Name the property involved in the following examples
Name the property involved in the following examples
Distributive law
This property is know as the distributive law of multiplication over addition.
For all rational numbers a, b and c
a(b + c) = ab + ac
⇒
Name the property involved in the following examples
Multiplicative identity
The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.
Name the property involved in the following examples
Multiplicative identity
The multiplicative identity property states that any time you multiply a number by 1, the result, or product, is that original number.
Name the property involved in the following examples
Commutative law of addition
In commutative law of addition, a, b is rational number where
a + b = b + a
Name the property involved in the following examples
Closure law in multiplication
We find that rational numbers are closed under multiplication. For any two rational numbers a and b, ab is also rational number.
Name the property involved in the following examples
7a + (-7a) = 0
(vii) Additive inverse law
Any two numbers whose sum is 0 are called the additive inverses of each other. In general if ‘a’ represents any rational number then a + (-a) = 0 and (-a ) + a = 0
Then a, (-a) are additive inverse of each other.
Name the property involved in the following examples
(viii) Multiplicative inverse
We say that a rational number is called the reciprocal or the multiplicative inverse of another rational number if
Name the property involved in the following examples
Distributive property
This property is known as distribution law of multiplication over addition. For all rational numbers a, b and c
a + b = b + a
Write the additive and the multiplicative inverses of the following.
Additive inverse,
Multiplicative inverse,
Explanation:- When a number is added to its additive inverse, the result zero. When a number is multiplied to its multiplicative inverse, the result is 1.
Solving for the additive inverse:-
(add to both sides)
Solving for the multiplicative inverse:-
(dividing both sides by )
Write the additive and the multiplicative inverses of the following.
1
Additive inverse, -1
Multiplication inverse, 1
Explanation:- When a number is added to its additive inverse, the result is zero. When a number is multiplied to its multiplicative inverse, the result is 1.
Solving for additive inverse:-
1 + x = 0
(add (-1) to both sides)
X = -1
Solving for the multiplicative inverse:-
1X = 1
(dividing both sides by 1)
X = 1
Write the additive and the multiplicative inverses of the following.
0
Does not exist as the answer will be 0 itself.
Write the additive and the multiplicative inverses of the following.
Additive inverse,
Multiplication inverse,
Explanation:- When a number is added to its additive inverse, the result is zero. When a number is multiplied to its multiplicative inverse, the result is 1.
Solving for additive inverse:-
(add () to both sides)
Solving for the multiplicative inverse:-
(dividing both sides by )
Write the additive and the multiplicative inverses of the following.
−1
Additive inverse, -1
Multiplication inverse, 1
Explanation:- When a number is added to its additive inverse, the result is zero. When a number is multiplied to its multiplicative inverse, the result is 1.
Solving for additive inverse:-
(-1) + x = 0
(add 1 to both sides)
X = 1
Solving for the multiplicative inverse:-
(-1)X = 1
(dividing both sides by(-1))
X = 1
Fill in the blanks.
let the blank be x
⇒
⇒
⇒
Fill in the blanks.
let the blank be x
(add on both sides)
X = 0
Fill in the blanks.
let the blank be x
Fill in the blanks.
Multiply by the reciprocal of
Reciprocal of is
According to the given question
Which properties can be used in computing
Multiplicative associative, multiplicative inverse, multiplicative identity, closure with addition are the properties used in computing.
Verify the following
LHS:-
RHS:-
LHS = RHS
Hence verified
Evaluate
after rearrangement.
Given,
(rearranging the like fractions at one place)
(Since + - = -)
(L.C.M. of 53 = 15)
Subtract
from
Given,
(By taking L.C.M.)
Subtract
from 2
Given,
(Since - - = + )
(By taking L.C.M.)
Subtract
−7 from
Given,
(Since - - = + )
(By taking L.C.M.)
What numbers should be added toso as to get.
let the unknown number be x
According to the given question,
(Add on both the sides)
(By taking L.C.M.)
The sum of two rational numbers is 8 If one of the numbers is find the other.
let the unknown number be x
According to the given question,
(Add on both the sides)
(By taking L.C.M.)
Is subtraction associative in rational numbers? Explain with an example.
Subtraction is not associative for rational numbers because when the numbers (say a,b,c) are subtracted by grouping any two at first and the other two at second [(a-b)-c and then a-(b-c)] the answer is not same. Thus subtraction is not associative in rational numbers.
Example:- let the 3 numbers be 5,8,9
Then, at first --(9-5)-8 = -4
And in second - 9-(5-8) = 9-(-3) = 12
Since, first case is not equal to second case’s answer
Verify that – (–x) = x for
x =
According to the question,
-(-x) = x
LHS:- -(-X) RHS:- X
(Since - - = + )
LHS = RHS
Hence verified
Verify that – (–x) = x for
x =
According to the question,
-(-x) = x
LHS:- -(-X) RHS:- X
(Since - - = + )
LHS = RHS
Hence verified
Write-
(i) The set of numbers which do not have any additive identity
(ii) The rational number that does not have any reciprocal
(iii) The reciprocal of a negative rational number.
(i) Natural numbers
(ii) 0(zero) is the rational number which does not have a reciprocal.
(iii) Is a negative rational number
The reciprocal of a negative number must itself be a negative number so that the number and its reciprocal multiply to 1.
Example:-
Reciprocal
Represent these numbers on the number line.
(i) 9/7 (ii) -7/5
In a rational number, the number below the bar i.e. the denominator tells the number of equal parts into which the first unit has been divided. The numerator tells ‘how many’ of these parts are considered.
(i) Here means 9 markings of each on the right of zero and starting from 0. The 9th marking is.
(ii) Here means 7 markings of each on the left of zero and starting from 0. The 7th marking is.
Write five rational numbers which are smaller than.
Now we have to write 5 numbers which are less than
It is very simple.
Therefore
are 5 numbers which are less than
Find 12 rational numbers between -1 and 2.
let us multiply and divide (-1) and 2 by 12
12 rational numbers are,
Find a rational number betweenand.
[Hint: First write the rational numbers with equal denominators.]
make denominators same
Therefore lies between and
Find ten rational numbers betweenand .
make denominators same
10 rational numbers are,
Express each of the following decimal in theform.
(i) 0.57
(ii) 0.176
(iii) 1.00001
(iv) 25.125
(i)
(ii)
(iii)
(iv)
Express each of the following decimals in the rational form .
let x =
x = 0.99999….. -→(i)
Here the periodicity of the decimal is one
So, we multiply both sides of (i) by 10 and we get
10x = 9.999…-→(ii)
Subtract (i) from (ii)
10x = 9.999….
x = 0.999…
10x - x = 9.999... - 0.999...9x = 9.0
x = 1
Hence = 1
Express each of the following decimals in the rational form .
let x =
X = 0.575757….. -→(i)
Here the periodicity of the decimal is two
So, we multiply both sides of (i) by 100 and we get
100x = 57.575757…-→(ii)
Subtract (i) from (ii)
100x = 57.5757….
X = 0.5757…
99x = 57.0
(divide by 99 on both sides)
Hence =
Find (x + y) ÷ (x − y) if
According to the question we have,
(x + y) ÷ (x − y)
Put the values of x and y
Find (x + y) ÷ (x − y) if
x = , y =
According to the question we have,
(x + y) ÷ (x − y)
Put the values of x and y
Divide the sum of and by the product ofand.
To find the sum,
To find the sum,
According to the given question,
If of a number exceeds of the same number by 36. Find the number.
let the number is x
Then of x
According to the question,
9x = 3635
(multiply 35 on both the sides)
9X = 1260
(divide by 9 on both the sides)
X = 140
Two pieces of lengths m and m are cut off from a rope 11 m long. What is the length of the remaining rope?
total length of the rope = 11m
Let the third part of rope be x
Length of first piece = m = m
Length of second piece = m = m
According to the question,
(By taking L.C.M.)
The cost of meters of cloth is. Find the cost per metre.
cost of cloth = =
Length of cloth = =
Cost per meter =
(divide cost of cloth by length of cloth)
= 1.66 is the cost per meter
Find the area of a rectangular park which ism long and m broad.
length = m =
Breadth = m =
Area = length breadth
=
What number shouldbe divided by to get?
let the number which be divided by be x
According to the question
(Multiply by x on both the sides)
If 36 trousers of equal sizes can be stitched with 64 meters of cloth. What is the length of the cloth required for each trouser?
number of trousers = 36
Length of cloth = 64m
Length required for each trouser = m
When the repeating decimal 0.363636 .... is written in simplest fractional form, find the sum p + q.
x = 0.363636…(i)
Periodicity = 2
So,
100x = 36.363636….(ii)
From (i) and (ii)
100x = 36.363636….
X = 0.3636363…
_____________________
99x = 36
X =
Then p = 4 and q = 11
p + q = 4 + 11 = 15