6 Write Five Rational Numbers Greater Than 2
How to add, subtract, multiply and divide rational numbers
The number -4 is a distance of 4 units away from 0 on the number line. The number -63 is more than 4 units away from 0 on the number line. The number 4 is greater than the number -4. The numbers 4 and -4 are the same distance away from 0 on the number line. The number -63 is less than the number 4. Rational numbers can be negative and negative rational numbers are smaller than zero. Question 66: Match the following: Solution: Question 67: Write each of the following rational numbers with positive denominators. Solution: Question 68: Express as a rational number with denominator: (a)36 (b) 80 Solution: Question 69.
A rational number is a number that can be written as a simple fraction (i.e. as a ratio ). Examples: Number As a Fraction 5 5/1 1.75 7/4 .001 1/1000 0.111.. 1/9 In general ..
So a rational number looks like this:
p q
But q cannot be zero, as that is dividing by zero. How to Add, Subtract, Multiply and Divide
When the rational number is something simple like 3 , or 0.001 , then just use mental arithmetic, or a calculator!
But what about when it is in p q form?
Well, a rational number is a fraction, so we can use:
Adding Fractions,
Subtracting Fractions,
Multiplying Fractions and
Here we will see those operations in a more general Algebra style.
You might also like to read Fractions in Algebra.
Let us start with multiplication, as that is the easiest. Multiplication
To multiply two rational numbers multiply the tops and bottoms separately , like this:
Here is an example: Division
To divide two rational numbers, first flip the second number over (make it a reciprocal) and then do a multiply like above:
Here is an example: Addition and Subtraction
We will cover Addition and Subtraction in one go, as they are the same method.
Before we add or subtract, the rational numbers should have the same bottom number (called a Common Denominator).
The easiest way to do this is to
Multiply both parts of each number by the bottom part of the other
Like this (note that the dot means multiply):
Here is an example of addition:
And an example of subtraction (the middle step is skipped to make it quicker): Simplest Form
Sometimes we have a rational number like this:
10 15
But that is not as simple as it can be!
We can divide both top and bottom by 5 to get: 5 10 15 = 2 3 5
Now it is in 'simplest form', which is how most people want it! Be Careful With 'Mixed Fractions'
We may be tempted to write an Improper Fraction (a fraction that is 'top-heavy', i.e. where the top number is bigger then the bottom number) as a Mixed Fraction:
For example 7 / 4 = 1 3 / 4 , shown here:
Improper Fraction
Mixed Fraction 7 / 4 1 3 / 4 =
But for mathematics the 'Improper' form (such as 7 / 4 ) is actually better .
Because Mixed fractions (such as 1 3 / 4 ) can be confusing when we write them down in a formula, as it can look like a multiplication : Mixed Fraction: What is: 1 + 2 1 4 ? Is it: 1 + 2 + 1 4 = 3 1 4 ? Or is it: 1 + 2 1 4 = 1 1 2 ? Improper Fraction: What is: 1 + 9 4 ? It is: 4 4 + 9 4 = 13 4
So try to use the Improper Fraction when doing mathematics.
Rational Numbers between Two Rational Numbers :
Let us consider the two rational numbers a/b and c/d. Here a, b, c and d are integers and also b 0, d 0.
We can find many rational numbers between a/b and c/d using the two methods given below.
1. Formula method
2. Same denominator method Formula Method
Let a and b be any two given rational numbers. We can find many rational numbers q1, q2, q3,..in between a and b as follows :
The numbers q2, q3 lie to the left of q1. Similarly, q4, q5 are the rational numbers between a and b lie to the right of q1 as follows:
Important Note :
Average of two numbers always lies between them.
Same Denominator Method
Let a and b be two rational numbers.
(i) Convert the denominator of both the fractions into the same denominator by taking LCM. Now, if there is a number between numerators there is a rational number between them.
(ii) If there is no number between their numerators, then multiply their numerators and denominators by 10 to get rational numbers between them.
To get more rational numbers, multiply by 100, 1000 and so on.
Important Note :
By following different methods one can get different rational numbers between a and b. Rational Numbers between Two Rational Numbers
Example 1 :
Find a rational number between 3/4 and 4/5
Solution :
Formula Method :
Let a = 3/4 and b = 4/5
Let q be the rational number between 3/4 and 4/5.
Then, we have
q = 1/2 x (a + b)
q = 1/2 x (3/4 + 4/5)
q = 1/2 x (15 + 16) / 20
q = 1/2 x 31/20
q = 31/40
So, the rational number between 3/4 and 4/5 is 31/40.
Same Denominator Method :
Let a = 3/4 and b = 4/5
L.C.M of the denominator (4, 5) is 20.
So, we can write 'a' and 'b' as given below
a = 3/4 x 5/5 = 15/20
and
b = 4/5 x 4/4 = 16/20
To find a rational number between 15/20 and 16/20 , we have to multiply the numerator and denominator by 10.
Then, we have
15/20 x 10/10 = 150/200
16/20 x 10/10 = 160/200 Sqlpro studio 1 0 169 powerful database manager roles.
Therefore, the rational numbers between 150/200 and 160/200 are 151/200, 152/200, 153/200, 154/200, 155/200, 156/200, 157/200, 158/200 and 159/200.
Example 2 :
Find two rational numbers between -3/5 and 1/2.
Solution :
Let a = -3/5 and b = 1/2
Natural Numbers
Let q1 and q2 be the rational number between -3/5 and 1/2.
First, let us get q1.
q1 = 1/2 x (a + b)
q1 = 1/2 x (-3/5 + 1/2)
q1 = 1/2 x (-6 + 5) / 10
q1 = 1/2 x (-1/10)
q1 = -1/20
Now, let find q2.
q2 = 1/2 x (a + q1)
q2 = 1/2 x (-3/5 - 1/20)
q2 = 1/2 x (-12 - 1) / 20
q2 = 1/2 x (-13/20) 6 Write Five Rational Numbers Greater Than 22
q2 = -13/40
So, the two rational number are -1/20 and -13/40.
Note :
The two rational numbers can be inserted as
-3/5 -13/40 -1/20 1/2 Real Numbers
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
ALGEBRA
Negative exponents rules
COMPETITIVE EXAMS
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
WORKSHEETS
TRIGONOMETRY
Trigonometric identities
MENSURATION
GEOMETRY
COORDINATE GEOMETRY
CALCULATORS
MATH FOR KIDS
LIFE MATHEMATICS
SYMMETRY
CONVERSIONS
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Trigonometry word problems Integers
Word problems on mixed fractrions
OTHER TOPICS
Ratio and proportion shortcuts 6 Write Five Rational Numbers Greater Than 24
Converting repeating decimals in to fractions
SBI!
The number -4 is a distance of 4 units away from 0 on the number line. The number -63 is more than 4 units away from 0 on the number line. The number 4 is greater than the number -4. The numbers 4 and -4 are the same distance away from 0 on the number line. The number -63 is less than the number 4. Rational numbers can be negative and negative rational numbers are smaller than zero. Question 66: Match the following: Solution: Question 67: Write each of the following rational numbers with positive denominators. Solution: Question 68: Express as a rational number with denominator: (a)36 (b) 80 Solution: Question 69.
A rational number is a number that can be written as a simple fraction (i.e. as a ratio ). Examples: Number As a Fraction 5 5/1 1.75 7/4 .001 1/1000 0.111.. 1/9 In general ..
So a rational number looks like this:
p q
But q cannot be zero, as that is dividing by zero. How to Add, Subtract, Multiply and Divide
When the rational number is something simple like 3 , or 0.001 , then just use mental arithmetic, or a calculator!
But what about when it is in p q form?
Well, a rational number is a fraction, so we can use:
Adding Fractions,
Subtracting Fractions,
Multiplying Fractions and
Here we will see those operations in a more general Algebra style.
You might also like to read Fractions in Algebra.
Let us start with multiplication, as that is the easiest. Multiplication
To multiply two rational numbers multiply the tops and bottoms separately , like this:
Here is an example: Division
To divide two rational numbers, first flip the second number over (make it a reciprocal) and then do a multiply like above:
Here is an example: Addition and Subtraction
We will cover Addition and Subtraction in one go, as they are the same method.
Before we add or subtract, the rational numbers should have the same bottom number (called a Common Denominator).
The easiest way to do this is to
Multiply both parts of each number by the bottom part of the other
Like this (note that the dot means multiply):
Here is an example of addition:
And an example of subtraction (the middle step is skipped to make it quicker): Simplest Form
Sometimes we have a rational number like this:
10 15
But that is not as simple as it can be!
We can divide both top and bottom by 5 to get: 5 10 15 = 2 3 5
Now it is in 'simplest form', which is how most people want it! Be Careful With 'Mixed Fractions'
We may be tempted to write an Improper Fraction (a fraction that is 'top-heavy', i.e. where the top number is bigger then the bottom number) as a Mixed Fraction:
For example 7 / 4 = 1 3 / 4 , shown here:
Improper Fraction
Mixed Fraction 7 / 4 1 3 / 4 =
But for mathematics the 'Improper' form (such as 7 / 4 ) is actually better .
Because Mixed fractions (such as 1 3 / 4 ) can be confusing when we write them down in a formula, as it can look like a multiplication : Mixed Fraction: What is: 1 + 2 1 4 ? Is it: 1 + 2 + 1 4 = 3 1 4 ? Or is it: 1 + 2 1 4 = 1 1 2 ? Improper Fraction: What is: 1 + 9 4 ? It is: 4 4 + 9 4 = 13 4
So try to use the Improper Fraction when doing mathematics.
Rational Numbers between Two Rational Numbers :
Let us consider the two rational numbers a/b and c/d. Here a, b, c and d are integers and also b 0, d 0.
We can find many rational numbers between a/b and c/d using the two methods given below.
1. Formula method
2. Same denominator method Formula Method
Let a and b be any two given rational numbers. We can find many rational numbers q1, q2, q3,..in between a and b as follows :
The numbers q2, q3 lie to the left of q1. Similarly, q4, q5 are the rational numbers between a and b lie to the right of q1 as follows:
Important Note :
Average of two numbers always lies between them.
Same Denominator Method
Let a and b be two rational numbers.
(i) Convert the denominator of both the fractions into the same denominator by taking LCM. Now, if there is a number between numerators there is a rational number between them.
(ii) If there is no number between their numerators, then multiply their numerators and denominators by 10 to get rational numbers between them.
To get more rational numbers, multiply by 100, 1000 and so on.
Important Note :
By following different methods one can get different rational numbers between a and b. Rational Numbers between Two Rational Numbers
Example 1 :
Find a rational number between 3/4 and 4/5
Solution :
Formula Method :
Let a = 3/4 and b = 4/5
Let q be the rational number between 3/4 and 4/5.
Then, we have
q = 1/2 x (a + b)
q = 1/2 x (3/4 + 4/5)
q = 1/2 x (15 + 16) / 20
q = 1/2 x 31/20
q = 31/40
So, the rational number between 3/4 and 4/5 is 31/40.
Same Denominator Method :
Let a = 3/4 and b = 4/5
L.C.M of the denominator (4, 5) is 20.
So, we can write 'a' and 'b' as given below
a = 3/4 x 5/5 = 15/20
and
b = 4/5 x 4/4 = 16/20
To find a rational number between 15/20 and 16/20 , we have to multiply the numerator and denominator by 10.
Then, we have
15/20 x 10/10 = 150/200
16/20 x 10/10 = 160/200 Sqlpro studio 1 0 169 powerful database manager roles.
Therefore, the rational numbers between 150/200 and 160/200 are 151/200, 152/200, 153/200, 154/200, 155/200, 156/200, 157/200, 158/200 and 159/200.
Example 2 :
Find two rational numbers between -3/5 and 1/2.
Solution :
Let a = -3/5 and b = 1/2
Natural Numbers
Let q1 and q2 be the rational number between -3/5 and 1/2.
First, let us get q1.
q1 = 1/2 x (a + b)
q1 = 1/2 x (-3/5 + 1/2)
q1 = 1/2 x (-6 + 5) / 10
q1 = 1/2 x (-1/10)
q1 = -1/20
Now, let find q2.
q2 = 1/2 x (a + q1)
q2 = 1/2 x (-3/5 - 1/20)
q2 = 1/2 x (-12 - 1) / 20
q2 = 1/2 x (-13/20) 6 Write Five Rational Numbers Greater Than 22
q2 = -13/40
So, the two rational number are -1/20 and -13/40.
Note :
The two rational numbers can be inserted as
-3/5 -13/40 -1/20 1/2 Real Numbers
Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.
If you have any feedback about our math content, please mail us :
v4formath@gmail.com
We always appreciate your feedback.
You can also visit the following web pages on different stuff in math.
ALGEBRA
Negative exponents rules
COMPETITIVE EXAMS
APTITUDE TESTS ONLINE
ACT MATH ONLINE TEST
TRANSFORMATIONS OF FUNCTIONS
ORDER OF OPERATIONS
WORKSHEETS
TRIGONOMETRY
Trigonometric identities
MENSURATION
GEOMETRY
COORDINATE GEOMETRY
CALCULATORS
MATH FOR KIDS
LIFE MATHEMATICS
SYMMETRY
CONVERSIONS
WORD PROBLEMS
HCF and LCM word problems
Word problems on simple equations
Word problems on linear equations
Trigonometry word problems Integers
Word problems on mixed fractrions
OTHER TOPICS
Ratio and proportion shortcuts 6 Write Five Rational Numbers Greater Than 24
Converting repeating decimals in to fractions
SBI!
