. Write the properties of rational numbers with examples.
Answers & Comments
rishusaxena
Properties of rational number are (1) two rational numbers p/q and r/s are said to be equivalent if p×s=r×q For example - to show 4/-7 and 8/-14 are equivalent rational numbers Solution 4×(-14) = -56= 8×(-7) [by cross multiple] hence 4/-7 and 8/-14 are equivalent rational numbers. (2) if p/q is rational number and m be integer different from 0 ,then p/q=p×m/q×m For example - write three rational numbers which are equivalent to 3/5 Solution - to find equivalent rational number, multiple numerator and denominator by any non zero integer. 3×2/5×2= 6/10 3×(-3)/5×(-3)= -9/-15 3×5/5×5= 15/25 So the required number which are equivalent to 3/5 are 6/10 , -9/-15 , 15/25. (3) if p/q is rational number and m is common divisor of p and q then p/q= p÷m/q÷m For example - express -21/49 as a rational number with denominator 7 Solution to get denominator 7 , we must divide 49/7 Therefore , -21÷7/49÷7= -3/7 So required number is -3/7
Answers & Comments
(1) two rational numbers p/q and r/s are said to be equivalent if p×s=r×q
For example - to show 4/-7 and 8/-14 are equivalent rational numbers
Solution 4×(-14) = -56= 8×(-7) [by cross multiple] hence 4/-7 and 8/-14 are equivalent rational numbers.
(2) if p/q is rational number and m be integer different from 0 ,then p/q=p×m/q×m
For example - write three rational numbers which are equivalent to 3/5
Solution - to find equivalent rational number, multiple numerator and denominator by any non zero integer.
3×2/5×2= 6/10
3×(-3)/5×(-3)= -9/-15
3×5/5×5= 15/25
So the required number which are equivalent to 3/5 are 6/10 , -9/-15 , 15/25.
(3) if p/q is rational number and m is common divisor of p and q then p/q= p÷m/q÷m
For example - express -21/49 as a rational number with denominator 7
Solution to get denominator 7 , we must divide 49/7
Therefore , -21÷7/49÷7= -3/7
So required number is -3/7
Verified answer
Answer:
Let ∠AOC = x and ∠BOE = y.Properties of rational number are
(1) two rational numbers p/q and r/s are said to be equivalent if p×s=r×q
For example - to show 4/-7 and 8/-14 are equivalent rational numbers
Solution 4×(-14) = -56= 8×(-7) [by cross multiple] hence 4/-7 and 8/-14 are equivalent rational numbers.
(2) if p/q is rational number and m be integer different from 0 ,then p/q=p×m/q×m
For example - write three rational numbers which are equivalent to 3/5
Solution - to find equivalent rational number, multiple numerator and denominator by any non zero integer.
3×2/5×2= 6/10
3×(-3)/5×(-3)= -9/-15
3×5/5×5= 15/25
So the required number which are equivalent to 3/5 are 6/10 , -9/-15 , 15/25.
(3) if p/q is rational number and m is common divisor of p and q then p/q= p÷m/q÷m
For example - express -21/49 as a rational number with denominator 7
Solution to get denominator 7 , we must divide 49/7
Therefore , -21÷7/49÷7= -3/7
So required number is -3/7
Then x + y = 70° ( ∠AOC + ∠BOE = 70°)
Let Reflex ∠COE = z
We can see that AB and CD are two intersecting lines, so the pair of angles formed are vertically opposite angles and they are equal.
i.e, ∠AOD = ∠BOC and ∠AOC = ∠BOD.
Since ∠AOC = x and ∠AOC = ∠BOD = 40°
Thus, we can say that x = 40°.
Also we know that,
x + y = 70°
40° + y = 70°
y = 70° - 40° = 30°
∠BOE = 30°
If we consider line AB and ray OD on it, then ∠AOD and ∠BOD are adjacent angles.
∠AOD + ∠BOD = 180°
∠AOD + 40° = 180°
∠AOD = 180° - 40°
= 140°
Reflex ∠COE = ∠AOC + ∠AOD + ∠BOD + ∠BOE
= 40° + 140° + 40° + 30°
= 250°
Thus, ∠BOE = 30° and the reflex ∠COE = 250°.
Step-by-step explanation: