Reason - Examples, Exercises and Solutions

To easily solve ratio problems and to gain a better understanding of the topic in general, it is convenient to know about equivalent ratios.

Equivalent ratios are, in fact, ratios that seem different, are not expressed in the same way but, by simplifying or expanding them, you arrive at exactly the same relationship.

Think of it this way,

Equivalent ratios

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.

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 #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.

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 #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 than the radius of the blue circle?

210

Video Solution

Answer

212 2\frac{1}{2}

Exercise #5

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 #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. Ratio
  3. Division in a given ratio
  4. Direct Proportion
  5. Inverse Proportion