Tag: real numbers on number line

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Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic


$20$ is written as the product of primes as :

  1. ${2\times 5 }$
  2. ${2\times 2\times 3\times 5}$
  3. ${2\times 2\times 5}$
  4. ${2\times 2\times 3}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To write a number as product of its primes, we divide it by various prime numbers $ 2, 3, 5, 7 $ etc one by one and check by which prime numbers it is divisible with and how many times.

Hence, $ 20 = 2 \times 10 = 2 \times 2 \times 5 $          

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

In a division sum the divisor is $12$  times the quotient and  $5$  times the remainder. If the remainder is  $48$  then what is the dividend?

  1. $2404$
  2. $4808$
  3. $3648$
  4. $4848$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Divisor $= 5$  $\displaystyle \times $ Remainder = 5 $\displaystyle \times $ $48 = 240$
$\displaystyle \therefore $ Quotient = $\displaystyle \frac{1}{12}\times 240=20$
$\displaystyle \Rightarrow $ Dividend = Divisor $\displaystyle \times $Quotient + Remainder
$= 240 $ $\displaystyle \times $  $ 20 + 48 = 4800 + 48$
$=4848 $

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

A number $x$ when divided by $7$  leaves a remainder $1$ and another number $y$ when divided by $7$  leaves the remainder $2$. What will be the remainder if $x+y$ is divided by $7$?

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given numbers $x,y$ 

Let us assume $a$ is the quotient when $x$ is divided by $7$ and $b$ is the quotient when $y$ is divided by $7$ 

$x = 7$ $\displaystyle \times $$ a + 1 $   and  $y = 7 $ $\displaystyle \times $$ b + 2$

 $\displaystyle \therefore $ $ x + y = 7a + 7b + 1 + 2 = 7(a + b) + 3$

$\displaystyle \Rightarrow $$ (x + y)$ when divided by $7$ leaves a remainder $3$.

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

The ........... when multiplied always give a new unique natural number.

  1. decimal numbers

  2. fractions

  3. irrational numbers

  4. prime numbers
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

For example: $24$ is made by multiplying the prime numbers $2, 2, 2$ and $3$ together. $24 = 2 \times 2 \times 2 \times 3$
It makes a unique number using a unique combination of $2, 2, 2$ and $3.$
Therefore, $D$ is the correct answer.

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

Fundamental theorem of arithmetic is also called as ______ Factorization Theorem.

  1. Algebra

  2. Ambiguous

  3. Unique

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
$30 = 2 \times 3 \times 5$, where $2$ and $3$ are prime numbers.
We cannot get the number $30$ by multiplying any other prime numbers.
Example : $30 \neq 2 \times 5 \times 7.$ 
It is only with one particular set of prime numbers.
Hence, it is called Unique Factorization Theorem.
Therefore, $C$ is the correct answer.
Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

We need blocks to build a building. In the same way _______ are basic blocks to form all natural numbers .

  1. prime numbers

  2. real numbers

  3. unique numbers

  4. negative numbers
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let us consider some examples.
$10 = 2 \times 5$, we need $2$ and $5$ which are prime numbers to get a new number $10$.
$12= 2 \times 2 \times 3$, we need $2$ and $3$ which are prime numbers to get a new number $12$.
Therefore$,$ $A$ is the correct answer.

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

................. states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.

  1. Pythagora's theorem

  2. Remainder theorem

  3. Fundamental theorem of arithmetic

  4. none of the above
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Fundamental theorem of arithmetic says that composite number can be factorised as a product of prime numbers.
Therefore, $C$ is the correct answer.

Multiple choice maths real number fundemental theorem of arithmetic real numbers on number line fundamental theorem of arithmetic

Fundamental theorem of arithmetic is basically used for ________

  1. proving the irrationality of numbers.

  2. to explore when exactly the decimal expansion of a rational number is terminating or non-terminating repeating.

  3. prime numbers.

  4. both A and B.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Fundamental theorem of arithmetic is basically used for firstly proving the irrationality of numbers and secondly to explore when exactly the decimal expansion of a rational number is terminating and when it is non - terminating repeating.
Therefore, $ B$ is the correct answer.