Question

Write three equivalent rational number with denominations 98 , -105 and 245 corresponding to the rational number 2/7 . ​

Answer 1

✪ Question ✪

Write three equivalent rational number with denominations 98 , -105 and 245 corresponding to the rational number 2/7 .

✪ To find ✪

The equivalent rational numbers with denominations 98 , -105 and 245 corresponding to the rational number 2/7 .

✪ Solution ✪

To get the equivalent rational number of 2/7 with denominator 98, we have to multiply 2/7 with 14/14 because 98 when divided by 7 gives 14.

So, 2/7 × 14/14 = 28/98.

To get the equivalent rational number of 2/7 with denominator -105, we have to multiply 2/7 with -15/-15 because 98 when divided by 7 gives -15.

So, 2/7 × -15/-15 = -30/-105.

To get the equivalent rational number of 2/7 with denominator 245, we have to multiply 2/7 with 35/35 because 98 when divided by 7 gives 35.

So, 2/7 × 35/35 = 70/245.

✪ Hence ✪

☞ 2/7 = 28/98

☞ 2/7 = -30/-105

☞ 2/7 = 70/245

✪ Therefore ✪

• The equivalent rational number with denominations 98 corresponding to the rational number 2/7 is 28/98.
• The equivalent rational number with denominations -105 corresponding to the rational number 2/7 is -30/-105.
• The equivalent rational number with denominations 245 corresponding to the rational number 2/7 is 70/245.

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✪ Know more ✪

Rational numbers →

• The numbers in the form p/q, where p and q are integers and q ≠ 0, are called rational numbers.
• Rational numbers can be both positive and negative.
• 0 is a rational number as it can be written as 0/1, 0/2, 0/4 etc.
• Every fraction is a rational number but every rational number is not be a fraction.

Positive rational numbers →

A rational number is said to be positive if it's numerator and denominator are either both positive or both negative.

Negative rational numbers →

A rational number is said to be negative if its numerator and denominator are of opposite signs.

Points to know →

• Every positive rational number is greater than 0.
• Every negative rational number is less than 0.

Two properties of rational numbers →

• If a/b is a rational number and m is a non-zero integer then,

        ☞ a/b = (a×m)/(b×m)

• If a/b is a rational number and m is a common divisor of a and b then,

       ☞ a/b = (a÷m)/(b÷m)

Standard form of a rational number →

A rational number a/b is said to be in standard form if a and b are integers having no common divisor other than 1 and b is positive.

          ๑ Hope this helps you. ๑

Answer 2

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For 98

28/98

$\small\bold{\texttt { \red{Step\: 1} }}$

=>98÷7

$\small\bold{\texttt { \red{Step\: 2} }}$

=>14

$\small\bold{\texttt { \red{Step\: 3} }}$

=>2×14/7×14

$\small\bold{\texttt { \red{final\: A swer} }}$

=>28/98

$\huge\bold{{\red{A}}{\blue{N}}{\red{S}}{\blue{W}}{\red{E}}{\blue{R}}{\red{❥}}}$

-30/-105

For -105

$\small\bold{\texttt { \red{Step\: 1} }}$

=> -105÷7

$\small\bold{\texttt { \red{Step\: 2} }}$

=>—15

$\small\bold{\texttt { \red{Step\: 3} }}$

=>2×(-15)/7×(-15)

$\small\bold{\texttt { \red{final\: Answer} }}$

=> -30/-105

$\huge\bold{{\red{A}}{\blue{N}}{\red{S}}{\blue{W}}{\red{E}}{\blue{R}}{\red{❥}}}$

70/245

For 245

$\small\bold{\texttt { \red{Step\: 1} }}$

=>245÷7

$\small\bold{\texttt { \red{Step\: 2} }}$

=>35

$\small\bold{\texttt { \red{Step\: 3} }}$

=>2×35/7×35

$\small\bold{\texttt { \red{final\: Answer} }}$

=>70/245

$\color{Purple}{\large\underline{\underline\mathtt{Additional \ imformation↓↓↓}}}$

What are rational numbers?

➖▶A rational number is any number that can be named in the form a/b where a and are b are integers and b≠0.

➡Points to note:-

Every natural number is a rational number but not a rational number need not be a natural number.

1. We can write 1=1/1,2=2/1,3=3/1 and so on.
2. This shows that every natural number n can be written as a rational number.
3. But none of the rational numbers like 5/6,7/9,12/44 and sonon us a natural number.

Zero is a rational number

1. We can write zero in any forms 0/1,0/-1,0/2,0/-2 and so on.
2. Thus 0 can be exoressed as p/q where q is any non-zero integer.
3. Hence,0 is a rational number.

Every fraction is a rational number but a rational nunber need not be a fraction.

1. Let p/q be any integer.
2. Thus , p and q are natural numbers.
3. Since every natural number is an integer,therefore,p and q are integers.
4. Thus the feaction p/q is the quotient of two integers such thay q≠0.
5. Hence,p/q is a rational number..A number like 7/-8 is a rational number but it is not a fraction since its denominator is -8 is not a ratural number.

Hope it helped u buddy...

Thank you...☺❤