Compare and sort in ascending order the two ordinary fractions, which one is larger: - 71/40 and - 80/45. Ordinary fractions compared and sorted in ascending order, result explained below

Compare: - 71/40 and - 80/45

The operation of comparing fractions:
- 71/40 and - 80/45

Reduce (simplify) fractions to their lowest terms equivalents:

- 71/40 already reduced to the lowest terms;
the numerator and denominator have no common prime factors:
71 is a prime number;
40 = 23 × 5;


- 80/45 = - (24 × 5)/(32 × 5) = - ((24 × 5) ÷ 5)/((32 × 5) ÷ 5) = - 16/9


>> Reduce (simplify) fractions to their simplest form, online calculator


To sort fractions in ascending order, build up their denominators the same.

Calculate LCM, the least common multiple of the denominators of the fractions.

LCM will be the common denominator of the compared fractions.
In this case, LCM is also called LCD, the least common denominator.

The prime factorization of the denominators:


40 = 23 × 5


9 = 32


Multiply all the unique prime factors, by the largest exponents:


LCM (40, 9) = 23 × 32 × 5 = 360

Calculate LCM, the least common multiple, online calculator


Calculate the expanding number of each fraction

Divide LCM by the denominator of each fraction:


For fraction: - 71/40 is 360 ÷ 40 = (23 × 32 × 5) ÷ (23 × 5) = 9


For fraction: - 16/9 is 360 ÷ 9 = (23 × 32 × 5) ÷ 32 = 40



Expand the fractions

Build up all the fractions to the same denominator (which is LCM).
Multiply the numerators and denominators by their expanding number:

- 71/40 = - (9 × 71)/(9 × 40) = - 639/360


- 16/9 = - (40 × 16)/(40 × 9) = - 640/360



The fractions have the same denominator, compare their numerators.

The larger the numerator the smaller the negative fraction.

::: Comparing operation :::
The final answer:

The fractions sorted in ascending order:
- 640/360 < - 639/360

The initial fractions in ascending order:
- 80/45 < - 71/40

More operations of this kind:

Compare and sort the fractions in ascending order:
- 80/45 and - 84/47


Symbols: / fraction bar; ÷ divide; × multiply; + plus; - minus; = equal; < less than;

Compare and sort ordinary fractions, online calculator

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see more... compared fractions
see more... sorted fractions

Tutoring: Comparing ordinary fractions

How to compare two fractions?

1. Fractions that have different signs:

2. A proper and an improper fraction:

3. Fractions that have both like numerators and denominators:

4. Fractions that have unlike (different) numerators but like (equal) denominators.

5. Fractions that have unlike (different) denominators but like (equal) numerators.

6. Fractions that have different denominators and numerators (unlike denominators and numerators).

More on ordinary (common) math fractions theory:

(1) What is a fraction? Fractions types. How do they compare?


(2) Fractions changing form, expand and reduce (simplify) fractions


(3) Reducing fractions. The greatest common factor, GCF


(4) How to, comparing two fractions with unlike (different) numerators and denominators


(5) Sorting fractions in ascending order


(6) Adding ordinary (common, simple) fractions


(7) Subtracting ordinary (common, simple) fractions


(8) Multiplying ordinary (common, simple) fractions


(9) Fractions, theory: rational numbers