Compare the Two Common Fractions 357/408 and 364/416, Which One is Larger? Online Calculator

The operation of comparing fractions:
357/408 and 364/416

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


The fraction: 357/408

  • The prime factorizations of the numerator and denominator:
  • 357 = 3 × 7 × 17
  • 408 = 23 × 3 × 17
  • 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 (357; 408) = 3 × 17 = 51

357/408 = (357 ÷ 51)/(408 ÷ 51) = 7/8


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


357/408 = (3 × 7 × 17)/(23 × 3 × 17) = ((3 × 7 × 17) ÷ (3 × 17))/((23 × 3 × 17) ÷ (3 × 17)) = 7/8



The fraction: 364/416

  • 364 = 22 × 7 × 13
  • 416 = 25 × 13
  • GCF (364; 416) = 22 × 13 = 52

364/416 = (364 ÷ 52)/(416 ÷ 52) = 7/8


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


364/416 = (22 × 7 × 13)/(25 × 13) = ((22 × 7 × 13) ÷ (22 × 13))/((25 × 13) ÷ (22 × 13)) = 7/8




The fractions are equal.

This is one of the simplest cases when comparing two fractions.

Not only are the numerators of the fractions equal but their denominators are also equal.


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

The fractions sorted in ascending order:
7/8 = 7/8

The initial fractions sorted in ascending order:
357/408 = 364/416

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:
364/416 and 373/419

» 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: