Compare and sort in ascending order the two common ordinary fractions, which one is larger: 75/34 and 83/43. Common ordinary fractions compared and sorted in ascending order, result explained below
Compare: 75/34 and 83/43
To compare and sort multiple fractions, they should either have the same denominator or the same numerator.
The operation of comparing fractions:
75/34 and 83/43
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.
75/34 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
75 = 3 × 52
34 = 2 × 17
83/43 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors:
83 is a prime number.
43 is a prime number.
To compare and sort the fractions, make their denominators the same.
To make the fractions' denominators the same - we have to:
1) calculate their common denominator
2) then calculate the expanding number of each fraction
3) then make their denominators the same by expanding the fractions to equivalent forms, which all have equal denominators
Calculate the common denominator
The common denominator is nothing else than the least common multiple (LCM) of the denominators of the fractions.
The LCM will be the common denominator of the compared fractions.
To calculate the LCM, we need the prime factorization of the denominators:
34 = 2 × 17
43 is a prime number.
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 (34, 43) = 2 × 17 × 43 = 1,462
Calculate the expanding number of each fraction:
Divide the LCM by the denominator of each fraction.
75/34 : 1,462 ÷ 34 = (2 × 17 × 43) ÷ (2 × 17) = 43
83/43 : 1,462 ÷ 43 = (2 × 17 × 43) ÷ 43 = 34
Make the fractions' denominators 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 denominator:
75/34 = (43 × 75)/(43 × 34) = 3,225/1,462
83/43 = (34 × 83)/(34 × 43) = 2,822/1,462
The fractions have the same denominator, compare their numerators.
The larger the numerator the larger the positive fraction.
The larger the numerator the smaller the negative fraction.
::: The operation of comparing fractions :::
The final answer:
The fractions sorted in ascending order:
2,822/1,462 < 3,225/1,462
The initial fractions sorted in ascending order:
83/43 < 75/34
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.
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