Question

Unit 1 : Algebra basics Homework 1

I need help please .

Answer 1

Here I did some questions for you. But first understand these definitions:

`\sf\\\\\textsf{Real number is the union of irrational and rational numbers. It is denoted by R.}\\\\\textsf{A rational number is the real number which can be expressed as a fraction of }\\\textsf{two integers where denominator is not equal to zero. It is denoted by Q.}`

`\textsf{An irrational number is the real number which cannot be expressed as}\\\textsf{the fraction of two integers. There is no universally accepted symbol for irrational }\\\textsf{numbers, but the most commonly used are P and I.}`

`\textsf{An integer is a non-decimal and non-fractional rational number which may be zero, }\\\textsf{negative or positive. It is denoted by Z.}`

`\textsf{A natural number is an integer greater than zero. In other words, all positive}\\\textsf{integers are called natural numbers.}`

`\textsf{A whole number is an integer including zero and greater than zero. All the}\\\textsf{natural numbers are whole numbers.}`

Answer:

`\sf\\1.\ 12\\\\\rightarrow\textsf{12 is a rational number because it can be expressed as a fraction of two integers.}\\\textsf{\ \ \ For example, }(24)/(2),\ (12)/(1), \textsf{ etc.}`

`\rightarrow\textsf{12 is an integer because it does not contain any decimal and fractional part.}`

`\rightarrow\textsf{12 is a whole number and a natural number because it is a positive integer.}`

`\sf\\\therefore\ 12 \in R, Q, Z, W, N`

`\sf\\\textsf{2. -15}\\\rightarrow \textsf{-15 is a rational number because it can be expressed as the fraction of two}\\\textsf{\ \ \ \ integers. For example, }(-15)/(1),\ (-60)/(4),\ \textsf{etc.}`

`\rightarrow \textsf{-15 is an integer because it does not have any fractional or decimal part.}\\`

`\rightarrow \textsf{-15 is not a whole number and a natural number because it is negative. A whole}\\\textsf{\ \ \ \ number and a natural number are always non-negative integers.}`

`\therefore\ \textsf{-15} \in \textsf{R, Q, Z}`

`\sf\\\textsf{4. 3.18}\\\rightarrow\ \textsf{3.18 is a rational number as it can be expressed as a fraction of two integers.}\\\\\textsf{\ \ \ \ For example, }(318)/(100).\textsf{ Here, 318 and 100 are both integers because they do not}\\\\\textsf{\ \ \ \ contain any decimal part.}`

`\rightarrow \textsf{-3.18 is not an integer because it contains a decimal part, 0.18}`

`\sf\\\therefore\ 3.18\in R, Q`

`\sf\\\textsf{7. }-2(7)/(9)`

`\sf\\\rightarrow -2(7)/(9)=-(2*9+7)/(9)=-(25)/(9)`

`\rightarrow\sf{-2(7)/(9)}\textsf{ is a rational number because it can be expressed as a fraction of two}\\\textsf{\ \ \ integers. (-25 and 9 are both integers.)}`

`\rightarrow\sf{-2(7)/(9)}\textsf{ is not an integer because it contains fractional part. }`

`\therefore\ \sf{-2(7)/(9)\in}\textsf{\ R, Q}`

`\textsf{11. }\sf{-√(12)}\\\\\rightarrow\ \sf{-√(12)=-2\sqrt3}`

`\sf\\\rightarrow -2√(3)\textsf{ is not a rational number because it cannot be expressed as the fraction}\\\textsf{\ \ \ \ of two integers. So it is an irrational number.}`

`\sf\\\rightarrow \textsf{Therefore, }-2√(3)\textsf{ is not an integer because it is not a rational number. }`

`\therefore\ \sf{-√(12)}\in\textsf{ R, P}`

Hope this helps you to solve other questions!