- 24/31 × 31/78 = ? Multiply the Common (Ordinary) Fractions, Online Calculator. Multiplication Operation Explained Step by Step
The numerators and the denominators of the fractions are multiplied separately
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 24/31 × 31/78 = 24/78
Rewrite the equivalent simplified operation:
- 24/31 × 31/78 =
- 24/78
Simplify the operation
Reduce (simplify) the fractions to their lowest terms equivalents:
- A fully reduced (simplified) fraction is one with the smallest possible numerator and denominator, one that can no longer be reduced, and it is called an irreducible fraction.
- * By reducing the values of the numerators and denominators of fractions, subsequent calculations become easier to perform.
To reduce a fraction to the lowest terms equivalent divide its numerator and denominator by their greatest common factor, GCF.
- To calculate the GCF, factor the numerator and denominator of the fraction into prime factors.
- Then multiply all the common prime factors: if there are repeating prime factors we only take them once, and only the ones having the lowest exponents (the lowest powers).
The fraction: 24/78
The prime factorizations of the numerator and denominator:
24 = 23 × 3
78 = 2 × 3 × 13
GCF (24; 78) = 2 × 3 = 6
24/78 =
(24 ÷ 6)/(78 ÷ 6) =
4/13
Yet another method to reduce a fraction:
* To reduce a fraction without calculating the GCF: factor its numerator and denominator, then all the common prime factors are easily identified and crossed out.
24/78 =
(23 × 3)/(2 × 3 × 13) =
((23 × 3) ÷ (2 × 3))/((2 × 3 × 13) ÷ (2 × 3)) =
(23 ÷ 2 × 3 ÷ 3)/(2 ÷ 2 × 3 ÷ 3 × 13) =
(2(3 - 1) × 1)/(1 × 1 × 13) =
(22 × 1)/(1 × 1 × 13) =
4/13
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
- 24/78 =
- 4/13
Rewrite the fraction
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
- 4/13 =
- 4 ÷ 13 ≈
- 0.307692307692 ≈
- 0.31
As a percentage:
- A percentage value p% is equal to the fraction: p/100, for any decimal number p. So, we need to change the form of the number calculated above, to show a denominator of 100.
- To do that, multiply the number by the fraction 100/100.
- The value of the fraction 100/100 = 1, so by multiplying the number by this fraction the result is not changing, only the form.
- 0.307692307692 =
- 0.307692307692 × 100/100 =
( - 0.307692307692 × 100)/100 =
- 30.769230769231/100 ≈
- 30.769230769231% ≈
- 30.77%
External link » Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator
The final answer:
written in three ways
As a negative proper fraction:
(the numerator < the denominator)
- 24/31 × 31/78 = - 4/13
As a decimal number:
- 24/31 × 31/78 ≈ - 0.31
As a percentage:
- 24/31 × 31/78 ≈ - 30.77%
How are the numbers being written on our website: comma ',' is used as a thousands separator; point '.' used as a decimal separator; numbers rounded off to max. 12 decimals (if the case). The set of the used symbols on our website: '/' the fraction bar; ÷ dividing; × multiplying; + plus (adding); - minus (subtracting); = equal; ≈ approximately equal.