Which of the following terms is defined as any portion or part in relation to the whole?

Before we get into the following learning units, which will provide more detailed discussion of topics on different human body systems, it is necessary to learn some useful terms for describing body structure. Knowing these terms will make it much easier for us to understand the content of the following learning units. Three groups of terms are introduced here:

• Directional Terms
• Planes of the Body
• Body Cavities

Directional Terms

Directional terms describe the positions of structures relative to other structures or locations in the body.

Superior or cranial - toward the head end of the body; upper (example, the hand is part of the superior extremity).

Inferior or caudal - away from the head; lower (example, the foot is part of the inferior extremity).

Anterior or ventral - front (example, the kneecap is located on the anterior side of the leg).

Posterior or dorsal - back (example, the shoulder blades are located on the posterior side of the body).

Medial - toward the midline of the body (example, the middle toe is located at the medial side of the foot).

Lateral - away from the midline of the body (example, the little toe is located at the lateral side of the foot).

Proximal - toward or nearest the trunk or the point of origin of a part (example, the proximal end of the femur joins with the pelvic bone).

Distal - away from or farthest from the trunk or the point or origin of a part (example, the hand is located at the distal end of the forearm).

Planes of the Body

Coronal Plane (Frontal Plane) - A vertical plane running from side to side; divides the body or any of its parts into anterior and posterior portions.

Sagittal Plane (Lateral Plane) - A vertical plane running from front to back; divides the body or any of its parts into right and left sides.

Axial Plane (Transverse Plane) - A horizontal plane; divides the body or any of its parts into upper and lower parts.

Median plane - Sagittal plane through the midline of the body; divides the body or any of its parts into right and left halves.

Body Cavities

The cavities, or spaces, of the body contain the internal organs, or viscera. The two main cavities are called the ventral and dorsal cavities. The ventral is the larger cavity and is subdivided into two parts (thoracic and abdominopelvic cavities) by the diaphragm, a dome-shaped respiratory muscle.

Thoracic cavity

The upper ventral, thoracic, or chest cavity contains the heart, lungs, trachea, esophagus, large blood vessels, and nerves. The thoracic cavity is bound laterally by the ribs (covered by costal pleura) and the diaphragm caudally (covered by diaphragmatic pleura).

Abdominal and pelvic cavity

The lower part of the ventral (abdominopelvic) cavity can be further divided into two portions: abdominal portion and pelvic portion. The abdominal cavity contains most of the gastrointestinal tract as well as the kidneys and adrenal glands. The abdominal cavity is bound cranially by the diaphragm, laterally by the body wall, and caudally by the pelvic cavity. The pelvic cavity contains most of the urogenital system as well as the rectum. The pelvic cavity is bounded cranially by the abdominal cavity, dorsally by the sacrum, and laterally by the pelvis.

Dorsal cavity

The smaller of the two main cavities is called the dorsal cavity. As its name implies, it contains organs lying more posterior in the body. The dorsal cavity, again, can be divided into two portions. The upper portion, or the cranial cavity, houses the brain, and the lower portion, or vertebral canal houses the spinal cord.

Proportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. Here, a and b are any two integers. The ratio and proportion are key foundations to understand the various concepts in mathematics as well as in science.

Proportion finds application in solving many daily life problems such as in business while dealing with transactions or while cooking, etc. It establishes a relation between two or more quantities and thus helps in their comparison. 

What is Proportion?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal. 

Proportion- Definition

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  "::" or "=".

Proportion- Example

Two ratios are said to be in proportion when the two ratios are equal. For example, the time taken by train to cover 50km per hour is equal to the time taken by it to cover the distance of 250km for 5 hours. Such as 50km/hr = 250km/5hrs.

Continued Proportions

Any three quantities are said to be in continued proportion if the ratio between the first and the second is equal to the ratio between the second and the third. Similarly, four quantities in continued proportion will have the ratio between the first and second equal to the ratio between the third and fourth.

For example, consider two ratios to be a:b and c:d. In order to find the continued proportion for the two given ratio terms, we will convert their means to a single term/number. This in general, would be the LCM of means, and for the given ratio, the LCM of b & c will be bc. Thus, multiplying the first ratio by c and the second ratio by b, we have

• First ratio- ca:bc
• Second ratio- bc:bd

Thus, the continued proportion for the given ratios can be written in the form of ca:bc:bd.

Ratios and Proportions

The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.

When two or more such ratios are equal, they are said to be in proportion.

Fourth, Third and Mean Proportional

If a : b = c : d, then:

• d is called the fourth proportional to a, b, c.
• c is called the third proportional to a and b.
• The mean proportional between a and b is √(ab).

Tips and Tricks on Proportion

• a/b = c/d ⇒ ad = bc
• a/b = c/d ⇒ b/a = d/c
• a/b = c/d ⇒ a/c = b/d
• a/b = c/d ⇒ (a + b)/b = (c + d)/d
• a/b = c/d ⇒ (a - b/b = (c - d)/d
• a/(b + c) = b/(c + a) = c/(a + b) and a + b + c ≠0, then a = b = c.
• a/b = c/d ⇒ (a + b)/(a - b) = (c + d)/(c - d), which is known as componendo -dividendo rule
• If both the numbers a and b are multiplied or divided by the same number in the ratio a:b, then the resulting ratio remains the same as the original ratio.

Proportion Formula with Examples

A proportion formula is an equation that can be solved to get the comparison values. To solve proportion problems, we use the concept that proportion is two ratios that are equal to each other. We mean this in the sense of two fractions being equal to each other.

Ratio Formula

Assume that, we have any two quantities (or two entities) and we have to find the ratio of these two, then the formula for ratio is defined as a:b ⇒ a/b, where,

• a and b could be any two quantities.
• “a” is called the first term or antecedent.
• “b” is called the second term or consequent.

For example, in ratio 5:9, is represented by 5/9, where 5 is antecedent and 9 is consequent. 5:9 = 10:18 = 15:27

Proportion Formula

Now, let us assume that, in proportion, the two ratios are a:b and c:d. The two terms ‘b’ and ‘c’ are called ‘means or mean terms’, whereas the terms ‘a’ and ‘d’ are known as ‘extremes or extreme terms.’

a/b = c/d or a:b::c:d. For example, let us consider another example of the number of students in 2 classrooms where the ratio of the number of girls to boys is equal. Our first ratio of the number of girls to boys is 2:5 and that of the other is 4:8, then the proportion can be written as: 2:5::4:8 or 2/5 = 4/8. Here, 2 and 8 are the extremes, while 5 and 4 are the means.

Types of Proportions

Based on the type of relationship two or more quantities share, the proportion can be classified into different types. There are two types of proportions.

• Direct Proportion
• Inverse Proportion

Direct Proportion

This type describes the direct relationship between two quantities. In simple words, if one quantity increases, the other quantity also increases and vice-versa. For example, if the speed of a car is increased, it covers more distance in a fixed amount of time. In notation, the direct proportion is written as y ∝ x.

Inverse Proportion

This type describes the indirect relationship between two quantities. In simple words, if one quantity increases, the other quantity decreases and vice-versa. In notation, an inverse proportion is written as y ∝ 1/x. For example, increasing the speed of the car will result in covering a fixed distance in less time.

Important Notes

• Proportion is a mathematical comparison between two numbers.
• Basic proportions are of two types: direct proportions and inverse proportions.
• We can apply the concepts of proportions to geography, comparing quantities in physics, dietetics, cooking, etc.

Properties of Proportion

Proportion establishes equivalent relation between two ratios. The properties of proportion that is followed by this relation :

• Addendo – If a : b = c : d, then value of each ratio is a + c : b + d
• Subtrahendo – If a : b = c : d, then value of each ratio is a – c : b – d
• Dividendo – If a : b = c : d, then a – b : b = c – d : d
• Componendo – If a : b = c : d, then a + b : b = c + d : d
• Alternendo – If a : b = c : d, then a : c = b: d
• Invertendo – If a : b = c : d, then b : a = d : c
• Componendo and dividendo – If a : b = c : d, then a + b : a – b = c + d : c – d

Difference Between Ratio and Proportion

Ratio and proportion are closely related concepts. Proportion signifies the equal relationship between two or more ratios. To understand the concept of ratio and proportion, go through the difference between ratio and proportion given here.

Proportion Related Topics

Given below is the list of topics that are closely connected to Proportion in commercial math. These topics will also give you a glimpse of how such concepts are covered in Cuemath.

FAQs on Proportion

What do you Mean by Ratio?

A ratio is a mathematical expression written in the form of a:b, which expresses a fraction of the form a/b, where a and b are any integers. For example, fraction 1/3 can be expressed as 1:3 in form of a ratio.

What is Proportion in Math?

Proportion is a mathematical comparison between two numbers.  According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Proportions are denoted using the symbol  ‘::’ or ‘=’. For example, 2:5 :: 4:8 or 2/5 = 4/8. Here, 2 and 8 are the extremes, while 5 and 4 are the means.

How are Ratio and Proportion Used in Daily Life?

Ratios and proportions are used on a daily basis. Ratios and proportions are used in business transactions when dealing with money, comparing quantities for the price while shopping, etc. For example, a business might have a ratio for the amount of profit earned per sale of a certain product such as $5:1, which says that the business gains $2.50 for each sale.

How do you Know if Two Ratios Form a Proportion?

If two ratios are equivalent to each other, then they are said to be in proportion. For example, the ratios 1:2, 2:4, and 3:6 are equivalent ratios.

How do you Calculate Proportion?

Proportion is calculated using the proportion formula which says- a:b::c:d or a:b = c:d. We read it as “a" is to "b" as "c" is to "d”.

What are Different Types of Proportion?

Based on the type of relationship two or more quantities share, the proportion can be classified into different types. There are two types of proportions.

• Direct Proportion- describes the direct relationship between two quantities. In simple words, if one quantity increases, the other quantity also increases and vice-versa.
• Inverse Proportion- describes the indirect relationship between two quantities. In simple words, if one quantity increases, the other quantity decreases and vice-versa.

What are the Different Properties of Proportion?

Proportion establishes equivalent relation between two ratios. The properties of proportion that is followed by this relation :

• Addendo – If a : b = c : d, then value of each ratio is a + c : b + d
• Subtrahendo – If a : b = c : d, then value of each ratio is a – c : b – d
• Dividendo – If a : b = c : d, then a – b : b = c – d : d
• Componendo – If a : b = c : d, then a + b : b = c+d : d
• Alternendo – If a : b = c : d, then a : c = b: d
• Invertendo – If a : b = c : d, then b : a = d : c
• Componendo and dividendo – If a : b = c : d, then a + b : a – b = c + d : c – d

Which design principle refers to units that are opposite creates variety and stimulates interest select one a contrast B repetition C alternation D progression?

What type of balance is created when the way is positioned unequally from a center axis?

In which of the three levels of observation does the designer use qualitative analysis?

When three sectioning the facial area the middle or second section includes?