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Defining and Identifying Equivalent Ratios

equivalent ratio: fractions in a pie chart

Equivalent ratios, sometimes known as equivalent fractions, are ratios that have the same proportion to each other when put in simplest form. Let's take the following ratios as a quick example.

fractions

We know each of these fractions has the same ratio between the numerators and the denominators. They all equal ½ when put in simplest form.

Equivalent ratios have the same unit rate or constant of proportionality. For example, when we compare the denominators of the fractions above to the numerators, we see that the unit rate or ratio is 2.

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How to Find the Area and Perimeter of a Trapezoid

area and perimeter of a trapezoid

A trapezoid is a quadrilateral, or a polygon with four sides, with one pair of parallel sides and one pair of non-parallel sides. Outside of North America, trapezoids may be referred to as trapeziums.

How do we go about finding the perimeter and area of a trapezoid? Read through for examples.

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Is a Rectangle a Parallelogram? Or Is a Parallelogram a Rectangle?

is a rectangle a parallelogram: different colors of blocks

Both rectangles and parallelograms are quadrilaterals, which means that they are polygons with four sides. But is a rectangle a parallelogram? Or is a parallelogram a rectangle? Here's a review of the different properties of both parallelograms and rectangles.

A parallelogram is a quadrilateral that has:

  • Two pairs of parallel sides
  • Two pairs of opposite sides that are congruent

A rectangle is a quadrilateral that has:

  • Four right angles
  • Two pairs of opposite sides that are congruent

A rhombus is a quadrilateral that has:

  • Four sides of equal length
  • Two pairs of equal opposite angles
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How to Work With Absolute Value Inequalities, Step by Step

absolute value inequalities: absolute value sample

You might already be familiar with solving inequalities, but what happens when you add an absolute value expression into the mix? Let’s go through the steps it takes to solve absolute value inequalities.

The absolute value symbol looks like this: |a|, where a is any real number. The absolute value sign means that the expression is no longer just a, but the distance a is from 0 on a number line.

A quick example: |2| = 2, because positive 2 is a distance of 2 from 0 on a number line.

Similarly, |-2| = 2, because negative 2 is also a distance of 2 from 0 on a number line.

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What Are the Four Coordinate Plane Quadrants?

coordinate plane quadrants drawn on a blackboard

There are four coordinate plane quadrants you’ll need to know when plotting points or graphing lines on the coordinate plane. The coordinate plane, also known as the coordinate grid, cartesian coordinate system, or Cartesian plane, is constructed by taking a vertical axis, or the y-axis and setting it against a horizontal axis, or the x-axis. This creates a grid with four quadrants.

The four coordinate plane quadrants don't have names but are simply known as the first quadrant, second quadrant, third quadrant, and fourth quadrant.

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