Compare and sort in ascending order the two common ordinary fractions, which one is larger: 164/419 and 167/429. Common ordinary fractions compared and sorted in ascending order, result explained below
Compare: 164/419 and 167/429
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions: 164/419 and 167/429
Simplify the operation Reduce (simplify) the fractions to their lowest terms equivalents:
164/419 is already reduced to the lowest terms. The numerator and denominator have no common prime factors: 164 = 22 × 41 419 is a prime number.
167/429 is already reduced to the lowest terms. The numerator and denominator have no common prime factors: 167 is a prime number. 429 = 3 × 11 × 13
Build up the fractions to the same common numerator:
Expand each fraction: multiply both its numerator and denominator by its corresponding expanding number, calculated at the step 2, above.
This way all the fractions will have the same numerator:
164/419 = (167 × 164)/(167 × 419) = 27,388/69,973
167/429 = (164 × 167)/(164 × 429) = 27,388/70,356
The fractions have the same numerator, compare their denominators.
The larger the denominator the smaller the positive fraction.
The larger the denominator the larger the negative fraction.
::: The operation of comparing fractions ::: The final answer:
The fractions sorted in ascending order: 27,388/70,356 < 27,388/69,973
The initial fractions sorted in ascending order: 167/429 < 164/419
How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.
The latest common ordinary fractions compared and sorted in ascending order