What are the Associative Properties of Addition and Multiplication?The associative property is one of those fundamental properties of math that make math work. You probably take this property for granted because it's so ingrained, but it's important to see how the guts of math work, so check out the tutorial and make sure you're solid on your fundamentals! Show
Addition and Subtraction with Positive and Negative NumbersThe key to knowing whether to add or subtract is to know what kind of numbers you are working with; positive or negative numbers. It is up to us to determine what we’re working with, and practicing multiple types of problems is important in becoming familiar with the different kinds of numbers. This video will review what we have covered on addition and subtraction with positive and negative numbers: Video Source (08:49 mins) | Transcript Additional Resources
Practice Problems Evaluate the following expression:
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Core Math WorksheetsFraction WorksheetsWord ProblemsOther WorksheetsMeasurement & ConversionsPatterns and PuzzlesColor by NumberHoliday & SeasonalEarly LearningPrintablesCalculatorsMath Worksheets by GradeWorksheet NewsWorksheets for adding negative numbers and subtracting negative numbers. Negative Numbers: Addition and Subtraction 1Negative Numbers: Addition and Subtraction 2Negative Numbers: Addition and Subtraction 3Negative Numbers: Three Terms: Addition and Subtraction 4Negative Numbers: Three Terms: Addition and Subtraction 5Negative Numbers: Four Terms: Addition and Subtraction 6Negative Numbers: Four Terms: Addition and Subtraction 7Negative Numbers: Order of Operations Parentheses: Addition and Subtraction 8Negative Numbers: Order of Operations Parentheses: Addition and Subtraction 9Tricks for Adding and Subtracting Negative NumbersAdding and subtracting numbers can be confusing at first because the idea of a negative quantity of something can be a strange concept, even to a 6th grader. Instead, introduce the concept of negative numbers using measurements that might convincingly have negative results. A good example is temperature, where values can fall below zero (This is especially good if Celcius temperatures are understood as zero has a very clear meaning there.) Another good choice would be altitude above or below sea level. Working with a number line is another great strategy for visualizing how subtracting can create negative integers in a more abstract context. Keeping Track of the SignsPart of the challenge with adding and subtracting negative numbers is figuring out what to do with the signs. We learn our subtraction facts and become conditioned to that minus symbol immediately meaning to take the second number away from the right. With negative numbers, this is often wrong. Here are the rules for adding or subtracting negative numbers:
Normally, of course, we don’t show the signs on positive numbers, so two of the rules above look just like standard addition and subtraction! The other two rules are the key ones to remember for combining negative numbers… Subtracting a negative value is the same as addition, and adding a negative is the same as subtraction. If students can keep these two new twists in mind, addition and subtraction with negative numbers will be a breeze! Video transcriptLet's have some practice adding and subtracting negative numbers. So the first example I want to look at is 2 minus 3. So right now I'm just subtracting a positive number from another positive number, but you might already see that I'm subtracting a larger number from a smaller number. So I'm probably, or I will, definitely end up with a negative number. But let's just think about this a little bit. And I'm going to do it with a number line. So there's my number line right over there. Now this is 0, this is 1, this is 2, this is negative 1, this is negative 2. We could view this as starting at 2. So this is 2 right over here, and then we're going to subtract 3 from that 2. So we're going to move 3 to the left on the number line. So we're going to move 3 to the left, 1, 2, 3. And that gets us to negative 1. This is equal to negative 1. Now let's mix it up a little bit more. Let's imagine what would happen if we had negative 2 minus 3. So this was positive 2 minus 3. Now let's think about negative 2 minus 3. So once again, let's draw our number line. And I'll put 0 over here. So this is 0, this is 1, this is negative 1, negative 2, negative 3, negative 4, negative 5, negative 6, and I could keep going. But we're starting at negative 2, and then we're subtracting 3 again. So once again, we're going to move three to the left of negative 2. So we go 1, 2, 3. We end up at negative 5. So this is negative 5. So notice in both situations we subtracted 3, we moved 3 to the left on the number line. It's just here we started 2 to the right of 0. Here we started 2 to the left of 0. This is negative 2. Let's do another example with these same numbers. Let's imagine negative 2 plus 3. I encourage you to pause this video, and try to think about this on your own. So we could draw the number line-- I could draw a straighter number line than that-- so draw the number line again. And let's say that this is negative 2, negative 1, 0, 1, and 2 again. We're starting at negative 2, we're starting 2 to the left of zero. So we're starting at negative 2, and we're going to add 3. So we're going to go 3 to the right now, 1, 2, 3, and we end up at positive 1. Now let's think about 2, so positive 2, and we're going to subtract a negative 3. And other videos we've already talked about this. In fact, there's a video explaining why this actually makes sense. But when you subtract a negative, this is the same thing as adding the positive. So 2 minus negative 3 is the exact same thing as 2 plus 2 plus positive 3. These two statements are equivalent, and this just boils down to, this right over here, is just going to be 5. Now, let's mix it up a little bit more. Let's imagine negative 2 minus negative 3. Now, this might seem really intimidating to have all of these negatives in place here, but you just have to remember subtracting a negative, like this, is going to get you a positive. So this is the exact same thing as negative 2 plus 3, and negative 2 plus 3, we've already seen it right over here. You start at negative 2, you start 2 to the left of 0, and then we're going to go 3 to the right, we're adding 3, 1, 2, 3. How do you add negative and positive numbers?To get the sum of a negative and a positive number, use the sign of the larger number and subtract. For example: (–7) + 4 = –3. 6 + (–9) = –3.
What are the rules for positive and negative numbers?The Rules:. What are the two rules for adding positive and negative numbers?Adding Positive and Negative Numbers. Rule 1: Adding positive numbers to positive numbers—it's just normal addition.. Rule 2: Adding positive numbers to negative numbers—count forward the amount you're adding.. Rule 3: Adding negative numbers to positive numbers—count backwards, as if you were subtracting.. |
Addition and subtraction of positive and negative numbers
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