If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Early math review>Unit 8

Lesson 4: Fractions of shapes

# Equal parts of circles and rectangles

Sal determines if shapes are divided into 2 or 4 equal sections.

## Want to join the conversation?

• Can a triangle be divided in to 3rds?
• You can achieve this to my knowledge atleast three different ways.
• Can a circle be divided by 6 equally?
• Yes! A circle can be divided into any number of equal parts.
• I already know that circles and rectangles can be equally divided, but how can triangles be divided into more than 2 pieces?
• Assuming you are talking about an equilateral triangle (a triangle with similar side lengths and angles for all three sides), you can split a triangle into three congruent (absolutely equal) pieces by drawing lines from each of the corners until they all reach the middle. To split an equilateral triangle into four pieces, Draw a horizontal line slightly above the middle to make one triangle, then split the lower part into a (going horizontally) regular triangle, upside-down triangle, and then another regular triangle.

Pictures of both are shown here: https://math.stackexchange.com/questions/158290/is-it-possible-to-divide-an-equilateral-triangle-into-12-congruent-triangles
• can you cut 5 equal section?
(1 vote)
from the photo
(1 vote)
• why do you think this fun
• if a circle is 360 degrees, how many degrees is a square? i use degrees in splitting, don't ask me why, hard to explain.
• Just like a circle, a square also has 360 degrees. The only difference is with a square, the degrees are calculated by adding up the angles. Each angle in a square is equal to 90 degrees. There are 4 angles in a square so 90 + 90 + 90 + 90, or 90 x 4 = 360.

## Video transcript

- [Voiceover] Which circles are divided into fourths? Select all that apply. Well to be divided into fourths, that means we have to be divided into four equal sections. Cause a fourth is gonna be one of the four equal sections. So all of these are divided into four sections but not all of them are divided into four equal sections. For example this one is divided into four sections but this section right over here is bigger than this section right over here. and its bigger than this section over here. So this isn't four equal sections. But these top three, it looks like four equal sections. It looks like each of these four sections are equal. Each of these four sections are equal, each of these four sections are equal. So all of these up here are divided into fourths and this one isn't so I wont click on that one. Let's keep going, this is fun. Which squares are divided into fourths? Select all that apply. Well same idea. We have to be divided into four equal sections. So all of these are divided into four sections. One, two, three, four, one, two, three, four. But not all of them are divided into four equal sections. For example, this one right over here, this section, this little triangle is much smaller than this section. So these aren't equal sections. But for the other three they are four equal sections. Each of these triangles that this squares divided into, these are all equal. They all have the same area. So that's four equal sections. Each of these smaller squares, they all have the same area. So that's four equal sections. And then each of these four rectangles are all the same size. They all have the same area. So that's for equal sections. Let's keep going. I'm having a lot of fun. Alright, which circles are divided into thirds? Well if your to divide to thirds, you have to be dividing into three equal sections. So this one is divided into four equal sections. So this is divided into fourths. So it's not thirds. This is divided into three sections but they're not equal. This section right over here is smaller than this section right over here. This one is divided into three sections and they're all equal. This section has the same area as this section, has the same area as that section. So I'll check that one. This one is three sections but they're not equal just like this one. This section is much smaller than this section. So this is the only one that is really divided into thirds. Which circles are divided into thirds? Same idea. This is divided into fourths. These are aren't equal sections. Not equal sections. This one is divided into thirds. Let's do one more. Which rectangles are divided into fourths? Remember fourths, it needs to be four equal sections. This looks like four equal sections. This is two equal sections. This is divided into halves not fourths. This is four equal sections. This is divided into six equal sections. So it's equal sections but not fourths. Six equal sections. So this right here is divided into sixths. So our two rectangles that are divided into fourths, are this one and that one. Four equal sections.