Direct Speech and Indirect Speech

Direct Speech and Indirect Speech
Direct and Indirect Speech is one of the very important concepts in English learning. Speech can be classified into direct speech and indirect speech. Let’s have a look at the same in this post along with some examples for better understanding.

Direct Speech
Direct speech is a type of speech that exactly says what someone has said. In direct speech, the exact saying is repeated or quoted and the words spoken are written within inverted commas (“-----“). Direct speech is therefore also referred as quoted speech.

Examples of Direct Speech
1. Uncle John said, “I have bought an infant play gym for my son. It is not just fun but is also healthy.”
2. Mary asked, “Have you tried online diaper purchase?”

Here, in the first sentence, the speech of Uncle John speaking about his buying an infant play gym for his son is exactly presented. On the other hand, in the second sentence Mary’ question to on trying online diaper purchase is repeated exactly.

Indirect Speech
Indirect speech is a type of speech that encloses what a person has said. It doesn’t use quotations and is not repeated exactly like direct speech. In indirect speech, the tense usually changes as when we use indirect speech, we generally speak about something in the past.

Examples of Indirect Speech
1. Roy said that he enjoys to shop baby online products as it is easy and fast.
2. Mohan asked to Riya whether her kid has started going to school.
Here, in the first sentence, the Roy’s enjoying to shop baby online products is reported indirectly and not repeated. On the other hand, in the second sentence Mohan’s question about Riya’s kid going to school is similarly reported and not repeated.

Change direct speech to indirect speech:
1. Tony said, “I enjoy shopping for kids online.”
Tony said that he enjoys shopping for kids online.
2. Maria asked, “Do you eat non-vegetarian food?”
Maria asked me if I eat non-vegetarian food.
3. Father asked, “How long have you worked here?”
Father asked me how long I was working there.

Active and Passive Voice

Active and Passive Voice are two of the most essential concepts in English grammar. Taught in early middle school, active and passive voice is used extensively while speaking English language. Active voice and passive voice are two special forms of verbs. Let’s have a look at active voice definition and passive voice definition along with examples.

Active Voice
When the subject of a sentence performs the action expressed by the verb, the verb form is in active voice. In other words, the object receives the action of the verb. Active voice is most commonly used while speaking English.

Examples of Active Voice:
1. Mrs. Shah gets two baby dresses from  Little Kangaroo Kids wear collection. (Here, ‘Mrs. Shah’ is the subject, ‘gets’is the verb and ‘two baby dresses from Little Kangaroo Kids’ wear collection’ is the object.)
2. Maya shops baby clothing from online newborn baby clothes India stores. (Here, ‘Maya’ is the subject, ‘shops’ is the verb and ‘baby clothing from online newborn baby clothes India stores’ is the object.)
3. Ram sings a song. (Here, ‘Ram’ is the subject, ‘sings’ is the verb and ‘a song’ is the object.)

Passive Voice
When a subject in a sentence is acted by some other agent or something unnamed, the verb form is in passive voice. Passive voice is generally used when the action is more important than the subject in a conversation.

Examples of Passive Voice:
1. Infant clothes online India collection is explored by Mina. (Here, the subject Infant clothes online India collection’ is acted by the other agent ‘Mina’.)
2. Disney toys are loved by kids. (Here, ‘Disney toys’ is the subject, ‘is loved’ is the verb and ‘by kids’ is the object.)
3. Fish are eaten by cats. (Here, ‘Fish’ is the subject, ‘are eaten’ is the verb and ‘by cats’ is the object.

Active to Passive Voice:
1. Rama loves Sita
Answer: Sita is loved by Rama
2. Everybody believes in God
Answer: God is believed by everybody
3. Mother shops baby essentials from online stores
Answer: Baby essentials from online stores are shopped by mother
These are the basics about active and passive voice.

Scientific Notation Definition

Scientific Notations are standard way of writing number which are too small or too big.
In this standard notation all numbers are written in the form of:
m * 10n
here exponent n is an integer, m is mantissa which is a real number.
Scientific Notation Rules are as follows:
The value of mantissa holds a real number from 1 to 9 and exponent n contains the place value to get the original number.
If the decimal shifts to left by ‘n’, then the value of exponent increases by ‘n’. if decimal shifts to right the exponent decreases by 1 for each shift.
For addition or subtraction of numbers in scientific notations form their exponents should be same.
For multiplication of two such numbers, mantissa is multiplied and exponents are added.  
For division exponents are subtracted.

Scientific Notation Problems are as follows:
Q.1) Write the following numbers in scientific notations form:
1) 56788
2) 67.345
3) -6890
4) 0.000009888
5) 978.0 * 10-5
Sol.1)
1) 56788 = 5.6788 * 104. As we know that the mantissa can be real number from one to 9 so we shifted decimal to left four times and hence the exponent of 10 increases by 4.
2) 67.345 = (67.345)*100, in this number, value of mantissa is greater than 1 hence we shift the decimal to left and increase exponent by 1. So its scientific notations form is: 6.7345 * 101
3) -6890 = (-6.890)*103 by using rule used in above solution.
4) 0.000009888 = (0.000009888)*100. This number is less than one hence we will shift the decimal to the write and decrease the decimal by 1 for each right shift.
(9.888)* 10(0-6) = 9.888*10-6.
5) 978.0 * 10-5 is in exponential form but not in standard scientific notations as mantissa is greater than 1. So, shift it to let two time and increase exponent by 2 to get 9.78 * 10-5+2 = 9.78*10-3

Q.2) Solve the following:
1) (7.0  x  102)+(9.4 x 106)
2) (9.4 x 104)(3.5 x 10 –5)
3) (3.5  x  10 – 2)/(9.6 x 10 – 4)
Sol.2)
1) As exponents are not same. 9.4x106 = 94000 x 102
    (3.0  x  102)
  + (94000.0  x  102)
      94003.0 x 102 = 9.4003 x 106
2) (9.4 x 104) (3.5 x 10 –5)=(9.4 x 3.5) x 10(4+(-5))  (exponents are added as multiplication operation)
= 32.9 x 10-1
= 3.29 x 100
3) (3.5  x  10 – 2) / (1.5 x 10 – 4)
= (3.5/1.5) x 10 (-2-(-4)) (exponents are subtracted as division operation)
= 2.33 x 102

Present Tense and its types

Tense in English refers to the time of the verb’s action or state of being. There are three types of tenses – Present tense, Past tense and Future tense. Present tense refers to present action or state of being; past tense refers to past action or state of being while future tense refers to a future state of action or being. These three major types of tenses can be further classified into sub-categories. Let’s have a look at present tense and its classifications in this post.
Present Tense: Present tense is a type of tense that refers to some action or expression in the present time. For example: I am exploring online baby stores for new born shopping for my niece. Here, the sentence is referring to an action of exploring online baby stores for new born shopping in the present time and therefore, it is in present tense.

Types of Present Tense:
•         Present Continuous
•         Present Perfect
•         Present Perfect Continuous

Present Continuous Tense
Present continuous tense talks about an action that is still going on in the present time i.e.  continuing. For example: My cousin is using mustard seeds pillow for her baby. Here, mustard seeds pillow is still on use and therefore, the sentence is in present continuous tense.
Present Perfect Tense
Present perfect tense is that which speaks about something that began in the past and completes in the present. For example: John has solved the jigsaw puzzle. Here, John started solving the jigsaw puzzle in the past and finished it in the present and therefore, the sentence is in present perfect tense.
Present Perfect Continuous Tense
Present perfect tense is that which speaks about something that began in the past and is continuing in the present. For example: Jane has been buying baby essentials from online shopping baby stores from quite some time. Here, Jane started buying baby essentials from online shopping baby stores in the past and continuing in the present and therefore, the sentence is in present perfect continuous tense.
These are the basics about present tense and its types.

Subject and Predicate

Subject and Predicate are the most important concepts of English grammar. Introduced in the middle-school studies, subject and predicate plays an important role throughout the usage of English language. Every complete sentence conveying a meaning has two parts – the subject and the predicate. Let’s have a look at these two parts, its definitions and examples for better understanding.
Subject:
The subject is what or whom, the sentence is about. In simple terms, a person or thing that is discussed, described or dealt with in a sentence is called a subject of a sentence. For example:
• Mina has bought Pigeon products for babies. (Here, ‘Mina’ is the subject because the sentence talks about her buying Pigeon products for babies.
• Pigeon has wide range of products like baby diapers, shampoo, soap etc. (Here, ‘Pigeon’ is the subject as the sentence is talking about the brand.)
Predicate:
Predicate is a part of sentence that speaks something about the subject. It is a verb that states something about the subject. For example:
• John’s parents usually buy baby products India collection from online stores. (Here, ‘usually buy baby products India collection from online stores’ is the predicate of the sentence as it talks about the subject.)
• My uncle has recently started buying accessories from baby product online India stores. (Here, ‘has recently started buying accessories from baby product online India stores’ is the predicate of the sentence.)
More examples:
• I love my pet a lot. (‘I’ is the subject while ‘love my pet’ is the predicate)
• Hari is a busy person. (‘Hari’ is the subject while ‘is a busy person’ is the predicate)
• Online baby stores have made shopping easy for parents. (‘Online baby stores’ is the subject and ‘have made shopping easy for parents’ is the predicate.)
• Jack sings well. (‘Jack’ is the subject and ‘sings well’ is the predicate.)
• India is our motherland. (‘India’ is the subject and ‘is our motherland’ is the predicate.)

Introduction to parallel line extender:

Properties of parallel lines are the under the base of Euclid's parallel property. Two lines in a single plane that not even intersect or meet at any point then it is called as parallel lines. In other words Parallel lines are nothing but “A pair of lines in a plane which do not intersect or meet each other” then they are called parallel lines.

i.e. m1 = m2,

Where, m1 = slope of the first line.

m2 = slope of the second line.

Parallel Line Extender Problem:

Example for parallel line extender: Define the equation parallel to 4y + 4x = 8 and the line extender, with point (6.5,4).

Solution:

Given 4y - 4x = 8 and the point (6.5, 4)

To detect the perpendicular line, we have to find slope first.

For finding the slope, we need to change the given equation into slope intercept form.

4y + 4x = 8

Add 4x on both side,

4y + 4x = 8

- 4x = -4x

4y = -4x + 8

Divide by 4 on both sides,

y = (-x + 2)

The obtained equation is in the form, y = mx + b

So, the slope from the obtained equation m = -1

From generally we know that the slope of parallel lines are equal i.e. m1 = m2

Here, m1 = -1

So, m2 = -1

The line equation is,

(y - y1) = m(x - x1)

(y - (4)) = -1 (x - ( 6.5))

(y - (4)) = (-x + 6.5)

Y - 4 = - x + 6.5

Subtract 4 on both sides,

y = -x + 2.5

Answer: Thus, the parallel line extender is given through the line y = -x + 2.5

Example for Parallel Line Extender:

Example for parallel line extender: Define the equation parallel to 2y - 2x = 4 and the line extender is gets through the point (-2, 0.5).

Solution:

Given 2y - 2x = 4 and the point (4, 3)

To detect the perpendicular line, we have to find slope first.

For finding the slope, we need to change the given equation into slope intercept form.

2y - 2x = 4

Add 2x on both side,

2y - 2x = 4

+ 2x = +2x

2y = 2x + 4

Divide by 2 on both sides,

y = (x + 2)

The obtained equation is in the form, y = mx + b

So, the slope from the obtained equation m = 1

From generally we know that the slope of parallel lines are equal i.e. m1 = m2

Here, m1 = 1

So, m2 = 1

The line equation is,

(y - y1) = m(x - x1)

(y - (3)) = 1 (x - (4))

(y - (3)) = (x - 4)

Y - 3 = x - 4

Subtract 3 on both sides,

y = x - 1

Answer: Thus, the parallel line extender is used to find the line y = x - 1

Introduction to positive divisors

In math divisor is defined as “the number that you are going to divide by”. Divisor of a given integer can also be called as the divisor of a given integer.

Dividend /Divisor = Quotient.

Positive number/ Negative number = negative number

Negative number/Positive number = negative number

Positive/Positive  = Positive

Let us have an example 16/2 = 8 here 2 is a divisor.

16/4= 4 here 4 is a divisor.

16/8= 2 here 4 is a divisor.

In the above shown example the divisors are positive and also known as positive divisors.

The positive divisors when the dividend is 16 are 8, 4, and 2.

Example Problems for Positive Divisors:

Example problem 1:

Find the positive divisors of 28

Solution:

Positive Divisors of 28 are 1, 2, 4, 7, 14, and 28

Where 28 /1 = 28.

28 /2 = 14.

28 /4 = 7.

28 /7 = 4.

28 /14 = 2.

28 / 28 = 1

Hence for 28 we have 6  Positive divisors

Moreover 28 is a composite number

Example problem 2:

Find the positive divisors of 52

Solution

Positive   Divisors of 52 are 1, 2, 4, 13, 26, and 52.

Where 52/1=52.

52/2=26.

52/4=13.

52/13=4.

52/26=2.

52/52=1.

Hence for 52 we have 6   Positive divisors

Example problem 3:

Find the positive divisors of 30

Solution

Positive Divisors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30.

Where 30/1=30

30/2= 15.

30/3=10.

30/5=4.

30/6=5.

30/10=3.

30/15=2.

30/30=1

Hence for 30 we have 8 Positive divisors

Example problem 4:

Find the positive divisors of 100

Solution

The positive divisors of  100 are  1,2,4,5,10,20,25,50,100

Where 100/1=100

100/2= 50.

100/4=25.

100/5=20.

100/10=10.

100/20=5.

100/25=4.

100/50=2.

100/100=1.

Hence for 100 we have 9 Positive divisors

Example problem 5:

Find the positive divisor of 31

Solution

Given that 31 is a prime number

All the prime numbers have only two divisors

The two divisors are 1 and the numbers itself

So the positive divisor of the number 31 is 1, 31 alone.

Finally the divisors of the prime numbers are 1 and the number itself.

Practice Problems for Positive Divisors:

Problem 1:

Find the positive divisor of 63

Solution:

The divisors of 63 is 1, 3,7,9,21,63

So the number 63 has 6 divisors.

Problem 2:

Find the positive divisor of 37

Solution:

The divisors of 37 are 1, 37

Problem 3:

Find the positive divisor of 15

Solution:

The divisors of 15 is 1, 3, 5, 15

Problem 4:

Find the positive divisor of 35

Solution:

The divisors of 35 is 1, 5, 7, 35