Integers & Negatives
Operations with negative numbers and integer properties
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Have you ever owed your friend money for a slice of pizza? Or played a video game where your score dropped below zero? Welcome to the wild world of negative numbers! 🍕🎮 Integers are just whole numbers (no fractions or decimals allowed), but they have a secret alter ego: negatives. Think of a number line like a giant tug-of-war. Zero is the referee standing right in the middle. Positive numbers pull to the right, and negative numbers pull to the left. If you have 5 dollars in your piggy bank and want to buy a cool toy for 8 dollars, you don't just have zero dollars—you actually owe 3 dollars. In math language, we write that as . 🏦 On the SSAT, test-makers love to see how well you can juggle these positive and negative numbers. Adding a negative is just like taking away points in a video game. But subtracting a negative? That’s like a referee taking away a penalty—it actually gives you points back! 🚀 So, whenever you see two minus signs right next to each other, simply smash them together to make a giant plus sign. Master these simple rules, and you'll be an integer ninja ready to crush the math section!
Practice Questions
3 practice questions for SSAT Middle Level
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- According to the order of operations (PEMDAS), multiplication must be performed before subtraction. First, multiply and : . Next, substitute this back into the expression: . Subtracting a negative number is the same as adding a positive number, so this becomes , which equals .
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- First, find the temperature at noon by adding the temperature rise to the morning temperature: . Next, subtract the evening temperature drop from the noon temperature: . The temperature at 8:00 PM was .
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- By the order of operations, perform division and multiplication before addition. First, divide: . Next, multiply: (remember that multiplying two negative numbers results in a positive number). Finally, add the two results together: .
Tips & Strategies
- Draw a quick number line on your scratch paper! It helps you physically count hops left and right so you don't get your positive and negative directions mixed up.
- Think of money! If a problem has lots of plus and minus signs, pretend you are earning and spending dollars. It makes the math feel much more real and easier to solve.
Common Mistakes
- Watch out for the 'double minus' trap! When you see , don't subtract. Taking away a negative penalty is a good thing, so it becomes a plus: .
- Don't confuse the rules for adding and multiplying! Adding two negatives makes a bigger negative (), but multiplying two negatives makes a positive ().
Frequently Asked Questions
Do I need to memorize the rules for negative numbers for the SSAT?
Yes! Knowing that 'a negative times a negative is a positive' will save you tons of time. You will see these concepts all over the test.
What exactly is an integer? Are fractions integers?
Integers are only whole numbers and their negatives (like , , and ). Fractions like and decimals are NOT integers!
Is zero positive or negative?
Zero is the referee of the number line—it is neither positive nor negative! It's just a neutral integer.
How many negative number questions are on the SSAT?
You'll see them everywhere! They don't just appear in basic arithmetic; they pop up in algebra and word problems too, making them super important to master.