Compare the Two Common Fractions 881/824 and 886/828, Which One is Larger? Online Calculator
Fractions 881/824 and 886/828 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:
881/824 and 886/828
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: 881/824
881/824 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
- 881 is a prime number.
- 824 = 23 × 103
- GCF (881; 824) = 1
The fraction: 886/828
- The prime factorizations of the numerator and denominator:
- 886 = 2 × 443
- 828 = 22 × 32 × 23
- 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 (886; 828) = 2
886/828 = (886 ÷ 2)/(828 ÷ 2) = 443/414
The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:
886/828 = (2 × 443)/(22 × 32 × 23) = ((2 × 443) ÷ 2)/((22 × 32 × 23) ÷ 2) = 443/414
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:
824 = 23 × 103
414 = 2 × 32 × 23
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 (824, 414) = 23 × 32 × 23 × 103 = 170,568
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
881/824 ⟶ 170,568 ÷ 824 = (23 × 32 × 23 × 103) ÷ (23 × 103) = 207
443/414 ⟶ 170,568 ÷ 414 = (23 × 32 × 23 × 103) ÷ (2 × 32 × 23) = 412
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:
881/824 = (207 × 881)/(207 × 824) = 182,367/170,568
443/414 = (412 × 443)/(412 × 414) = 182,516/170,568
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:
182,367/170,568 < 182,516/170,568
The initial fractions sorted in ascending order:
881/824 < 886/828
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: