15/21 × 7/3 = ? Multiply the Common (Ordinary) Fractions, Online Calculator. Multiplication Operation Explained Step by Step
The numerators and the denominators of the fractions are multiplied separately
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: 15/21
The prime factorizations of the numerator and denominator:
15 = 3 × 5
21 = 3 × 7
GCF (15; 21) = 3
15/21 =
(15 ÷ 3)/(21 ÷ 3) =
5/7
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.
15/21 =
(3 × 5)/(3 × 7) =
((3 × 5) ÷ 3)/((3 × 7) ÷ 3) =
(3 ÷ 3 × 5)/(3 ÷ 3 × 7) =
(1 × 5)/(1 × 7) =
5/7
The fraction: 7/3
7/3 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
7 is a prime number (it cannot be factored into other prime factors)
3 is a prime number (it cannot be factored into other prime factors)
GCF (7; 3) = 1
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
Rewrite the equivalent simplified operation:
15/21 × 7/3 =
5/7 × 7/3
These fractions reduce each other:
They have numerators and denominators of equal values.
The fractions: 5/7 × 7/3 = 5/3
Simplify the operation
Reduce (simplify) the new fractions to their lowest terms equivalents:
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: 5/3
5/3 is already reduced to the lowest terms.
The numerator and denominator have no common prime factors.
The prime factorizations of the numerator and denominator:
5 is a prime number (it cannot be factored into other prime factors)
3 is a prime number (it cannot be factored into other prime factors)
GCF (5; 3) = 1
Rewrite the fraction
As a mixed number (also called a mixed fraction):
- A mixed number: a whole number and a proper fraction, both having the same sign.
- A proper fraction: the value of the numerator is smaller than the value of the denominator.
- Divide the numerator by the denominator and write down the quotient and the remainder of the division, as shown below:
5 ÷ 3 = 1 and the remainder = 2 ⇒
5 = 1 × 3 + 2 ⇒
5/3 =
(1 × 3 + 2)/3 =
(1 × 3)/3 + 2/3 =
1 + 2/3 =
1 2/3
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
1 + 2/3 =
1 + 2 ÷ 3 ≈
1.666666666667 ≈
1.67
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.
1.666666666667 =
1.666666666667 × 100/100 =
(1.666666666667 × 100)/100 =
166.666666666667/100 ≈
166.666666666667% ≈
166.67%
External link » Convert and write integer and decimal numbers, fractions and ratios as percentages, online calculator
The final answer:
written in four ways
As a positive improper fraction:
(the numerator >= the denominator)
15/21 × 7/3 = 5/3
As a mixed number (also called a mixed fraction):
15/21 × 7/3 = 1 2/3
As a decimal number:
15/21 × 7/3 ≈ 1.67
As a percentage:
15/21 × 7/3 ≈ 166.67%
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.