State true or false \[21:6=35:10\]. (a). True. (b). False.
ANSWER
Verified
Hint: To solve this question we would obtain the ratio of both the sides of the equation and convert it into fraction. Then would go for converting the simplest form of the fraction and comparing if they are equal.
Complete step-by-step solution -
Given two ratios of real numbers. We have to check if the given ratio is equal or not. \[21:6=35:10\]. To solve this question, we will first of all solve the left-hand side ratio and then will solve the right-hand side ratio. Then we check if both are equal or not. Observing the left-hand side ratio, we have 21:6 which is\[\dfrac{21}{6}\]. Because 21 is not a multiple of 6 therefore, it cannot be properly divided by 6. Hence, the given fraction would not reduce further. Now considering the right-hand side of the above expression we get that the ratio is 35:10. Converting the ratio 35:10 into fraction we have \[\dfrac{35}{10}\]. Noe dividing both the numerator and the denominator by 5 we get, \[\dfrac{7}{2}\]. Now \[\dfrac{7}{2}\] cannot be reduced further. Equating both the obtained fractions we have left-hand side fraction as 21/6 and right hand side fraction as 7/2. We see that both of the obtained fractions are not equal. Hence, we obtained that the expression \[21:6=35:10\] is False. Matching from the options given below we have, option (b) is correct.
Note: The possibility of error in this question is not converting the fraction into simplest form and comparing without doing so. Which would ultimately give the wrong result. Always go for converting in simplest form first and then doing further calculation.