Reason - Examples, Exercises and Solutions

What is ratio?

The ratio describes the "relationship" between two or more things.

The ratio connects the given terms and describes how many times greater or smaller a certain magnitude is than another.

Let's see an example from everyday life:

When asked in a class, what is the ratio between boys and girls, it refers to how many girls there are in relation to a certain number of boys.

Or, for example, if in a certain vase there are red and white balls, the ratio between them can describe how many red balls there are in relation to a certain number of white balls or vice versa.

Practice Reason

Exercise #1

There are 18 balls in a box, 23 \frac{2}{3} of which are white.

How many white balls are there in the box?

Video Solution

Answer

12

Exercise #2

In a box there are 28 balls, 14 \frac{1}{4} of which are orange.

How many orange balls are there in the box?

Video Solution

Answer

7

Exercise #3

There are two circles.

The length of the diameter of circle 1 is 4 cm.

The length of the diameter of circle 2 is 10 cm.

How many times larger is the area of circle 2 than the area of circle 1?

Video Solution

Answer

614 6\frac{1}{4}

Exercise #4

There are two circles.

The length of the radius of circle 1 is 6 cm.

The length of the diameter of circle 2 is 12 cm.

How many times greater is the area of circle 2 than the area of circle 1?

Video Solution

Answer

They are equal.

Exercise #5

There are two circles.

One circle has a radius of 4 cm, while the other circle has a radius of 10 cm.

How many times greater is the area of the second circle than the area of the first circle?

Video Solution

Answer

614 6\frac{1}{4}

Exercise #1

How many times longer is the radius of the red circle than the radius of the blue circle?

220

Video Solution

Answer

5

Exercise #2

How many times longer is the radius of the red circle, which has a diameter of 24, than the radius of the blue circle, which has a diameter of 12?

Video Solution

Answer

2

Exercise #3

How many times longer is the radius of the red circle than the radius of the blue circle?

168

Video Solution

Answer

2 2

Exercise #4

How many times longer is the radius of the red circle (14 cm) than the radius of the blue circle, which has a diameter of 7?

Video Solution

Answer

4

Exercise #5

How many times longer is the radius of the red circle than the radius of the blue circle?

210

Video Solution

Answer

212 2\frac{1}{2}

Exercise #1

ABCD is a deltoid with an area of 58 cm².

DB = 4

AE = 3

What is the ratio between the circles that have diameters formed by AE and and EC?

S=58S=58S=58333AAABBBCCCDDDEEE4

Video Solution

Answer

3:26

Exercise #2

Given the rectangle ABCD

AB=X

The ratio between AB and BC is x2 \sqrt{\frac{x}{2}}

We mark the length of the diagonal A the rectangle in m

Check the correct argument:

XXXmmmAAABBBCCCDDD

Answer

m2+1=(x+1)2 m^2+1=(x+1)^2

Exercise #3

Given the rectangle ABCD

AB=X the ratio between AB and BC is equal tox2 \sqrt{\frac{x}{2}}

We mark the length of the diagonal A A with m m

Check the correct argument:

XXXmmmAAABBBCCCDDD

Answer

x2+2x=m2 x^2+2x=m^2

Topics learned in later sections

  1. Scale Factors, Ratio and Proportional Reasoning
  2. Equivalent Ratios
  3. Division in a given ratio
  4. Direct Proportion
  5. Inverse Proportion