Integers & Negatives
Operations with negative numbers and integer properties
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Imagine you are playing your favorite video game. 🎮 You grab a lucky coin and gain 10 points! But then, oh no, you touch a spike and lose 15 points. How many points do you have now? You have -5 points! Welcome to the world of integers and negative numbers.
Integers are just whole numbers, but they can be positive (like having points or money), negative (like losing points or owing money), or exactly zero. On the ISEE, you will see a lot of questions asking you to add, subtract, multiply, or divide these numbers. The great news is that integers follow very strict rules, so once you learn the "cheat codes," these questions become super easy points on test day! 🚀
When adding and subtracting, think of a number line or a piggy bank. If you are at and add , you just hop 5 spaces to the right to land on . Multiplying and dividing has an even cooler trick: if the two numbers have the same sign, the answer is positive. If they have different signs, the answer is negative! It is like a secret code. Master this code, and you will totally crush the Quantitative Reasoning and Mathematics Achievement sections of the ISEE! 🌟
Practice Questions
4 practice questions for ISEE Lower Level
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- When adding two negative numbers, you add their absolute values and keep the negative sign. So, first add the absolute values: . Since both numbers are negative, the sum is negative. Therefore, .
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- The starting temperature was degrees Celsius. A drop of degrees means we subtract from the initial temperature. So, the calculation is .
Think of a number line: starting at and moving units to the left (because it's a drop/subtraction) brings you to .
Therefore, the temperature on Tuesday morning was degrees Celsius.
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- Subtracting a negative number is the same as adding its positive counterpart. The expression can be rewritten as . Adding these numbers gives .
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- A depth of feet below sea level can be represented as feet. When the submarine rises feet, we add to its current position. So, the calculation is .
To add a negative number and a positive number, you subtract their absolute values and use the sign of the number with the larger absolute value.
.
Since (the negative number in the original sum) has a larger absolute value than (the positive number), the result will be negative.
So, feet. This means the new depth is feet below sea level.
Tips & Strategies
- For Quantitative Comparison questions, quickly check the signs before doing the math! If Column A turns out to be positive and Column B turns out to be negative, you don't even need to calculate the exact numbers to know Column A is bigger.
- When you see minus a negative, like , turn those two minus signs into one giant plus sign: .
- If a question involves a negative fraction, remember that is the exact same thing as or . The negative sign can float to the top, bottom, or middle!
Common Mistakes
- Watch out for multiplying three negative numbers! Two negatives make a positive, but that third negative turns the whole answer negative again. For example, .
- Don't confuse adding negatives with multiplying negatives. is (you just owe more money), but is positive .
Frequently Asked Questions
Is zero a positive or negative number?
Zero is completely neutral! It is neither positive nor negative. It sits right in the exact middle of the number line.
How do I easily remember the rules for adding and subtracting?
Think of money! Positive numbers are money you have in your pocket, and negative numbers are money you owe a friend. If you have $5 but owe $8 (which is ), you still owe $3, so the answer is .
Are there a lot of negative numbers on the ISEE?
Yes! The ISEE loves testing integers in both the Quantitative Reasoning and Mathematics Achievement sections. It's one of their favorite ways to test your attention to detail.
What if I get confused during the test?
Draw a quick number line on your scratch paper! It only takes a few seconds and gives you a great visual way to see if you are moving left (getting smaller) or right (getting bigger).