $3, 402 \div 14$ .
1. $14$ goes into $34$ two times ( $14 \times 2 = 28$ ), with a remainder of $6$ .
2. Bring down the $0$ to make $60$ . $14$ goes into $60$ four times ( $14 \times 4 = 56$ ), with a remainder of $4$ .
3. Bring down the $2$ to make $42$ . $14$ goes into $42$ exactly three times ( $14 \times 3 = 42$ ).

The quotient is $243$ , meaning there will be 243 books on each bookshelf.

Answer: B

Tips & Strategies

Use estimation to check your answers! If you are multiplying $48 \cdot 11$ , think 'That's close to $50 \cdot 10$ , which is 500.' If your answer is 5,280, you know you made a mistake!
On Quantitative Comparison questions, you don't always have to do the full math. If Column A is $100 \cdot 5$ and Column B is $99 \cdot 4$ , you can easily see Column A has bigger numbers being multiplied, so it must be larger!
The ISEE has NO guessing penalty! If you get stuck on a really long division problem, don't waste 5 minutes on it. Eliminate the crazy answers, take your best guess, and move on.

Common Mistakes

Watch out for sloppy handwriting! When adding or subtracting big numbers, make sure you line up your ones, tens, and hundreds columns perfectly. If they get crooked, you'll add the wrong numbers together.
Don't forget to write down your 'carries' in addition and 'borrows' in subtraction. Trying to hold those numbers in your head is a fast track to choosing a trick answer!

Frequently Asked Questions

Do I get a calculator on the ISEE?

No calculators allowed! 🚫 You'll need to do all the addition, subtraction, multiplication, and division on your scratch paper.

What if I completely forget my times tables during the test?

Take a deep breath! If you forget what $7 \cdot 8$ is, just use what you know. You probably know $7 \cdot 10 = 70$ . Just subtract 7 twice ( $70 - 14 = 56$ ). You can always build up to the answer!

Should I double-check my math on every single question?

Only if you have extra time at the end! The ISEE is timed, so it's better to work carefully the first time and keep moving. If you finish a section early, then go back and check your work.

What is a Quantitative Comparison question?

It's a special puzzle on the ISEE Quantitative Reasoning section! You get two columns (A and B) and have to decide which side is bigger, if they are equal, or if it's a mystery (Cannot be determined). 🕵️‍♀️

Generate Unlimited Practice Questions

Learn This Topic

Practice Questions

Tips & Strategies

Common Mistakes

Frequently Asked Questions

Related Topics

More Arithmetic & Number Sense

Other Levels

Browse

Generate Unlimited Practice Questions