Positive and negative multiplication series#

So while -7 is negative seven, 7 is positive seven, or simply seven. Watch the video below to learn more about negative numbers.Īny number without a minus sign in front of it is considered to be a positive number, meaning a number that's greater than zero. Not only will I have no money in the bank-I'll actually have less than none because I owe the bank money. If I overdraw my account (take out more money than I actually have), my new bank balance will be a negative number. For instance, in finances negative numbers can be used to show debt. You can also use negative numbers for more abstract ideas. For instance, the temperature on this thermometer is -20, or twenty degrees below zero. For example, have you ever been outside on a really cold winter day when the temperature was below zero? Any temperature below zero is a negative number. However, there are instances in real life where you use numbers that are less than zero.

It's difficult to imagine having less than nothing in this case. For instance, if you have 0 pieces of chocolate left in your candy bowl, you have no candy. After all, we often think of zero as meaning nothing. It might seem a little odd to say that a number is less than 0. For instance, -7 is a number that is seven less than 0. Something similar is taking place with our multiplying a negative by a negative./en/algebra-topics/exponents/content/ What are negative numbers?Ī negative number is any number that is less than zero. However, if we really think about this, both negatives cancel out here and that sentence suggests it will in fact rain today. This is really hard to understand, but with all the work we did above multiplying positive by a positive and positives with negatives, hopefully the logic can follow.Ī contextual idea we might consider is from language where double negatives result in a positive. Using this intrinsic relationship between positive and negative values, we now head to multiplying a negative by a negative showing both a negative number of groups and negative values in those groups: Please do let me know in the comments!įrom what we’ve learned earlier, it would make sense that -2 groups of 4 also equals -8: I’m curious to hear feedback around this one to learn what the majority of students think. While this is less intuitive, leaning on our prior understanding from earlier in the video, one might argue that if we ignore the colour of the squares (i.e.: the absolute value), we recognize that the result will involve 8 squares. Then, we move onto a prompt where our squares are positive (black) and our groups are negative. We then show students the different possible products that result in -10 really focusing on driving home the idea that positive and negative values are intrinsically related and are inverse values on the number line. We note that 2 groups of (-5) is the same as 5 groups of (-2). Therefore, we want the student to identify this visual as:īy simply using the same skills developed on the adding and subtracting integers series, we can easily arrive at a simplified result of -10. Multiplying a Positive By a NegativeĪs the viewer should recall, the red squares represent negative values in our series. We also show that we can rearrange our groupings to be:Įasy stuff so far. Since I’m sure students who are multiplying integers are comfortable with multiplying 3 x 4, we give this result immediately as 12 and show it on the number line. Thus we are looking for the viewer to be able to say and possibly write: In previous videos, we represented the black squares as positive integers. Here were are trying to help the viewer “see” the 3 groups of 4 black squares. The beginning of the video prompts the viewer with this visual: See the instructional guide below aimed to help teachers and/or parents use this activity with their own students/children. The video shown at the top of the post has the entire visual progression of integer multiplication as described below in the visual prompts. YES, finally, onto multiplying negative and positive values as many have requested to date.

Positive and negative multiplication series#

Now that students have developed a solid understanding of how integers work, we will continue the series by introducing the multiplication of integers. Throughout the integer operation series, we have focused only on adding and subtracting integers. Let's extend our integer operation visuals to multiplying positive and negative values using coloured square tiles and number lines!