(10/3) > (33/10) true or false
Answers
Answer:
FALSE
Step-by-step explanation:
(10/3) > (33/10)
=> (3.3) > (3.3) { NOT POSSIBLE AS 3.3 = 3.3 }
HENCE, THE ANSWER WILL BE FALSE AS 3.3 = 3.3
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Answer:
10/3 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
10 = 2 × 5;
3 is a prime number;
33/10 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
33 = 3 × 11;
10 = 2 × 5;
LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.
The prime factorization of the denominators:
3 is a prime number
10 = 2 × 5
Multiply all the unique prime factors, by the largest exponents:
LCM (3, 10) = 2 × 3 × 5 = 30
Calculate the expanding number of each fraction
Divide LCM by the denominator of each fraction:
For fraction: 10/3 is 30 ÷ 3 = (2 × 3 × 5) ÷ 3 = 10
For fraction: 33/10 is 30 ÷ 10 = (2 × 3 × 5) ÷ (2 × 5) = 3
Expand the fractions
Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:
10/3 = (10 × 10)/(10 × 3) = 100/30
33/10 = (3 × 33)/(3 × 10) = 99/30
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction.
::: Comparing operation :::
The final answer:
The fractions sorted in ascending order:
99/30 < 100/30
The initial fractions in ascending order:
33/10 < 10/3