Compare and sort in ascending order the two common ordinary fractions, which one is larger: - 44/137 and - 52/142. Common ordinary fractions compared and sorted in ascending order, result explained below
Compare: - 44/137 and - 52/142
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
- 44/137 and - 52/142
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- 44/137 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
44 = 22 × 11
137 is a prime number.
- 52/142 = - (22 × 13)/(2 × 71) = - ((22 × 13) ÷ 2)/((2 × 71) ÷ 2) = - 26/71
To compare and sort the fractions, build them up to the same numerator.
To build the fractions up to the same numerator we have to:
1) calculate their common numerator
2) then calculate the expanding number of each fraction
3) then build up their numerators the same by expanding 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.
The LCM will be the common numerator of the compared fractions.
To calculate the LCM, we need the prime factorization of the numerators:
44 = 22 × 11
26 = 2 × 13
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 (44, 26) = 22 × 11 × 13 = 572
Calculate the expanding number of each fraction:
Divide the LCM by the numerator of each fraction.
- 44/137 : 572 ÷ 44 = (22 × 11 × 13) ÷ (22 × 11) = 13
- 26/71 : 572 ÷ 26 = (22 × 11 × 13) ÷ (2 × 13) = 22
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:
- 44/137 = - (13 × 44)/(13 × 137) = - 572/1,781
- 26/71 = - (22 × 26)/(22 × 71) = - 572/1,562
The fractions have the same numerator, compare their denominators.
The larger the denominator the larger the negative fraction.
The larger the denominator the smaller the positive fraction.
::: The operation of comparing fractions :::
The final answer:
The fractions sorted in ascending order:
- 572/1,562 < - 572/1,781
The initial fractions sorted in ascending order:
- 52/142 < - 44/137
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:
The latest common ordinary fractions compared and sorted in ascending order
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).
- To compare them, fractions should be built up to the same denominator (or if it's easier, to the same numerator).
More on ordinary (common) fractions / theory: