3/5, 3/10 ,7/15, 9/20 arrange in ascending order
Answers
Answer:
Analyze the fractions to be compared and ordered, by category:
positive proper fractions: 3/5, 7/15, 9/20, 3/10;
Reduce (simplify) fractions to their lowest terms equivalents:
3/5 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
3 is a prime number;
5 is a prime number;
7/15 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
7 is a prime number;
15 = 3 × 5;
9/20 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
9 = 32;
20 = 22 × 5;
3/10 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
3 is a prime number;
10 = 2 × 5;
>> Reduce (simplify) fractions to their simplest
Calculate LCM, the least common multiple of the denominators of the fractions.
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:
5 is a prime number
15 = 3 × 5
20 = 22 × 5
10 = 2 × 5
Multiply all the unique prime factors, by the largest exponents:
LCM (5, 15, 20, 10) = 22 × 3 × 5 = 60
Calculate LCM, the least common multiple, online calculator
Calculate the expanding number of each fraction
Divide LCM by the denominator of each fraction:
For fraction: 3/5 is 60 ÷ 5 = (22 × 3 × 5) ÷ 5 = 12
For fraction: 7/15 is 60 ÷ 15 = (22 × 3 × 5) ÷ (3 × 5) = 4
For fraction: 9/20 is 60 ÷ 20 = (22 × 3 × 5) ÷ (22 × 5) = 3
For fraction: 3/10 is 60 ÷ 10 = (22 × 3 × 5) ÷ (2 × 5) = 6
Expand the fractions
Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:
3/5 = (12 × 3)/(12 × 5) = 36/60
7/15 = (4 × 7)/(4 × 15) = 28/60
9/20 = (3 × 9)/(3 × 20) = 27/60
3/10 = (6 × 3)/(6 × 10) = 18/60
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction
The fractions sorted in ascending order:
18/60 < 27/60 < 28/60 < 36/60
The initial fractions in ascending order:
3/10 < 9/20 < 7/15 < 3/5
Step-by-step explanation:
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Answer:
3/10< 9/20 < 7/15 < 3/5
Step-by-step explanation:
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