Compare and sort in ascending order the two common ordinary fractions, which one is larger: 53/106 and 55/115. Common ordinary fractions compared and sorted in ascending order, result explained below
Compare: 53/106 and 55/115
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
53/106 and 55/115
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.
53/106 = 53/(2 × 53) = (53 ÷ 53)/((2 × 53) ÷ 53) = 1/2
55/115 = (5 × 11)/(5 × 23) = ((5 × 11) ÷ 5)/((5 × 23) ÷ 5) = 11/23
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:
1/2 = (11 × 1)/(11 × 2) = 11/22
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:
11/23 < 11/22
The initial fractions sorted in ascending order:
55/115 < 53/106
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: