45/77 × 77/35 = ? 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: 45/77 × 77/35 = 45/35
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: 45/35
The prime factorizations of the numerator and denominator:
45 = 32 × 5
35 = 5 × 7
GCF (45; 35) = 5
45/35 =
(45 ÷ 5)/(35 ÷ 5) =
9/7
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.
45/35 =
(32 × 5)/(5 × 7) =
((32 × 5) ÷ 5)/((5 × 7) ÷ 5) =
(32 × 5 ÷ 5)/(5 ÷ 5 × 7) =
(32 × 1)/(1 × 7) =
9/7
Internal link » Reduce (simplify) common (ordinary) fractions to the lowest terms (to their simplest form equivalent), online calculator
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:
9 ÷ 7 = 1 and the remainder = 2 ⇒
9 = 1 × 7 + 2 ⇒
9/7 =
(1 × 7 + 2)/7 =
(1 × 7)/7 + 2/7 =
1 + 2/7 =
1 2/7
As a decimal number:
Simply divide the numerator by the denominator, without a remainder, as shown below:
1 + 2/7 =
1 + 2 ÷ 7 ≈
1.285714285714 ≈
1.29
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.
1.285714285714 =
1.285714285714 × 100/100 =
(1.285714285714 × 100)/100 =
128.571428571429/100 ≈
128.571428571429% ≈
128.57%
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)
45/77 × 77/35 = 9/7
As a mixed number (also called a mixed fraction):
45/77 × 77/35 = 1 2/7
As a decimal number:
45/77 × 77/35 ≈ 1.29
As a percentage:
45/77 × 77/35 ≈ 128.57%
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.