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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 a positive and a negative number
Discover what it means to multiply by negative numbers by using repeated addition and using the distributive property.
Extending multiplication to more numbers
Whether we use whole numbers, fractions, or integers, multiplication still has the same meanings.
Let's explore how different properties of multiplication help us make sense of multiplication with negative numbers.
Multiplication as repeated addition
Multiplication can be a shortcut for adding equal groups of the same size. For example, we can show groups of these ways:
We can make equal groups with negative values, too.
This makes sense on a number line, too.
Starting from , taking steps of units each in the negative direction leads us to .
Multiplication with the distributive property: positive times negative
The properties of multiplication work the same with negatives as with positive numbers and . Let's use the distributive property to convince ourselves of the value of .
Describe a general pattern for when we multiply a positive number times a negative number.
Want to join the conversation?
- why am I doing this if this ant for a grade im not doing this(22 votes)
- Idk why we need to read this(17 votes)
- the fact that some of us just do these to read the comments ;)(8 votes)
- What is the product of 10(-10)?(4 votes)
- It's -100 (negative 100)
I'll explain
multiplying with numbers of different signs is just basically regular multiplication with different signs.
A positive number times a negative number is negative.
This is because as multiplication is basically repeated addition, here you are adding -10 to itself a bunch.
In other words, subtracting regularly.
Also multiplying two numbers of the same sign is positive (example -5 x -5 = 25, 5 x 5 = 25)
And it's the opposite with two numbers of different signs.
I hope I helped :)(7 votes)
- Why do we even have these articles?(2 votes)
- We have the articles so they can teach us how to do the exercises. Think of them as lessons at school.(3 votes)
- these comments got me wheezing(3 votes)
- i'm confuzzled
with this thingy(3 votes) - why is negative numbers important
?(2 votes)- Negative numbers often represent losses, things below the surface, etc. For instance, in a bank, negative numbers are used to represent withdrawals. I hope this helps!(1 vote)
- HUH- why does math have to be so hard?!(2 votes)
- This is still multiplication, you know how to do that, right? The only thing is, if one of the numbers that are multiplied is negative, then your result will be negative.
Eg.-5 * 8 = -40
7 * -6 = -42
That's all it is lol. Good luck(1 vote)
- How to remember the different negative number formulas such as negative times negative equals posative?(1 vote)
- Best way:
- Same signs => Positive
- Different signs => Negative
So,2 * 3 = 6
,-2 * 3 = -6
,2 * -3 = -6
, and-2 * -3 = 6
.
Good luck!(2 votes)