Compare and sort the fractions in ascending order: 171/103, 177/120, 89/172. Common ordinary fractions compared and sorted in ascending order, result explained below
Sort: 171/103, 177/120, 89/172
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of sorting fractions in ascending order:
171/103, 177/120, 89/172
Analyze the fractions to be compared and ordered, by category:
1 positive proper fraction: 89/172
positive improper fractions: 171/103, 177/120
How to compare and sort the fractions in ascending order, by categories:
- any positive proper fraction is smaller than...
- any positive improper fraction.
Sort the positive improper fractions in ascending order:
171/103 and 177/120
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.
To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.
171/103 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
171 = 32 × 19
103 is a prime number.
177/120 = (3 × 59)/(23 × 3 × 5) = ((3 × 59) ÷ 3)/((23 × 3 × 5) ÷ 3) = 59/40
To compare and sort the fractions, make their denominators the same.
To make the fractions' denominators the same - we have to:
1) calculate their common denominator
2) then calculate the expanding number of each fraction
3) then make their denominators the same by expanding the fractions to equivalent forms, which all have equal denominators
Calculate the common denominator
The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
The LCM will be the common denominator of the compared fractions.
To calculate the LCM, we need the prime factorization of the denominators:
103 is a prime number.
40 = 23 × 5
Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).
LCM (103, 40) = 23 × 5 × 103 = 4,120
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
171/103 : 4,120 ÷ 103 = (23 × 5 × 103) ÷ 103 = 40
59/40 : 4,120 ÷ 40 = (23 × 5 × 103) ÷ (23 × 5) = 103
Make the fractions' denominators the same:
Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.
This way all the fractions will have the same denominator:
171/103 = (40 × 171)/(40 × 103) = 6,840/4,120
59/40 = (103 × 59)/(103 × 40) = 6,077/4,120
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction.
The larger the numerator the smaller the negative fraction.
The fractions sorted in ascending order:
6,077/4,120 < 6,840/4,120
The initial fractions sorted in ascending order:
177/120 < 171/103
::: The operation of comparing fractions :::
The final answer:
Sort the positive improper fractions in ascending order:
177/120 < 171/103
All the fractions sorted in ascending order:
89/172 < 177/120 < 171/103
How are the numbers written: comma ',' used as a thousands separator; point '.' as a decimal separator; numbers rounded off to max. 12 decimals (if the case). Used symbols: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.
Other similar operations
Compare and sort common ordinary fractions, online calculator: