The post NCERT 5th Class (CBSE) Mathematics: Introduction To Algebra appeared first on Class Notes.

]]>**Can you give the mathematical expressions for these words?**

- Seventy three minus forty -two
- Twelve less two
- Six times fifteen
- Thirty plus eleven take away nine

Sometimes, in a mathematical expression, we use letters to represent numbers we do not know.

If we say that there were some people at a party and 7 people left, we can show this as an expression, n-7, where n represents the number of people in the party.

If there were 12 people at the party, then n would represent 12. If there were 20 people at the party, then n would represent 20.

**These letters are called variable because they can represent any number.**

**CHECKPOINT:** When we write an expression using variables, words and/or operations, it is called an algebraic expression.

Let *p* be the number of pencils in your pencil box. Study the algebraic expressions for each:

12 pencils more than the number of pencils in your box → *p* + 12 or 12 + *p*

4 pencils less than the number of pencils in your box → *p* – 4

Three times the number of pencils in your box. → 3 × *p* also written as 3*p*

The number of pencils in your box divided by 4 → *p* ÷ 4 also written as p/4

**Here, the expressions have been put into words. The unknown number or the variable is ***w.*

18 + *w *→ *w* added to 18

10 – *w *→ *w* subtracted from 10

7*w *→ The product of *w* and 7

6 ÷ *w *→ 6 divided by *w*

If we know that *w* = 3, Then expressions above can be simplified and a value can be obtained for each expression.

If we substitute 3 in place of *w*, we get

18 + *w* = 18 + 3 = 21

10 – *w = *10 – 3 = 7

7*w* = 7 × 3 = 21

6 ÷ *w = *6 ÷ 3 = 2

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]]>The post NCERT 5th Class (CBSE) Mathematics: Area And Volume appeared first on Class Notes.

]]>This stamp has been stuck on centimeter-squared paper. Take each square to have a side of 1 cm.

So, the perimeter of the stamp is 14 cm.

Perimeter = 2 × (l + b)

We can say that the stamp covers an area of 12 square centimeters or 12 sq. cm.

You can count half squares and add them to make full squares while finding the are of shapes like this. 9 full squares, 8 half squares = 4 full squares, 9 + 13, Area = 13 sq. cm

This is the image of a thumbprint. It does not have a regular shape. We have to estimate the area of shapes like this. Complete squares = 5, Incomplete squares combining to make complete squares = about 5 squares, 5 + 5 = 10 squares, Area of thumbprint = about 10 sq. cm

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]]>The post NCERT 5th Class (CBSE) Mathematics: Polygons And Circles appeared first on Class Notes.

]]>The word triangle means three angles. The given triangle has three angles ∠A, ∠B and ∠C. Points A, B and C are the vertices of triangle ABC. The sides of the triangle are AB, BC and CA.

A quadrilateral is a closed shape with 4 straight sides.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Lines And Angle appeared first on Class Notes.

]]>**CHECK IN**

A protractor is used to measure angles.

This angle is measured on the inner scale as the baseline arm point to 0° on the inner scale. The other arm crosses 50° showing that ∠ AOB = 50°.

Angles are named according to their measures.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Graphical Representation appeared first on Class Notes.

]]>- Pictograph use pictures or symbols to represent information.
- It has a title.
- It gives the definition of the symbol or the key. The key is defined such that it represents the entire data.
- pictographs help you understand the information by allowing you to compare the data shown.

(a) The table shows the number of magazines published for children.

Weekly magazines

50

Fortnightly magazines

30

Monthly magazines

100

Quarterly magazines

50

This pictograph shows the same information.

(b) Represent the following information in the form of a pictograph. Give the pictograph a title and show what your symbol stands for

Favorite TV channels in Class V:

Comedy – 15 children, Cartoons – 25 children, Sports – 10 children, Adventure – 5 children.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Application Of Percentage appeared first on Class Notes.

]]>Mr Gupta makes very good rocking chairs. It coast him Rs. 795 to make one rocking chair. He sells it in his furniture shop at Rs. 900.

Rs. 795 is the Cost Price (CP) of the chair.

Rs. 900 is the Selling Price (SP) of the chair.

Since he sells it for more than it costs to make, he earn money by doing so. This is called his **profit**.

Rs. 900 SP

Rs. – 795 CP

Rs. 105 **Profit**

Formula to calculate profit → **SP – CP = Profit**

There is one rocking chair with a small scratch on it. Mr Gupta sells this particular chair for Rs. 715. Since he sells it for less than what it costs him to make it, he loses money on the sale. This is called his **loss**.

Rs. 795 CP

Rs. – 715 SP

Rs. 80 **Loss**

Formula to calculate Loss → **CP**** – SP = Loss**

**CHECKPOINT**

- When SP > CP the difference (SP – CP) is Profit.
- When SP < CP the difference (CP – SP) in Loss.

Mr Gupta delivered one rocking chair to another town. It costs him Rs. 105 to do so. The cost price of this particular chair is now Rs. 975 + Rs. 105 = Rs. 900. If he sell this chair at Rs. 1000 what is his profit or loss on the chair?

SP = Rs. 1000

CP = Rs. 900

Comparing the SP and CP, we see that SP > CP , so there is a profit.

SP – CP = Profit

1000 – 900 = 100

Mr Gupta makes a profit of Rs. 100 on the chair.

Ramu bought apples from a farmer and sold them in the market. He sells them at Rs. 70 for a kilo and makes a profit of Rs. 23 on each kilo. How much did Ramu pay per kilo apples?

He also bought oranges from the farmer. He sold them in the market at Rs. 95 per dozen. This was at a loss of Rs. 12 per dozen. What did 1 dozen oranges cost him?

Selling price of one kilo apples = Rs. 70

Selling price of one dozen oranges = Rs. 95

Profit = Rs. 23

Loss = Rs. 12

Cost price = ?

Cost price = ?

CP = SP – Profit

CP = SP + Loss

CP = Rs. 70 – Rs. 23 = Rs. 47

CP = Rs.95 + Rs. 12 = Rs. 107

SP – CP = Profit

CP – Sp = Loss

Rs. 70 – Rs. 23 = Rs. 47

Rs. 107 – Rs. 95 = Rs. 12

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]]>The post NCERT 5th Class (CBSE) Mathematics: Percentage appeared first on Class Notes.

]]>Using fractions we can say 43/100 of her coins are Indian coins.

Using decimals we can say 0.43 coins of her collection are Indian coins. We can also express this as a percentage. The word per cent means ‘per one hundred’. We use the sign % to represent per cent.

43% of Anisha’s coins collection is Indian.

We use percentage very often in our every day lives. Sometimes we use it to compare numbers, sometimes just to understand them. If you see a sale sign that says 20% off it means that for every item that costs Rs. 100 you have to pay Rs. 20 less. If we say that 9% of people were spectacles it means that for every 100 people 9 people were spectacles.

So, 1% means 1 out of 100 or 1/100.

99% means 99 out of 100 or 99/100.

This is a page out of Sunil’s stamp album. The page has 100 stamps. He has stuck them according to their color.

Blue

50/100

0.5

50%

Yellow

15/100

0.15

15%

Red

30/100

0.3

30%

Green

5/100

0.05

5%

**CHECK POINT**

- Any number that can be written as a fraction or decimal can also be written as a percent.
- We use per cent to compare a number with hundred.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Ratio And Proportion appeared first on Class Notes.

]]>Subtraction is one way to compare the quantities of yellow and blue paint that Yash used 2 tubes (of blue) – 1 tube (of yellow) = 1 tube. So, we can say that he used one more tube of blue paint than yellow paint to find his perfect green.

Another way to compare the amounts of yellow and blue paint is to use ration.

**A ratio compares like quantities.**

The ration of the yellow tubes to the blue tubes is 1:2 and read as 1 is to 2 or 1 to 2.

we can write it as 1 : 2, 1 to 2 or 1/2. ←** Written in from a ration looks like a fraction**

Look at this group of parrots and sparrows. the ratio of parrots to sparrows is 3 parrots to 4 sparrows.

We write it as 3 : 4, 3 to 4 or 3/4

We say the ration of parrots to sparrows is three is to four.

The ratio of sparrows to parrots is 4 sparrows to 3 parrots.

We write it as 4 : 3, 4 to 3 or 4/3

We say the ratio of sparrow to parrots is four is to three.

- The order of numbers in a ratio is very important.
- The second term in a ratio cannot be zero.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Decimals appeared first on Class Notes.

]]>The Decimals point is always placed after the ones place.

After the decimal point, the place values are tenths, hundredths, thousandths, … All these places have a value less than one.

1.37 is read as one thirty-seven hundredths. It is also read as one point three seven.

Three and four tenths or three point four.

4/10 = 0.4

Four tenths or zero point four

Three and six hundredths or three point zero six

6/100 = 0.06

Six hundredths or zero point zero six.

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]]>The post NCERT 5th Class (CBSE) Mathematics: Fractions appeared first on Class Notes.

]]>A whole can be region or a collection.

You are familiar with these fractions.

**Like Fractions:**Fractions that have same denominator are called like fractions, e.g., 3/7, 5/7, 1/7**Unlike fractions:**Factions that have different denominators are called unlike fractions, e.g., 4/7, 3/8, 2/3**Proper fractions****:**A fractions with the numerator less than the denominator is a proper fraction. A proper fraction has a value less than 1. For example, 1/8, 4/9, 3/5**Improper fraction:**A fraction that has the numerator greater that equal to the denominator is called an improper fraction and its value is 1 or more than 1. For example, 5/2, 10/7, 8/3, 9/9**Mixed number:**When we combine a whole number and a fraction, we get a mixed number. For example,

**Equivalent fractions: **Fractions that name the same part are called equivalent fractions.

You can find equivalent fractions by multiplying or dividing the numerator and the denominator by the same number.

1 (×4)/2 (×4) = 4/8

4 (÷2)/8 (÷2) = 2 (÷2)/4 (÷2) = 1/2

You can cross multiply to check whether two fractions are equivalent.

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