Compare and sort in ascending order the two ordinary fractions, which one is larger: - 139/618 and - 142/628. Ordinary fractions compared and sorted in ascending order, result explained below
Compare: - 139/618 and - 142/628
The operation of comparing fractions:
- 139/618 and - 142/628
Reduce (simplify) fractions to their lowest terms equivalents:
- 139/618 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
139 is a prime number;
618 = 2 × 3 × 103;
- 142/628 = - (2 × 71)/(22 × 157) = - ((2 × 71) ÷ 2)/((22 × 157) ÷ 2) = - 71/314
To sort fractions, build them up to the same numerator.
Calculate LCM, the least common multiple of the fractions' numerators
LCM will be the common numerator of the compared fractions.
The prime factorization of the numerators:
139 is a prime number
71 is a prime number
Multiply all the unique prime factors, by the largest exponents:
LCM (139, 71) = 71 × 139 = 9,869
Calculate the expanding number of each fraction
Divide LCM by the numerator of each fraction:
For fraction: - 139/618 is 9,869 ÷ 139 = (71 × 139) ÷ 139 = 71
For fraction: - 71/314 is 9,869 ÷ 71 = (71 × 139) ÷ 71 = 139
Expand the fractions
Build up all the fractions to the same numerator (which is LCM).
Multiply the numerators and denominators by their expanding number:
- 139/618 = - (71 × 139)/(71 × 618) = - 9,869/43,878
- 71/314 = - (139 × 71)/(139 × 314) = - 9,869/43,646
The fractions have the same numerator, compare their denominators.
The larger the denominator the larger the negative fraction.
::: Comparing operation :::
The final answer:
The fractions sorted in ascending order:
- 9,869/43,646 < - 9,869/43,878
The initial fractions in ascending order:
- 142/628 < - 139/618
More operations of this kind:
Writing numbers: comma ',' used as a thousands separator;
Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; < less than;
Compare and sort ordinary fractions, online calculator
The latest fractions compared and sorted in ascending order
Tutoring: Comparing ordinary fractions
How to compare two fractions?
1. Fractions that have different signs:
- Any positive fraction is larger than any negative fraction:
- ie: 4/25 > - 19/2
2. A proper and an improper fraction:
- Any positive improper fraction is larger than any positive proper fraction:
- ie: 44/25 > 1 > 19/200
- Any negative improper fraction is smaller than any negative proper fraction:
- ie: - 44/25 < -1 < - 19/200
3. Fractions that have both like numerators and denominators:
- The fractions are equal:
- ie: 89/50 = 89/50
4. Fractions that have unlike (different) numerators but like (equal) denominators.
- Positive fractions: compare the numerators, the larger fraction is the one with the larger numerator:
- ie: 24/25 > 19/25
- Negative fractions: compare the numerators, the larger fraction is the one with the smaller numerator:
- ie: - 19/25 < - 17/25
5. Fractions that have unlike (different) denominators but like (equal) numerators.
- Positive fractions: compare the denominators, the larger fraction is the one with the smaller denominator:
- ie: 24/25 > 24/26
- Negative fractions: compare the denominators, the larger fraction is the one with the larger denominator:
- ie: - 17/25 < - 17/29
6. Fractions that have different denominators and numerators (unlike denominators and numerators).
- To compare them, fractions should be built up to the same denominator (or if it's easier, to the same numerator).
More on ordinary (common) math fractions theory: