Compare the Two Common Fractions 30/198 and 40/207, Which One is Larger? Online Calculator
Fractions 30/198 and 40/207 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:
30/198 and 40/207
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
To reduce a fraction to the lowest terms equivalent: divide both the numerator and denominator by their greatest common factor, GCF.
30/198 = (2 × 3 × 5)/(2 × 32 × 11) = ((2 × 3 × 5) ÷ (2 × 3))/((2 × 32 × 11) ÷ (2 × 3)) = 5/33
40/207 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
40 = 23 × 5
207 = 32 × 23
To compare and sort the fractions, make their numerators the same.
To make the fractions' numerators the same - we have to:
1) calculate their common numerator
2) then calculate the expanding number of each fraction
3) expand the fractions to equivalent forms, which all have equal numerators
Calculate the common numerator
The common numerator is nothing else than the least common multiple (LCM) of the numerators of the fractions.
To calculate the LCM, we need the prime factorization of the numerators:
5 is a prime number.
40 = 23 × 5
Multiply all the unique prime factors: if there are repeating prime factors we only take them once, and only the ones having the highest exponent (the highest powers).
LCM (5, 40) = 23 × 5 = 40
Calculate the expanding number of each fraction:
Divide the LCM by the numerator of each fraction.
5/33 : 40 ÷ 5 = (23 × 5) ÷ 5 = 8
40/207 : 40 ÷ 40 = (23 × 5) ÷ (23 × 5) = 1
Make the fractions' numerators the same:
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:
5/33 = (8 × 5)/(8 × 33) = 40/264
40/207 = (1 × 40)/(1 × 207) = 40/207
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:
40/264 < 40/207
The initial fractions sorted in ascending order:
30/198 < 40/207
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.
Compare and sort common fractions, online calculator: