Compare the Two Common Fractions 270/262 and 277/271, Which One is Larger? Online Calculator
Fractions 270/262 and 277/271 are compared by building equivalent fractions, which have either equal denominators or equal numerators
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
270/262 and 277/271
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.
The fraction: 270/262
- The prime factorizations of the numerator and denominator:
- 270 = 2 × 33 × 5
- 262 = 2 × 131
- Multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponent (the lowest powers).
- GCF (270; 262) = 2
270/262 = (270 ÷ 2)/(262 ÷ 2) = 135/131
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
270/262 = (2 × 33 × 5)/(2 × 131) = ((2 × 33 × 5) ÷ 2)/((2 × 131) ÷ 2) = 135/131
The fraction: 277/271
277/271 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 277 is a prime number.
- 271 is a prime number.
- GCF (277; 271) = 1
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) expand the fractions to equivalent forms having the same denominator
Calculate the common denominator
The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
To calculate the LCM, we need the prime factorization of the denominators:
131 is a prime number.
271 is a prime number.
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 (131, 271) = 131 × 271 = 35,501
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
135/131 ⟶ 35,501 ÷ 131 = (131 × 271) ÷ 131 = 271
277/271 ⟶ 35,501 ÷ 271 = (131 × 271) ÷ 271 = 131
Make the denominators of the fractions the same:
- Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated above.
- This way all the fractions will have the same denominator:
135/131 = (271 × 135)/(271 × 131) = 36,585/35,501
277/271 = (131 × 277)/(131 × 271) = 36,287/35,501
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 operation of comparing fractions :::
The final answer:
The fractions sorted in ascending order:
36,287/35,501 < 36,585/35,501
The initial fractions sorted in ascending order:
277/271 < 270/262
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.
Compare and sort common fractions, online calculator: