Rational Numbers Test - 4

Zero is called the identity for addition on rational numbers, integers and whole numbers. Since the addition of zero doesn’t affect the value of above given numbers.

Eg: a+0=0+a=a.

Rational numbers can be compared by making their denominators equal.
We have the following fractions - 223,254,152,172,132 and the integer 8 which can be written as 81
LCM of 1, 2, 3 and 4, i.e., the denominators of the above fractions, is 12.
Converting all the fractions above into fractions with a common denominator, we get:
223=22×43×4=8812
254=25×34×3=7512
132=13×62×6=7812
152=15×62×6=9012
172=17×62×6=10212
8=81=8×121×12=9612

Arranging these fractions in an ascending order, we get
7512,7812,8812,9012,9612,10212

Thus, the number between 223 and 254 is 7812, i.e. 132

LCM of 7, 3, 3, 9=63∴
4/7=4/7×9/9=36/63,1/3=1/3×21/21=21/63,
2/3=2/3×21/21=42/63,5/9=5/9×7/7=35/63So, ascending 
order is 21/63,35/63,36/63,42/63i.e., 1/3<5/9<4/7<2/3Now, the
 average of 5/9 and 4/7 is 1/2 [ 5/9 +4/7 ]=1/2[35+36/63]=71/126

An operation is commutative if changing the order of operands does not change the result.

Division of whole numbers is not commutative. a/b ≠ b/a;

For example: a = 2, b = 3; 2/3 ≠ 3/2

1/4 can be written as 1×4/4×4=4×(−1)/16×(−1)=−4/−16∴1/4and 
−4/−16 are equivalent rational numbers. 

Weight of each mango =1/10kg Wight of box =3/5kgNumber of mangoes =3/5÷1/10=3/5×10=6