Calculating average velocity or speed | One-dimensional motion | Physics | Khan Academy Khan Academy Khan Academy

Example of calculating speed and velocity. Created by Sal Khan. Watch the next lesson:
https://www.khanacademy.org/science/p... Missed the previous lesson?
https://www.khanacademy.org/science/p... Physics on Khan Academy: Physics is the study of the
basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry. About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

Intro to vectors & scalars | One-dimensional motion | Physics | Khan Academy

Distance, displacement, speed and velocity. Difference between vectors and scalars. Created by Sal Khan.

Watch the next lesson: https://www.khanacademy.org/science/p...

Missed the previous lesson? https://www.khanacademy.org/science/p...

Physics on Khan Academy: Physics is the study of the basic principles that govern the physical world around us. We'll start by looking at motion itself. Then, we'll learn about forces, momentum, energy, and other concepts in lots of different physical situations. To get the most out of physics, you'll need a solid understanding of algebra and a basic understanding of trigonometry.

About Khan Academy: Khan Academy offers practice exercises, instructional videos, and a personalized learning dashboard that empower learners to study at their own pace in and outside of the classroom. We tackle math, science, computer programming, history, art history, economics, and more. Our math missions guide learners from kindergarten to calculus using state-of-the-art, adaptive technology that identifies strengths and learning gaps. We've also partnered with institutions like NASA, The Museum of Modern Art, The California Academy of Sciences, and MIT to offer specialized content.

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Basic Mathematics - Stacked Multiplication Problems

When you multiply a number or amount, you're increasing it many times. In the last lesson, you learned that multiplication can be a way to understand things that happen in real life. For instance, imagine that a store sells boxes of pears. The small boxes contain five pears each. You buy two. You could write the situation like this, and use the times table to solve it:

Now, imagine that you decide to buy two larger boxes containing 14 pears each. That situation would look like this:

This problem is harder to solve. Counting the pears would take a while. Plus, there's no 14 on the times table. Fortunately, there's a way to write the problem so that you can break it into smaller pieces. It's called stacking. It means that we'll write the numbers on top of one another instead of side by side.

Basic Mathematics - Multiplication

What is Multiplication?

When you multiply, you're increasing a number over and over again. Basically, multiplication is adding something more than once. For instance, if you eat 4 pieces of candy, then you eat another 4, then 4 more, you can say that you multiplied the amount of candy you ate.

Multiplication happens all the time in real life. For example, consider the situation below.

Imagine that you buy a 6-pack of soda. You have 1 set of 6 cans.




Writing Multiplication Expressions

As you just saw, a multiplication expression is written like this:

2 x 6

You can read that expression as two times six. The multiplication symbol (x) can also be called the times symbol. Remember, you always put it between the numbers you want to multiply.

Many real-life situations can be expressed with multiplication. For instance, imagine that you want to make three cakes. The recipe says that each cake will need two eggs. In other words, you need 3 x 2 eggs.

Basic Mathematics - Subtracting Larger Numbers

In Lesson 3, we learned that counting and using visuals can be useful for solving basic subtraction problems. For instance, say you have 9 apples and you use 6 to make a pie. To find out how many apples are left, you could represent the situation like this:

It's easy to count and see that 3 apples are left.

What if you need to solve a subtraction problem that starts with a large number? For instance, let's say instead of making an apple pie, you want to pick apples from an apple tree. The tree has 30 apples and you pick 21. We could write this as 30 - 21.

You might see why counting to solve this problem isn't a good idea. When you have a subtraction problem that starts with a large number, it could take a long time to set up the problem. Imagine the time it would take to count out 30 objects and then take away 21! Also, it would be easy to lose track as you counted. You could end up with the wrong answer.

For this reason, when people solve a subtraction problem with large numbers, they set up the problem in a way that makes it easy to solve one step at a time. Let's see how this works with another problem: 79 - 13.

In the last lesson, we learned how to write expressions. However, subtracting with larger numbers is easier when the expressions are written in a different way.

We can see that 79 - 13 and  mean the same thing — they're just written differently.

Basic Mathematics - Substraction

Subtraction is taking things away. When you have an amount and you subtract from it, the amount becomes smaller. Subtraction happens a lot in real life.


For instance, imagine we have 8 eggs...

As we saw, if you have 8 eggs and subtract 3 of them, you'll have 5 eggs left. In other words:

8 - 3 = 5

8 - 3 = 5 is a mathematical expression. You could read it like this: five minus three equals two. As we learned in Lesson 1, a mathematical expression is basically a math sentence that uses numbers and symbols. When we write a subtraction expression, we use two symbols: - and =.

The minus sign (-) means one thing is being subtracted from another. This is why we put it after the first group of eggs — we had 8 eggs and subtracted 5 of them.



The Equals Sign

The other symbol in our expression is the equals sign (=). As we learned in Lesson 1, the equals sign means two numbers or expressions are equivalent, or equal. Even though they might look different, they mean the same thing.

In our eggs example, since 3 eggs were left, we wrote 3 to the right of the equals sign. That shows each side means 3. 3 eggs on the left, and the number 3 on the right. Both sides are equal.

Basic Mathematics - Adding Larger Numbers

As we saw in Lesson 1, you can often use counting and visuals to solve basic addition problems. For instance, imagine that 3 people are going on a trip and 2 more decided to join. To find out how many people were going total, you could represent the situation like this:

Once you look at the problem visually, you can count and see that 5 people are going on the trip.

What if you have a bigger problem to solve? Imagine that a few groups of people are going somewhere together. 30 people travel on one bus, and 21 travel on another. We could write this as 30 + 21.

It might not be a good idea to solve this problem by counting. First of all, no matter how you choose to count, it would probably take a pretty long time to set up the problem. Imagine drawing 30 and 21 pencil marks on the page, or counting out that many little objects! Second, actually counting the objects could take long enough that you might even lose track.

For this reason, when people solve a large addition problem, they set up the problem in a way that makes it easier to solve one step at a time. Let's look at the problem we discussed above, 30 + 21.

In the last lesson, we learned how to write expressions. However, when we're adding larger numbers, it helps to write the expressions in a different way.

We can see that 30 + 21 and   mean the same thing. They're just written differently.