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How Do You Find the Area of a Quarter Circle?

area of a quarter circle: Image of a blue circle with a quarter of it separated and colored red

Finding the perimeter and area of a quarter circle is a good exercise in working with the two circle formulas you should be aware of: the formulas for the perimeter and area. Let's review these two formulas:

Circumference = 2ℼr

Area = ℼr²

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What You Need to Know About Proportional Relationships

Graph of a proportional relationship

A proportional relationship, sometimes known as the constant of proportionality, relates two quantities according to a common ratio. In other words, the same proportion!

If you are in seventh grade and looking to review common core state standards (CCSS), you will need to be familiar with this term. Not only will you see it in school, but you'll find it has many real-world applications. Let's dive in!

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What Do Consecutive Integers Represent In Math Problems?

consecutive integers: Colorful number blocks

What do consecutive integers mean, and how do you approach consecutive integer problems? Well, consecutive simply means "in a row." So, the term consecutive integers just means "numbers in a row."

1, 2, 3, 4, 5 are a series of five consecutive integers.

1, 3, 5, 7 are a series of consecutive odd integers.

-12, -11, -10, -9, -8 are a consecutive series of negative integers.

And so on!

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What Are the Properties of Real Numbers?

properties of real numbers: Colorful diagram showing the different types of numbers

In math, there are many different sets of numbers to work with. One set of numbers is known as real numbers. When it comes to the properties of real numbers, there are several important properties to know:

  • Additive identity
  • Multiplicative identity
  • Commutative property of addition
  • Commutative property of multiplication
  • Associative property of addition
  • Associative property of multiplication
  • Distributive property of multiplication

A property is just a way of expressing a characteristic or something that is true about real numbers. Knowing these properties will help you reduce or simplify algebraic expressions. Let's look at each property in detail to understand them better.

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How to Recognize Adjacent Supplementary Angles

adjacent supplementary angles: Figures showing different pairs of angles

In geometry, we give different names to different types of angles depending on the measure of the given angle: right angles, adjacent supplementary angles, vertical angles. But how do we know which is which?

Let’s start with the basics.

If the measure of the angle is exactly 90 degrees, it’s known as a right angle. If an angle is less than 90 degrees, it’s an acute angle. An angle greater than 90 degrees is an obtuse angle. If the measure of an angle is equal to 180 degrees, it’s known as a straight angle.

There are also names given to pairs of angles.

Vertical angles, or opposite angles, are the two angles directly opposite each other when two straight lines cross (Figure 1).

Complementary angles are two angles that add to 90 degrees (Figure 2).

Supplementary angles are two angles that add up to 180 degrees (Figure 3).

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