Compare the Two Common Fractions - 678/90 and - 686/98, Which One is Larger? Online Calculator

Fractions - 678/90 and - 686/98 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:
- 678/90 and - 686/98

Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:


The fraction: - 678/90

  • The prime factorizations of the numerator and denominator:
  • 678 = 2 × 3 × 113
  • 90 = 2 × 32 × 5
  • 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 (678; 90) = 2 × 3 = 6

- 678/90 = - (678 ÷ 6)/(90 ÷ 6) = - 113/15


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


- 678/90 = - (2 × 3 × 113)/(2 × 32 × 5) = - ((2 × 3 × 113) ÷ (2 × 3))/((2 × 32 × 5) ÷ (2 × 3)) = - 113/15



The fraction: - 686/98

  • 686 = 2 × 73
  • 98 = 2 × 72
  • GCF (686; 98) = 2 × 72 = 98

- 686/98 = - (686 ÷ 98)/(98 ÷ 98) = - 7/1 = - 7


The fraction can also be reduced without calculating GCF; factor the numerator and denominator and cross out all the common prime factors:


- 686/98 = - (2 × 73)/(2 × 72) = - ((2 × 73) ÷ (2 × 72))/((2 × 72) ÷ (2 × 72)) = - 7/1 = - 7




To compare and sort the fractions, make their denominators the same.

Expand the fraction that has 1 as a denominator.

Multiply the numerator and denominator by the same number:

- 7 = - (15 × 7)/(15 × 1) = - 105/15

The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.

The larger the numerator the larger the positive fraction.


::: The operation of comparing fractions :::
The final answer:

The fractions sorted in ascending order:
- 113/15 < - 105/15

The initial fractions sorted in ascending order:
- 678/90 < - 686/98

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 the fractions in ascending order:
686/98 and 693/102

» New. All the Calculations Performed by Our Visitors: Common Fractions Compared and Sorted. Data organized on a Monthly Basis

Compare and sort common fractions, online calculator:

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).

More on ordinary (common) fractions / theory: