MATHS M.C.Q. [1 Marks Each]

A set of numbers which do not have any other common factor other than $1$ are called co-prime.

Given expression:
$= 8 - [28 ÷ \{34 - (36 - 18 ÷ 9 × 8)\}] [$Performing division$]$
$= 8 - [28 ÷\{34 - (36 - 2 × 8)\}] [$Performing multiplication$]$
$= 8 - [28 ÷ \{34 - (36 - 16)\}]$
$= 8 - [28 ÷ \{34 - 20\}] [$Removing parentheses$]$
$= 8 - [28 ÷ 14] [$Removing braces$]$
$= 8 - 2$
$= 6 [$Removing square brackets$]$

We have:
Whole number $= 1$
Successor of $1 = 1 + 1 = 2$
Their product $= 1 \times 2 = 2$
Thus, $2$ is an even number.

Let $7589 - x = 3434$
Then, $x = 7589 - 3434 = 4155$

Given expression:
$= 100 \times 10 - 100 + 2000 ÷ 100$
$= 100 \times 10 - 100 + 20 [$performing division$]$
$= 1000 - 100 + 20 [$performing multiplication$]$
$= 1020 - 100 [$performing addition$]$
$= 920 [$performing subtraction$]$

The smallest prime number is $2.$
Thus, when we multiply any natural number we will always get an even number.

Commutative property of addition: Changing the order of addends does not change the sum.
For example, $a + b = b + a$

The whole numbers between $437$ and $487$ are $438, 439, 440, 441, … , 484, 485$ and $486.$ To find the required number of whole numbers,
We need to subtract $437$ from $487$ and then subtract again $1$ from the result.
Thus, there are $(487 - 437) - 1$ whole numbers between $437$ and $487.$
Now, $(487 - 437) - 1$
$= 50 - 1 = 49$
Hence, the correct option is $(b).$

Predecessor of $1 = 1 - 1 = 0$

The predecessor of an odd number is an even number.
The successor of an odd number is also an even number.
These two even numbers are two consecutive even numbers, and the product of two consecutive even numbers is always divisible by $8.$

The additive identity property says that if you add a real number to zero or add zero to a real number, then you get the same real number back.
The number zero is known as the identity element.
Then zero $(0)$ is the additive identity of a real number and all rational numbers are real.
Hence, $0$ is the additive identity of rational numbers.

We have:
Successor of $99 = 99 + 1 = 100$
Predecessor of $99 = 99 - 1 = 98$
Their product $= 100 \times 98 = 9800$

Therefore, the identity element for addition of whole numbers is $0.$

 By using the distributive property, we have;
$1568 \times 185 - 1568 \times 85$
$= 1568 \times (185 - 85)$
$= 1568 \times 100$
$= 156800$

$ 5$ and $8$ are whole numbers but $-3$ is not a whole number.

 Apart from $B,$ the other options contain a negative sign.
Negative numbers do not belong to whole numbers.

The whole number which has no predecessor is $0.$
i.e., $0 - 1 = -1,$ which is not a whole number.

Let the number is $n$
Then the successor of the number $= n + 1$
and the predecessor of the number $= n − 1$
Difference $= n+1−(n−1)$
$= n + 1 − n + 1$
$= 2$

Here we have to tell what least number should be subtracted from $10004$ to get a number exactly divisible by $12.$
So, we will first divide $10004$ by $12.$

Remainder $= 8$
So, $8$ should be subtracted from $10004$ to get the number exactly divisible by $12.$
i.e., $10004 - 8 = 9996$​​​​​​​

Hence, $9996$ is exactly divisible by $12.$

The distributive property of multiplication states that a number is multiplied by the sum of two numbers, when the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
So $(4 \times 8) + (4 \times 60) = 4 \times (8 + 60)$

Commutative property for addition holds true in the case of whole numbers.
For example:
$7 + 4 = 11$
$4 + 7 = 11$
$\Rightarrow 7 + 4 = 4 + 7$

$(18 + 59) + 1 = 18 + (59 + 1) ($associative property$)$
$= 18 + 60$
$= 78$
$($Here, to find the result, we avoided $18 + 59,$ which could be time consuming$).$

Smallest whole number is $0$ and natural number is $1$

Number $-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5$ lies between $-6$ and $6.$
Among them $0, 1, 2, 3, 4, 5$ are whole numbers.
$\therefore 6$ whole numbers lies between $-6$ and $6$

The multiplicative identity property states that any time you multiply a number by $1,$ the result, or product, is that original number.
So it is clear that multiplicative property is given by

Addition of whole numbers is commutative.
So, for any two whole numbers, $x$ and $y, x + y = y + x$

Even natural number $= 2$
Predecessor of $2 = 2 - 1 = 1$
Successor of $2 = 2 + 1 = 3$
Their product $= 1 \times 3 = 3$
Thus, the product is an odd number.

 Addition is associative for whole numbers
i.e. $a + (b + c) = (a + b) + c$
$\therefore 571 + (429 + 394) = (571 + 429) + 394$ 
$\therefore$ The missing terms are $429, 571.$

$\frac{-4}{7}+\frac{0}{9}=\frac{-4}{7}$
$\frac{-4}{7}-\frac{0}{9}=\frac{-4}{7}$
Therefore we use both $+$ or $-$

Since in succession we move from left to the right on the number line.
And , $-17$ lies on right side of $-18$
Hence, $-17$ is the successor of $-18$

 The smallest whole number is $0.$
Greatest three digit number $= 999$
The number of whole numbers from $0$ to $999$ is $1000.$
So, the number of whole numbers between $0$ and $999 ($excluding $0$ and $999)$ is $1000 - 2 = 998.$
Hence, the correct option is $(c).$

$ (888 + 777 + 555) = (111 \times ?)$
$\Rightarrow (888 + 777 + 555) = 111 \times (8 + 7 + 5) [$by taking $111$ common$]$
$= 111 \times 20 = 2220$

Here, Divisor $= 53,$ Quotient $= 8$ and Remainder $= 5.$
Now, using the relation Dividend $=$ Divisor $\times $ Quotient $+$ Remainder
We get Dividend,
$= 53 \times 8 + 5$
$= 424 + 5$
$= 429$
Thus, the required number is $429.$
Hence, the correct option is $(c).$

 $\frac{11}{4}=2\frac{3}{4}$
So $\frac{11}{4}$ lies between $2$ and $3.$