Expressing -4/7 as a Rational Number with Different Denominators

Rational Numbers:
Rational numbers are any numbers that can be expressed as a ratio of two integers. Rational numbers can be positive or negative, and they can be expressed as either fractions or decimals. For example, 3/4 and 0.75 are both rational numbers.

Denominators:
The denominator of a fraction is the number below the fraction line. It represents the total number of equal parts that make up a whole. For example, in the fraction 3/4, the denominator is 4, which means that the whole is divided into four equal parts.

Different Denominators:
To express a fraction with a different denominator, we need to find the equivalent fraction with the desired denominator. This can be done by multiplying or dividing both the numerator and denominator of the original fraction by the same number.

Expressing -4/7 as a Rational Number with Different Denominators:
To express -4/7 as a rational number with the following denominators, we need to find the equivalent fraction with the desired denominator.

Denominator 28:
To express -4/7 as a fraction with a denominator of 28, we need to find the equivalent fraction by multiplying both the numerator and denominator by 4.

-4/7 x 4/4 = -16/28

Therefore, -4/7 as a rational number with a denominator of 28 is -16/28.

Denominator 35:
To express -4/7 as a fraction with a denominator of 35, we need to find the equivalent fraction by multiplying both the numerator and denominator by 5.

-4/7 x 5/5 = -20/35

Therefore, -4/7 as a rational number with a denominator of 35 is -20/35.

Denominator 49:
To express -4/7 as a fraction with a denominator of 49, we need to find the equivalent fraction by multiplying both the numerator and denominator by 7.

-4/7 x 7/7 = -28/49

Therefore, -4/7 as a rational number with a denominator of 49 is -28/49.

Denominator 70:
To express -4/7 as a fraction with a denominator of 70, we need to find the equivalent fraction by multiplying both the numerator and denominator by 10.

-4/7 x 10/10 = -40/70

Therefore, -4/7 as a rational number with a denominator of 70 is -40/70.

In conclusion, -4/7 can be expressed as a rational number with a denominator of 28, 35, 49, and 70 as -16/28, -20/35, -28/49, and -40/70, respectively.

I) expressing denominator as 28:-
-4/7=(-4×4) /(7×4) =-16/28
ii) expressing denominator as 35:-
-4/7=(-4×5) /(7×5)=-20/35
iii) expressing denominator as 49:-
-4/7=(-4×7) /(7×7) =-28/49
iv) expressing denominator as 70:-
-4/7=(-4×10) /(7×10) =-40/70