Compare and sort in ascending order the two common ordinary fractions, which one is larger: 31/1,006 and 39/1,014. Common ordinary fractions compared and sorted in ascending order, result explained below
Compare: 31/1,006 and 39/1,014
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
31/1,006 and 39/1,014
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
By reducing the values of the numerators and denominators of the fractions, further calculations with these fractions become easier to do.
To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.
31/1,006 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
31 is a prime number.
1,006 = 2 × 503
39/1,014 = (3 × 13)/(2 × 3 × 132) = ((3 × 13) ÷ (3 × 13))/((2 × 3 × 132) ÷ (3 × 13)) = 1/26
To compare and sort the fractions, make their numerators the same.
Expand the fraction that has 1 as a numerator.
Multiply the numerator and denominator by the same number:
1/26 = (31 × 1)/(31 × 26) = 31/806
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:
31/1,006 < 31/806
The initial fractions sorted in ascending order:
31/1,006 < 39/1,014
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 common ordinary fractions, online calculator: