Category: Mathematics

In this article, you will learn about the Addition Operation and how to perform the Addition of Rational Numbers. Usually, the Addition of Rational Numbers is much similar to the Addition of Fractions. The First and Foremost Step to keep in mind when it comes to the Rational Numbers Addition is the denominators should be positive. If the denominators aren’t positive simply rearrange them to make them positive.

The two subcategories that you encounter while dealing with the Addition Operation in Rational Numbers are listed below. You can check out the solved examples explained step by step for reference and get a grip on the concept.

Rational Numbers with the Same Denominator

Let suppose a/b, c/b be two rational numbers having the common denominator b then Addition of Rational Numbers is given by the summation of numerators leaving the common denominator unchanged i.e. (a+c)/b.

Solved Examples

(i) Add 4/7 and 13/7?

Solution:

Given Rational Numbers are 4/7 and 13/7

Adding them we get 4/7+13/7

= (4+13)/7

= 17/7

Therefore, the Sum of 4/7 and 13/7 is 17/7.

(ii) Add 5/12 and -3/12?

Solution:

Given Rational Numbers are 5/12, -3/12

Adding them we get 5/12+(-3)/12

= (5-3)/12

= -2/12

Rational Numbers with the Different Denominator

In the case of Rational Numbers with Different Denominators, we need to find the LCM of Denominators. After that, express the given rational numbers with a common denominator and then add the numerators of the obtained rational numbers while keeping the denominator unchanged.

Solved Examples 

(i) Add 4/5 and 7/9?

Solution:

Clearly, the denominators are different and we need to figure out the LCM of Denominators.

LCM(5,9) is 45

Express the Given Rational Numbers with a Common Denominator using the LCM obtained.

4/5 = 4*9/5*9 = 36/45

7/9 = 7*5/9*5 = 35/45

Add the Numerators of the Rational Numbers while keeping the Denominator unchanged to get the sum of Rational Numbers.

= 36/45+35/45

= 71/45

Therefore the sum of 4/5 and 7/9 is 71/45.

(ii) Find the Sum of -7/6 and 5/12?

Solution: 

Given Rational Numbers are -7/6 and 5/12

Since the denominators aren’t equal find the LCM of them

LCM of 6, 12 is 12

Express the given rational numbers with a common denominator using the LCM acquired.

-7/6 = -7*2/6*2 = -14/12

5/12 = 5*1/12*1 = 5/12

Adding the Rational Numbers we get

= (-14+5)/12

=-9/12

Therefore, the Sum of -7/6 and 5/12 is -9/12.

Let us discuss in detail How to Add Rational Numbers with Different Denominators. To find the Sum of Rational Numbers you can have a look at the below examples provided. Check the detailed procedure to add rational numbers not having the common denominator.

How to Add Rational Numbers with Different Denominators?

Go through the below-mentioned steps to add rational numbers having different denominators. They are along the lines

Step 1: Check the Rational Numbers and see whether the denominators are positive or not. If any of the denominators is negative rearrange them to become positive.

Step 2: List out the denominators of rational numbers in the earlier step.

Step 3: Determine the LCM of the denominators of the given Rational Numbers.

Step 4: Express the Rational Numbers in a way that they have the Common Denominator using the LCM obtained.

Step 5: Write down the numerator as the sum of numerators of rational numbers obtained in the earlier step and denominators is the LCM obtained in Step 3.

Step 6: Rational Number obtained in Step 5 is the required sum and simplify if required.

Solved Examples on Adding Rational Numbers with Different Denominator

1.  Add Rational Numbers -8/21 and 3/9?

Solution:

Given Rational Numbers are -8/21, 3/9

= -8/21+3/9

Firstly, find the Least Common Multiple of the Denominators i.e. 21, 9

LCM(21, 9) = 63

Express the Rational Numbers with Common Denominator using the LCM Obtained.

-8/21 = -8*3/21*3 = -24/63

3/9 = 3*7/9*7 = 21/63

Adding them we get

-24/63+21/63

= (-24+21)/63

= -3/63

Simplifying further we get -1/21

Therefore the Sum of -8/21 and 3/9 is -1/21.

2. Add 3/4 and 5?

Solution:

Given Rational Numbers are 3/4 and 5/1

= 3/4+5/1

Find the LCM of 4, 1

LCM(4, 1) = 4

Express the Given Rational Numbers in terms of Common Denominator using the LCM obtained.

3/4 = 3*1/4*1 = 3/4

5/1 = 5*4/1*4 = 20/4

Add the obtained rational numbers numerators with a common denominator

= (3+20)/4

= 23/4

Therefore, the Sum of 3/4 and 5 is 23/4.

3. Simplify 5/-12+7/-4?

Solution:

Given Rational Numbers are 5/-12 and 7/-4

Since the rational numbers are having a negative denominator rearrange them to have a positive denominator.

5/-12 = 5*(-1)/-12*(-1) = -5/12

7/-4 = 7*(-1)/-4*(-1) = -7/4

Find the LCM of Denominators of the Rational Numbers.

LCM(12, 4) = 12

Express the Rational Numbers with Common Denominator using the LCM obtained.

-5/12 = -5*1/12*1 = -5/12

-7/4= -7*3/4*3 = -21/12

Add the Obtained Rational Numbers Numerators and keep the denominator unchanged.

= (-5-21)/12

= -26/12

Thus, 5/-12+7/-4 is -26/12.

Let us learn about the Addition of Rational Numbers with Same Denominator from here. Get to know the detailed procedure on how to add rational numbers with the same denominator. Have a look at the few examples to better understand the concept of Rational Numbers Addition having the Same Denominator.

How to Add Rational Numbers with the Same Denominator?

Below are easy guidelines listed on how to Add Rational Numbers with the Same Denominator. Follow them while adding rational numbers having the common denominator. They are along the lines

Step 1: Determine the numerators of two given rational numbers and their common denominator.

Step 2: Add the Numerator of the Rational Numbers obtained in the earlier step.

Step 3: Make a note of the Rational Number whose numerator is the sum of rational numbers obtained in step 2 and keep the denominator unaltered. Simplify the Rational Number if Required.

From the above steps, we can infer that a/b, c/b are two rational numbers then the Addition of Two Rational Numbers with the Same Denominator is given by (a+b)/c.

Solved Examples on Addition of Rational Numbers with Same Denominator

1. Find the Sum of 3/9 and -7/9?

Solution:

Given Rational Numbers are 3/9 and -7/9

= 3/9+(-7)/9

= (3-7)/9

= -4/9

Sum of 3/9, -7/9 is -4/9.

2. Find the Sum of 8/-10 and 4/10?

Solution:

Given Rational Numbers are 8/-10, 4/10

Since the rational numbers don’t have a common denominator. Firstly, make them into a positive denominator.

8/-10 = 8*(-1)/-10*(-1) = -8/10

Adding -8/10 and 4/10

= -8/10+4/10

= (-8+4)/10

= -4/10

3. Add 3/5 and 17/5?

Solution:

Given Rational Numbers are 3/5 and 17/5

Adding the given Rational Numbers we get

= 3/5+17/5

= (3+17)/5

= 20/5

On Simplifying we get the following Rational Number

= 4/1

To help you better understand the concept of Representing Rational Numbers on the Number Line we have taken a few examples. Check out the detailed explanation provided and understand the concept better. After going through this article, you will learn how to solve related problems on your own.

In general, Positive Rational Numbers are always represented on the right of the 0 on the number line. Negative Rational Numbers are represented to the left of 0 on the number line.

Solved Examples on Rational Numbers on the Number Line

1. Represent 1/8 and 3/8 on the Number Line?

Solution: 

Firstly, draw the number line mark 0 on it. Split the number line into 8 equal parts and then mark the first division to the right i.e. 1/8. The Second division is 2/8 and the third division is 3/8. The fourth division is 4/8 and so on.

2. Write the rational number for each point labeled with a letter below?

Solution:

We know the positive rational numbers are represented to the right of 0. As all of the rational numbers given are successive. Therefore the Rational Numbers Labelled with Letters A, B, C, D, E are 1/5, 4/5, 5/5, 8/5, 9/5.

Thus, All the Rational Numbers 0/5, 1/5, 2/5, 3/5, 4/5, 5/5, 6/5, 7/5, 8/5, 9/5, 10/5, 11/5, 12/5 will be adjacent to each other on the Number Line.

Let us learn how to find Rational Numbers in Different Forms using the properties in expressing a rational number. Get to see solved examples along with clear-cut explanations and learn how to express rational number in different forms.

1. Express Rational Number -4/10 as a rational number with the denominator 20?

Solution:

In Order to express -4/10 as a rational number with denominator 20, we first need to figure out the number that when multiplied by 10 results in 20.

Clearly, the number is 20 ÷ 10 = 2

Multiplying the numerator and denominator -4/10 with 2 we get

-4/10 = -4*2/10*2 = -8/20

Expressing Rational Number -4/10 with the denominator 20 we get -8/20.

2.  Express – 2/10 as a rational number with denominator -30?

Solution:

In order to express the rational number -2/10 with denominator -30, we need to find out the number that when multiplied by 10 results in -30.

It is clear the number is 10 ÷ -30 = -3

Multiplying both the numerator and denominator -2/10 with -3 we get

-2/10 = (-2*-3)/(10*-3) = 6/-30

3. Express 52/-39 as a Rational Number having the denominator 3?

Solution:

To express 52/-39 as a rational number having the denominator 3 we need to find the number which gives 3 when -39 is divided by it.

Clearly, the number is -39 ÷ 3 = -13

52/-39 = (52÷ -13)/(-39 ÷ -13) = -4/3

Thus, 52/-39 as a Rational Number having the denominator 3 is -4/3.

4. Fill up the blanks with the appropriate number in the denominator 6/12 = 36/….=-66/…..?

We have 36 ÷ 6 = 6

Therefore, 6/ 12 = 6*6/12*6 = 36/72

Similarly, we have -66 ÷ 6 = -11

Therefore, 6/ 12 = 6*-11/12*-11

=-66/-132

Thus, 6/12 = 36/72 =-66/-132

Let us learn how to represent Integers on a Number Line at first. To represent Integers on Number Line consider a Point called Zero. The Points to the right of 0 are denoted by + Sign and are Positive Integers. The Points to the left of 0 are denoted by – Sign and are Negative Integers. Now that you are aware of Representation of Integers on the Number Line representing Rational Numbers on the number line would be much easier to understand.

How to Represent Rational Numbers on the Number Line?

Let us discuss how to represent Rational Numbers on the Number Line. Similar to Positive Integers Positive Rational Numbers would be placed to the right of 0 and Negative Rational Numbers would be marked to the left of 0.

For instance which side you would mark -1/3 on the number line. The Answer is quite clear as it is negative you need to place it on the left of 0. While marking integers on the number line successive integers will be placed at equal intervals, i.e. 1 and -1 will be equidistant. The same is with 2, -2 and 3, -3 and so on.

This would be the case with Rational Numbers 1/2, -1/2 would be equidistant from 0.

Solved Examples

1.  Represent 1/2 and -1/2 on the Number Line?

Solution:

Draw a line and mark point 0 at the center. Set off units to the right and left of 0 as they are equidistant.

Mark the rational number 1/2 between 0 and 1.

So is the case with -1/2 and place it between 0 and -1.

2. Represent 4/3, 5/3, 6/3, 7/3 on the Number Line?

Solution:

Draw a line and mark point 0 at the center. The line extends indefinitely on both sides.

Split the number line into 3 equal parts between 0 and 1. The first point of the division is given by 1/3 and the second point of the division is 2/3, third point 3/3, fourth point as 4/3, 5th point as 5/3, sixth point as 6/3, seventh point as 7/3.

The concept of Profit and Loss is used in our daily life, which is like we will buy some essentials goods from the shopkeeper and the shopkeeper will buy them either from the manufacturer or from wholesalers. After that, the shopkeeper will sell those goods for a higher price than they bought so that he can earn some profit.

We can see many business people follow these tactics to earn money by buying and selling goods. If the Selling Price is higher than the Actual Price or Cost Price, then he will get a profit. And if the Cost Price is higher than the Selling Price, he will get a loss. Here in this article, we will guide you on how to solve problems on Profit and Loss. In addition, you can get the Formulas for Profit and Loss along with Solved Examples.

Basics of Profit and Loss

Before stepping into the concept of Profit and Loss you need to know the fundamentals involved to calculate the Profit and Loss. They are Selling Price and Cost Price.

Cost Price(CP): Amount you usually pay to buy a product or commodity is called the Cost Price. It is in short represented as CP. In fact, CP is subdivided into two categories namely Fixed Cost and Variable Cost. The major difference between Fixed Cost and Variable Cost is that Fixed Cost remains unchanged under any circumstances whereas variable cost changes depending on the units.

Selling Price(SP): Amount for which the product is sold is referred to as Selling Price. It is represented as SP and is also called as Sale Price.

Profit: The amount gained by selling a product or commodity more than its actual price or cost price.

Loss: The Amount the Seller gets after selling a product less than its actual price.

• Calculate Profit and Profit Percent
• Calculate Loss and Loss Percent

Profit and Loss Formulas

The Formula for Profit and Loss with reference to Cost Price and Selling Price is given as such.

Profit(P)= Selling Price(SP)- Cost Price(CP)
Loss(L)= Cost Price(CP) – Selling Price(SP)
On the other hand formulas to determine the Profit %, Loss % is as such
Profit % = (Profit/Cost Price)*100
Loss % = (Loss/Cost Price)*100

Examples on Profit and Loss

1. The actual price of the book is Rs 60 and the shopkeeper sold the book for Rs 100. Find the profit that shopkeeper earned?

Solution:
The cost price of the book= Rs 60
The selling price of the book= Rs 100
Profit(P)= Selling price(SP) – Cost price (CP)
Applying the S.P and C.P of the book in the Profit Formula we have
= Rs 100 – Rs 60
= Rs 40.
Profit= Rs 40.
Therefore, Profit Gained by the Shokeeper on selling the book for 100 is Rs.40/-

2.  A man bought a cycle for Rs 5000. After a year he sold it for Rs 4000. How much did he lose?

Solution:
The cost price of the cycle= Rs 5000.
The selling price of the cycle= Rs 4000.
Substituting the Cost Price and Selling Price of the cycle we get
Loss(L)= Cost Price(CP) – Selling Price(SP).
= Rs 5000- Rs 4000
= Rs 1000.
Loss = Rs 1000.
Therefore, the man had a loss of Rs. 1000/- on selling the cycle for Rs. 4000/-.

3. Consider a Shopkeeper bought 1kg of Apples for Rs. 80 and Sold it for Rs. 100 per kg. How much is the profit gained by him?

Solution:

Cost Price of Apples = Rs. 80

Selling Price of Apples = Rs. 100

Profit = S.P – C.P

= 100 – 80

= 20

Therefore, the shopkeeper gained a profit of Rs. 20/- on selling the Apples at Rs. 100/- per Kg.

4. Calculate the Profit% gained by the Shopkeeper for the above example?

Solution:
We know Profit Percentage = (Profit/Cost Price)*100
Profit = Rs. 20/-
Apply the Profit and Cost Price Values in the Formula for Profit %
Profit % = (20/80)*100
= 25
Therefore, the shopkeeper gained a 25 % Profit Percentage.

To calculate the Loss we need to know “What is Loss?” When we sold an item or a product less than it’s actual price, then Loss occurs which means the product is sold for a low price than the actual price. Now coming to the formula to calculate Loss we have
Loss(L)= Cost Price (CP) – Selling Price(SP)

Here we can see the new terms “Selling price” and “Actual Price” or “Cost Price.” Let us discuss what they refer to.
Selling Price: The price of the product which was sold by the shopkeeper to the customer for a certain price is known as the selling price. Selling Price can also be written as SP. To calculate the Selling Price, we have a formula i.e.

Selling Price(SP)= Cost Price(CP) – Loss(L)

Cost Price: It is also called Actual Price, which means the actual cost of a product or original cost of a product or an item that was bought from the merchant or retailer. To calculate Cost Price, we have a formula i.e,
Cost Price(CP)= Selling Price(SP) + Loss(L)
In the above, we have discussed the related terms. Let’s discuss more about Loss with some examples covering every detail.

Solved Examples on Loss

1.  Find the Loss if
a) SP= 80 and CP= 100
b) SP= 120 and CP= 150
c) SP= 200 and CP= 300

Solution:

a) SP= 80 and CP= 100

We know the formula to calculate the Loss as below
Loss(L)= Cost price (CP) – Selling price(SP).
Substituting the input data in the formula and doing basic math we get
= 100- 80
= 20
Loss= 20.

b) SP= 120 and CP= 150

Formula to calculate the Loss is as under
Loss(L)= Cost price (CP) – Selling price(SP).
Apply the input data you have in the formula and perform basic math
= 150-120
= 30
Loss= 30.

c) SP= 200 and CP= 300

Formula to calculate the Loss is as below
Loss(L)= Cost price (CP) – Selling price(SP).
Substitute the input information we have to find out the Loss
= 300- 200
= 100
Loss= 100.

2. A shopkeeper bought 5 dozens bananas for Rs 300 and sold them at Rs 250. How much he loses?

Solution:
The cost price of bananas= Rs 300
The selling price of bananas= Rs 250
Formula for Loss(L)= Cost Price (CP) – Selling Price(SP).
= Rs 300- Rs 250
= Rs 50.
Loss= Rs 50.

How to Calculate the Loss Percent?

Loss percent is the percent which is expressed as the percentage of the cost price. The formula of Loss Percent is
Loss %= (Loss/ Cost Price)×100. Cost Price is always considered for reference to determine whether you got Loss or Profit. We have listed few examples explaining the process on how to find the Loss Percentage. They are as such

1.  Find Loss % if
a) SP= 80 and CP= 100
b) SP= 120 and CP= 150
c) SP= 200 and CP= 300

Solution:

a) SP= 80 and CP= 100
Formula to calculate the Loss(L)= Cost price (CP) – Selling price(SP).
= 100- 80
= 20
Loss= 20.
After finding the Loss we can determine the Loss % easily
Loss %= (Loss/ Cost Price)×100.
= (20/100) × 100
= 20%

b) SP= 120 and CP= 150
Formula to calculate the Loss(L)= Cost price (CP) – Selling price(SP).
= 150-120
= 30
Loss= 30.
Substitute the Loss value in th Loss % formula we have the equation as such
Loss%= (Loss/ Cost price)×100.
= (30/150)×100
= (1/5)×100
= 20%

c) SP= 100 and CP= 200

Apply the given input data in the formula for
Loss(L)= Cost price (CP) – Selling price(SP).
= 200- 100
= 100
Loss = 100.
Substitute the Loss in the Loss % we have the equation as such
Loss %= (Loss/ Cost Price)×100.
= (100/200)×100
= (1/2)×100
= 50.

2. A man purchased a scooter for Rs 50,000 and after two years he sold it for Rs 30,000. Find Loss and Loss percent.

Solution:

The cost price of a scooter = Rs 50,000
The selling price of a scooter= Rs 30,000
Loss(L)= Cost price (CP) – Selling Price(SP).
Substitute the input values in the formula of Loss we have
= Rs 50,000 – Rs 30,000
= Rs 20,000.

Apply the Loss in the Loss Formula we have
Loss %= (Loss/ Cost price)×100.
= (20,000/50,000)×100
= (2/5)×100
= 2×20
= 40%.

Related Articles:

• Profit and Loss
• Calculate Profit and Profit Percent

To calculate the profit we need to know “What is Profit?” The term Profit refers to the amount which we gained after selling a product. This means the “Selling price” should be more than the “Actual price” or “Cost Price.”
Now coming to the calculation of the profit we have a formula i.e

Profit(P)= Selling price(SP) – Cost Price (CP)

Here we can see the new terms “Selling Price” and “Actual Price” or “Cost Price.” Let us discuss what they refer to.

Selling Price: The price of the product which was sold by the shopkeeper to the customer for a certain price is known as the selling price. The Selling price can also be written as SP. To calculate the Selling price, we have a formula i.e.

Selling Price(SP)= Profit(P) + Cost Price(CP)

Cost Price: It is also called Actual price, which means the actual cost of a product or original cost of a product or an item that was bought from the merchant or retailer. To calculate Cost Price, we have a formula i.e,
Cost price(CP)= Selling price(SP) – Profit (P).

In the above, we have discussed the related terms. Let’s discuss more on the concept of Profit with some examples.

Solved Examples on Profit

1. Find the Profit if
a) SP= 100 and CP= 60
b) SP= 125 and CP= 100
c) SP= 90 and CP= 75

Solution:
a) SP= 100 and CP= 60
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 100-60
= 40.
Profit= 40.

b) SP= 125 and CP= 100
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 125-100
= 25.
Profit= 25.

c) SP= 90 and CP= 75
Profit(P)= Selling price(SP) – Cost price (CP).
= 90-75
= 15.
Profit= 15.

2. The cost price of chocolate is Rs.10 and the selling price is Rs. 15. Find the profit?

Solution:
CP of the chocolate= Rs.10
SP of the chocolate= Rs.15
Profit= Selling price(SP) – Cost price(CP).
= 15 – 10
= 5.
Profit= 5.

3. Mark bought 4 dozens of apples at $15 a dozen and sold at $20 a dozen. Find the profit?

Solution:

The cost price of apples= $15
The selling price of apples= $20
Profit(P)= Selling price(SP) – Cost price (CP).
= $20-$15
= $5.
Profit= $5.

4. Mr.Singh bought a table for Rs 15,000 and spent Rs 500 on transportation. He sold the table for Rs 17,000. Find his profit?

Solution:
Cost price of the table= Rs 15,000.
Transportation cost= Rs 500.
So, Total Cost Price= Rs 15,000+Rs 500
= Rs 15,500The selling price of the table= Rs 17,000.
Profit(P)= Selling Price(SP) – Cost Price (CP).
= Rs 17,000- Rs 15,500
= Rs 1500
Profit= Rs 1500.

Solved Examples on Selling Price

1. Find the Selling Price if
a) P= 20 and CP= 100
b) P= 32 and CP= 150
c) P= 5 and CP= 22

Solution:

a) P= 20 and CP= 100
Selling price(SP)= Profit(P) + Cost price(CP).
= 20+100
= 120.
Selling price= 120.

b) P= 32 and CP= 150
Selling price(SP)= Profit(P) + Cost price(CP).
= 32+150
= 162.
Selling price= 162.

c) P= 5 and CP= 22
Selling price(SP)= Profit(P) + Cost price(CP).
= 5+22
= 27.
Selling Price= 27.

2. The cost price of a dining set is Rs 8000 and the shopkeeper got a profit of Rs 2000. Find the selling price of the dining set?

Solution:
The cost price of the dining set= Rs 8000.
The profit that the shopkeeper got= Rs 2000.
Selling price(SP)= Profit(P) + Cost price(CP).
= Rs 2000+ Rs 8000
= Rs 10,000.
The selling price of the dining set is Rs 10,000.

Solved Examples on Cost Price

1.  Find the Cost price if
a) SP= 200 and P= 20.
b) SP= 250 and P= 50.
c) SP= 125 and P= 25.

Solution:
a)SP= 200 and P= 20.
Cost price(CP)= Selling price(SP) – Profit (P).
= 200-20.
= 180.
Cost Price= 180.

b) SP= 250 and P= 50.
Cost Price(CP)= Selling Price(SP) – Profit (P).
= 250-50
= 50.

c) SP= 125 and P= 25.
Cost price(CP)= Selling price(SP) – Profit (P).
= 125-25
= 100.

2. A shopkeeper sold a chair for Rs 2000 and he got a profit of Rs 500. What is the actual price of the chair?

Solution:
The selling price of the chair= Rs 2000.
The profit that the shopkeeper got= Rs 500.
Cost price of the chair =
Cost price(CP)= Selling price(SP) – Profit (P).
= Rs 2000- Rs 500
= Rs 1500.
So the actual price of the chair is Rs. 1500.

How to Calculate the Profit %?

The profit percentage is the percentage which is calculated with the Cost Price in the base. To calculate Profit Percent we need to know profit and cost price. The formula of profit percent is
Profit % = Profit/CP × 100.
To know how to calculate profit %, refer to the solved examples below for better understanding and solve the problems on your own.

Solved Examples on Profit %

1. Find Profit % if,
a) SP= 140 and CP= 100
b) SP= 220 and CP= 200
c) SP= 70 and CP= 50

Solution:

a) SP= 180 and CP= 140
Profit(P)= Selling price(SP) – Cost Price (CP).
= 180-140
= 40.
Profit = 40
Profit % = Profit/CP × 100.
= (40/100)×100
= 40%

b) SP= 220 and CP= 200
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 220-200
= 20
Profit= 20
Profit% = profit/CP × 100.
= (20/200)×100
= (1/10)×100
= 10%.

c) SP= 60 and CP= 50
Profit(P)= Selling Price(SP) – Cost Price (CP).
= 60-50
= 10
Profit= 10
Profit%= profit/CP × 100.
= (10/50)×100
= (1/5)×100
= 20.

2. A man bought 50 bulbs for Rs 125 each. And sells them at Rs 150 each. Find the profit and profit percent?

Solution:

The selling price of the bulb= Rs 150
The cost price of the bulb= Rs 125.
So, Profit (P)= Selling Price(SP)- Cost Price(CP)
= Rs 150- Rs 125
= Rs 25
Profit = Rs 25.
Now to find the Profit percentage, apply the formula
Profit% = Profit/CP × 100.
= (25/125)×100
= (1/5)×100
= 20%.

Related Articles:

• Profit and Loss
• Calculate Loss and Loss Percent

Learn how to arrange Rational Numbers in Descending Order or Decreasing Order. In order to make you familiar with the concept of Rational Numbers in Decreasing Order we even listed examples explaining the step by step process. Check out the general method to arrange rational numbers from Largest to Smallest easily.

Procedure to arrange Rational Numbers from Largest to Smallest

Follow the easy guidelines on how to arrange Rational Numbers in Decreasing Order. They are as follows

Step 1: Express the given rational number in terms of the positive denominator.

Step 2: Find out the Least Common Denominator of the Positive Denominators.

Step 3: Express the given rational numbers using the LCM as Common Denominator.

Step 4: Compare the numerators and the one having the highest numerator is the largest one.

Solved Examples on Rational Numbers in Decreasing Order

1. Arrange the numbers 5/-3, 10/-7, -5/8 in Descending Order?

Solution:

Given Rational Numbers are 5/-3, 10/-7, -5/8

Express the Rational Numbers with Positive Denominators

5/-3 = 5*(-1)/-3*(-1) = -5/3

10/-7 = 10*(-1)/-7*(-1) = -10/7

-5/8 already has a positive denominator

Find the LCM of Positive Denominators

LCM of 3, 7, 8 is 168

Express the Rational Numbers with Common Denominator with the LCM obtained.

-5/3 = -5*56/3*56 = -280/ 168

-10/7 = -10*24/7*24 = -240/168

-5/8 = -5*21/8*21 = -105/168

Check the numerators of the rational numbers. Since all of them are negative numbers the lesser one is the highest fraction.

Therefore, Rational Numbers in Descending Order are -5/8, 10/-7, 5/-3.

2. Arrange the Rational Numbers 4/9, 5/6, 7/12 in Descending Order?

Solution: 

Given Rational Numbers are 4/9, 5/6, 7/12

Find the LCM of the Positive Denominators

LCM of 9, 6, 12 is 36

Express the Rational Numbers in terms of Common Denominator using the LCM obtained earlier.

4/9 = 4*4/9*4 = 16/36

5/6 = 5*6/6*6 = 30/36

7/12 = 7*3/12*3 = 21/36

Check the numerators of the rational numbers and the one having highest numerator is the highest rational number.

5/6, 7/12, 4/9 is the Descending Order of Rational Numbers.

3. Arrange the Rational Numbers 3/8, 5/7, 2/9 in Descending Order?

Solution:

Given Rational Numbers are 3/8, 5/7, 2/9

Determine the LCM of Positive Denominators.

LCM of 8, 7, 9 is 504.

Express the rational numbers with common denominator using the LCM obtained.

3/8 = 3*63/8*63 = 189/504

5/7 = 5*72/7*72 = 360/504

2/9 = 2*56/9*56 = 112/504

Check the numerators of the rational numbers and arrange the ones from highest to lowest.

Therefore Rational Numbers arranged in Descending Order is 5/7, 3/8, 2/9.

We are all familiar with the concept of comparing two integers or two fractions and determining which is smaller or greater. Let us go a step ahead and compare Two Rational Numbers. We know fact that every positive integer is greater than 0, and a negative integer is less than 0. By knowing this fundamental rule we can infer some facts about how to compare rational numbers. They are listed below

1. Every Positive Rational Number is Greater than Zero.
2. Every Negative Rational Number is Less than Zero.
3. Comparison of Positive and Negative Rational Number is quite obvious i.e. Positive Rational Number is greater than a negative rational number.
4. Every Rational Number represented on a number line is greater than every other rational number represented present to its left.
5. Every Rational Number represented on a number line is less than every other rational number represented present to its right.

How to Compare Rational Numbers?

In order to compare any two rational numbers, you can go through the below-mentioned steps. They are as under

Step 1: Check the given rational numbers

Step 2: Write down the given rational numbers in a way that they have their denominators the same.

Step 3: Determine the Least Common Multiple of the Positive Denominators you obtained in the earlier step.

Step 4: Express rational numbers obtained in the second step using the LCM obtained as Common Denominator.

Step 5: Compare the numerators of rational numbers obtained and declare the one having a greater numerator as a greater rational number.

Solved Examples

1. Of the two rational numbers which is greater 2/3 or 5/7?

Solution: 

Given Rational Numbers are 2/3, 5/7

LCM of 3, 7 is 21

Expressing the rational numbers with the same denominator using the LCM obtained we get

Therefore, we get 2/3 = (2*7)/(3*7) = 14/21

5/7 = (5*3)/(7*3) = 15/21

See the numerators of both the rational numbers obtained i.e. 14/21, 15/21

Since 15 is greater the rational number 5/7 is greater.

Therefore, of the two rational numbers, 2/3 and 5/7,  5/7 is greater.

2. Which of the two rational numbers 2/5 and -3/4 is greater?

Solution:

Given Rational Numbers are 2/5 and -3/4

We clearly know between a positive rational number and a negative rational number positive rational number is always greater.

Therefore, 2/5 is greater than -3/4.

3. Which is greater among -1/2 and – 1/5?

Solution: 

Given rational numbers are -1/2 and -1/5

LCM of 2, 5 is 10

Expressing the rational numbers with the same denominator using the LCM obtained.

-1/2 = (-1*5)/(2*5)= -5/10

-1/5 = (-1*2)/(5*2) = -2/10

-2 > -5

Therefore, – 1/5 is greater than -1/2.

4. Which of the numbers 3/4 and -3/4 are greater?

Solution:

We know that every positive rational number is greater than a negative rational number. Therefore, 3/4 is greater than -3/4.