Simplified Ratio = 2 : 1

GENERATE WORK

GENERATE WORK

**Input Data :**

Given Ratio = 6:3

**Objective :**

Express the ratio in simplest form

**Formula :**

Simplified Ratio = `frac{A}{GCD(A & B)} : frac{B}{GCD(A & B)}`

Simplified Ratio = `frac{A}{GCD(A, B & C)} : frac{B}{GCD(A, B & C)} : frac{C}{GCD(A, B & C)}`

**Solution :**

gcd(6, 3) = 3

Simplified Ratio = `6/3 : 3/3`

Simplified Ratio = 2 : 1

** Ratio Calculator**, formula, work with steps and practice problems to express the ratio of two or three numbers to its simplest form. It uses two or three whole numbers, integers, decimal numbers, fractions or mixed numbers $A, B$ and $C$ (optional) and simplifies ratios of the form $A : B: C$.

It is necessary to follow the next steps:

- Enter two or three numbers in the box. These numbers must be three whole numbers, integers, decimal numbers, fractions or mixed numbers;
- Press the "
**GENERATE WORK**" button to make the computation; - Ratio calculator will reduce the ratio of two or three numbers to its simplest form.

$$A:B=\frac{A}{GCF(A, B)}:\frac{B}{GCF(A, B)}$$

$$A:B:C=\frac{A}{GCF(A, B, C)}:\frac{B}{GCF(A, B, C)}:\frac{C}{GCF(A, B, C)}$$

A __2 numbers ratio__ is a relationship between two real or complex numbers indicating how many times the first number contains the second.
The numbers in a ratio may be any magnitudes, such as measurements of lengths, weights, time, etc.

A ratio may be either specified by giving both constituting numbers, written as

"$A$ to $B$" or "$A:B$", or $\frac{A}{B}$

Since a ratio is a quotient, its denominator cannot be zero, i.e. $B\ne0$. The numbers $A$ and $B$ are called Ratios should be expressed in simplified form. For example, the ratio $35:42$ is equivalent to $5:6$. It is clear that 5 and 6 are relatively prime unlike 35 and 42. To simplify calculations, it is better to consider ratios with relatively prime antecedents and consequents.

If two ratios are equal, $A:B=C:D$, they are called the equivalent ratios. Equivalent ratios can be found by multiplying the numerator and the denominator by the same non-zero number.

In many cases, ratios consist of three or more terms. A

An equation which express the equality of two ratios $A:B$ and $C:D$ is called

$$A:B=C:D\quad\mbox{or}\quad A:B::C:D$$

The numbers $A$, $B$, $C$ and $D$ are terms of the proportion. Usually, we say ($A$ is to $B$) as ($C$ is to $D$).
To find the simplified ratio we need to convert all values to whole numbers and to reduce the whole numbers to lowest terms using the greatest common factor (GCF). We distinguish two cases:

- If $A,B$ and $S$ are whole numbers;
- List the factors of the first number $A$;
- List the factors of the second number $B$
- List the factors of the third number $C$;
- Find the GFC of $A,B$ and $C$, $GCF(A, B, C)$. If the $GCF(A, B, C)= 1$, then the ratio is in simplest form;
- Divide $A,B$ and $C$ by the GCF, to get
$$A:B:C=\frac{A}{GCF(A, B, C)}:\frac{B}{GCF(A, B, C)}:\frac{C}{GCF(A, B, C)}$$

- If $A,B$ and $C$ are not whole numbers.
__Mixed number to ratio:__If some of the numbers `A`, $B$ or `C` are mixed numbers, then convert mixed numbers to improper fractions. If numbers $A,B$ and `C` are like fractions, multiply fractions by the denominator to eliminate it. If numbers `A` and `B` are unlike fractions, find the $LCD(A, B, C)$ and rewrite the fractions with the common LCD as the denominator. Then multiply fractions by the common denominator to eliminate it.__Decimal numbers to ratio:__If some of the numbers are decimal numbers, multiply all values by the same factor of $10$ to eliminate all decimal places.

To verify the resulting sum up all the profit share should bring a total profit of $\$18000$ or use this ratio calculator.

The Ratio Calculator work with steps shows the complete step-by-step calculation to simplify a ratio $6:3$ using the simplified ratio formula. For any other numbers, just supply two or three numbers and click on the "Generate Work" button. The grade school students may use this Ratio Calculator to generate the work, verify the results of dividing fractions, comparing ratios or proportions, derived by hand or do their homework problems efficiently.

The ratio can be applied to all physical quantities, finance and numbers such as the amount of sharing, investment, profit, loss, time taken, time, work, distance, speed etc.
Two magnitudes are in __the golden ratio__ if their ratio is equal to the ratio of the sum of the magnitudes to the larger of the magnitudes. This means, for magnitudes $a>b>0$, the golden ratio is

$$\frac{a+b}{a}=\frac{a}{b}=\frac{1+\sqrt{5}}{2}$$

The golden ratio is also called the golden mean or golden section. The division of a segment into the golden ratio is important in the geometry, especially in constructing regular pentagrams and pentagons.The ratio calculator can help to find equal ratios if we have three of the four parts of the two ratios. It is also useful in solving similar triangles. For instance, if the sides of one triangle are in proportion with the sides of another triangle, then these triangles are similar. It can also be used when resizing photos or video, etc.

**Practice Problem 1:**

The perimeter of a rectangle is $100$ centimeters. The ratio of its sides is $3:7$. Find the area of this rectangle.

**Practice Problem 2:**

he measures of the angles of a triangle are in the ratio $1:2:3$. Find the measures of the angles of the triangle.

**Practice Problem 3:**

The ratios of the side lengths of the triangle $\Delta ABC$ to the corresponding side lengths of $\Delta A'B'C'$ are in ratio $2:1$. Find perimeters of these triangles.