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Course: 7th grade (Eureka Math/EngageNY) > Unit 2
Lesson 2: Topic B: Multiplication and division of integers and rational numbers- Multiplying a positive and a negative number
- Multiplying two negative numbers
- Why a negative times a negative is a positive
- Why a negative times a negative makes sense
- Signs of expressions
- Multiplying positive & negative numbers
- Dividing positive and negative numbers
- Multiplying negative numbers
- Dividing negative numbers
- One-step equations with negatives (multiply & divide)
- Multiplying negative numbers review
- Dividing negative numbers review
- Rewriting decimals as fractions: 2.75
- Write decimals as fractions
- Rewriting decimals as fractions challenge
- Fraction to decimal: 11/25
- Worked example: Converting a fraction (7/8) to a decimal
- Fraction to decimal with rounding
- Converting fractions to decimals
- Multiplying positive and negative fractions
- Multiplying positive and negative fractions
- Dividing negative fractions
- Dividing positive and negative fractions
- Negative signs in fractions
- Negative signs in fractions
- Negative signs in fractions (with variables)
- Dividing mixed numbers
- Dividing mixed numbers with negatives
- Simplifying complex fractions
- Expressions with rational numbers
- Simplify complex fractions
- Equivalent expressions with negative numbers (multiplication and division)
- Equivalent expressions with negative numbers (multiplication and division)
- Why dividing by zero is undefined
- Dividing by zero
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Multiplying two negative numbers
If 3(-8) can be 3 equal groups of -8, what does -3(-8) mean? What does it mean to multiply any two negative numbers? Let's use the distributive property and other properties of multiplication to find out.
When we multiply a positive number times a negative number, the product is the opposite of the product of the absolute values of the numbers. This means the result is always negative.
But what about when we multiply a negative number times a negative number?
Let’s explore this idea using three different methods, starting with the distributive property.
Multiplication with the distributive property: negative times negative
The distributive property works the same with negative numbers as with positive numbers and . Let's use it to see what happens when we multiply two negative numbers, starting with the example .
Before we do, make a prediction.
What do you predict will be the value of ?
This is an ungraded prediction, because we learn more when we make a guess before we get feedback.
This is an ungraded prediction, because we learn more when we make a guess before we get feedback.
Now let's use the zero-product property and the distributive property to reason about the product.
Multiplication by a negative as repeated subtraction from
Number lines
As a general trend, the symbol " " changes the direction we move on a number line, whether we interpret it as a negative sign or a subtraction symbol.
Equal groups of objects
We represent multiplying by a positive number by adding equal groups of objects. We represent multiplying by a negative number by subtracting equal groups of objects.
So is the value we have left after we take away groups of objects. But how do we subtract groups of objects when we don't have any?
We can start with zero-pairs. The following diagram represents because there are positive integer chips and negative integer chips.
Now we can take away groups of .
Conclusion
Now that we have explored multiplying a negative number times a negative number using three different methods, what conclusions can we draw?
Describe a general pattern for when we multiply two negative numbers.
Want to join the conversation?
- Yes I indeed have a question. I get confused on diving the pairs and finding the answer. I need a breakdown on how to do it. Please and thankyou.(2 votes)
- When you divide a negative number by another negative number the answer is positive. -54/-6 = -9
When you divide a positive number by another positive number the answer is positive. 54/6 = 9
When you divide a positive number by a negative number the answer is negative. 54/-6 = -9
When you divide a negative number by a positive number the answer is negative. -54/6 = -9
Hope this helps!
(pls vote up)(3 votes)
- In short: If two signs are the same, the result will be always positive. In contrast, if the two signs are different, the result will be always negative. This way you only have to multiply the numbers as you'd normally do (without taking in account the sign) and then prefix the sign to the result as same as i exposed before.(2 votes)
- I understand this much more than his videos, this is only grade 7 math but kinda thanks for teacher Sal( did I get his name right)(2 votes)
- yeah his name is Sal Khan.(0 votes)
- Normally, whenever two negative numbers decide to meet, the two negatives (- times -) decide to mash together to make a (+)
One negative stays same while the other turns side ways .(1 vote) - Hi, My Name is Moses kaufman(1 vote)
- yes it is Moses Kaufman(1 vote)
- Find the answer for -3(-5)(0 votes)
- how do i do the communitive property ones?(0 votes)
- when you multiply two negative #sthe product will come out as positive. For example, -2(-45) will be 90(0 votes)
- -2(-45) means -(-45 + -45) = -(-90).
Let's think about it using debt. Debt would be 'negative money', so -3 is $3 in debt. If we had negative debt, that would be 'negative negative money' as if you're taking away your debt, so you'd have more money. So, -(-90) is like taking $90 away from your debt, so you'd have $90 more!
This is one reason why it equals 90.
Hope this helped.(0 votes)