# Equivalent Fractions are found.

If they have the same value, there are two fractions.Knowing how to convert a fraction into an equivalent one is an essential math skill that is necessary for everything from basic math to advanced math.There are a number of ways to calculate equivalent fractions from basic multiplication and division to more complex methods.

### Step 1: If you add the numerator and denominator, you get the same number.

Two fractions that are different but equivalent have multiples of each other.If you add the numerator and denominator of a fraction to the same number, you will get an equivalent fraction.The fractions will have the same value even though the numbers are different.If we take the fraction 4/8 and add the numerator and denominator by 2, we get 8/16.The two fractions are the same.When we add up the two fractions, we get 42/(82), which is essentially the same.When you carry out the division, you can see that 2/2 is equal to 1.It's easy to see why 4/8 and 8/16 are the same.It is fair to say that 4/8 is 8/16.There is an infinite number of equivalent fractions.If you want to get an equivalent fraction, you can divide the numerator and denominator by any whole number.

### Step 2: The numerator and denominator are the same number.

A new fraction that's equivalent to your starting fraction can be found using division.To get an equivalent fraction, divide the numerator and the denominator by the same number.The resulting fraction must have whole numbers in both the numerator and denominator to be valid.Let's look at that again.If we divide the numerator and denominator by 2, we get 2/4.This equivalent fraction is valid because 2 and 4 are both whole numbers.

### Step 3: To make the larger denominator, the smaller one needs to be multiplied.

If two fractions are equivalent, there are many problems with fractions.The fractions can be put in the same terms to determine equivalency.Take the fractions again.The smaller denominator is 8 and we would have to add x2 to make the larger one, which is 16.The number in this case is 2.You can divide the larger denominator by the smaller one for more difficult numbers.16 divided by 8 gets us 2.Sometimes the number is not a whole number.The number would be 3.5 if the denominators were 2 and 7.

### Step 4: The numerator and denominator of the fraction are expressed in lower terms from the first step.

Two fractions are the same but different.If you add the numerator and denominator of a fraction to the same number, you will get an equivalent fraction.The fractions will have the same value even though the numbers are different.If we take the fraction 4/8 from step one and add both the numerator and denominator by our previously determined number 2, we get (42)/(82).The two fractions are equivalent.

### Step 5: To calculate each fraction, use a decimal number.

You can use a decimal number to determine equivalency for simple fractions.This is the simplest way to determine equivalency since every fraction is a division problem.Take our previous use of 4/8.The fraction 4/8 is the same as saying 4 divided by 8.You can solve the other example as well.If the two numbers are exactly the same, they are equivalent.Before the lack of equivalence becomes apparent, remember that the decimal expression may go several digits.1/3 is repeating while 3/10 is not.The two fractions are not equivalent if we use more than one digit.

### Step 6: To find an equivalent fraction, divide the numerator and denominator by the same number.

The division method requires additional steps for more complex fractions.If you divide the numerator and the denominator by the same number, you can get an equivalent fraction.There is a caveat to this process.The fraction must have both the numerator and denominator in it.Let's look at that again.If we divide the numerator and denominator by 2, we get.This equivalent fraction is valid because 2 and 4 are both whole numbers.

### Step 7: The fractions should be reduced to their lowest terms.

If you divide fractions by their greatest common factor, you can convert them to their simplest terms.The same logic of expressing equivalent fractions by converting them to have the same denominator is used in this step.The numerator and denominator are both small when a fraction is in its simplest terms.Neither can be divided by the number.To convert a fraction that's not in simplest terms to an equivalent form that is, we divide the numerator and denominator by their greatest common factor.The largest number that divides into both is the GCF of the numerator and denominator.Since the largest number that divides evenly into both 4 and 8 is 4 we would divide the numerator and denominator by 4 to get it in simple terms.8 4) is the number of 4.1/2 is the simplest expression of the fraction for our other example of 8/16.

### Step 8: The two fractions need to be equal to each other.

We use cross multiplication for math problems where we know the fractions are equivalent, but one of the numbers has been replaced with a variable for which we must solve.We know these fractions are equivalent because they're the only terms on opposite sides of an equal sign, but it's not obvious how to solve for the variable.Cross multiplication makes it easy to solve these types of problems.

### Step 9: The equals sign is an "X" shape and the two equivalent fractions must be taken.

If you divide the numerator of one fraction by the denominator of the other and then set these two answers equal to each other, you can solve the problem.There are two examples of 4/8 and 8/16.We can prove the concept since we already know they're equivalent.It is obvious that 4 x 16 is 8 x 8 or 64 x 64.The fractions are not equivalent if the two numbers are different.

### Step 10: A variable can be introduced.

Since cross multiplication is the easiest way to determine equivalent fractions, let's add a variable.The equation 2/x is 10/13.If we want to cross multiply, we have to set our answers equal to each other.Getting an answer for our variable is a matter of simple math.The initial equivalent fractions are 2/2.6 and 10/13.

### Step 11: Cross multiplication is used in equations with multiple variables.

Cross multiplication works the same way if you're dealing with two simple fractions or more complex fractions.If both fractions contain variables, you just have to eliminate them at the end of the process.If the numerators or denominators of your fractions contain variable expressions, simply "multiply through" by using the distributive property and solve as you normally would.Let's look at the equation ((x + 3)/2).We can simplify the equation by subtracting 2x from the 4x + 12 equation.

### Step 12: Divide the two fractions.

We start equivalency problems by using cross multiplication.An expression that can't be solved via algebra is likely to result from a cross multiplication of variable terms.Factoring and/or the Quadratic Formula can be used in these cases.Let's look at the equation.Let's use the following formula: (x + 1) (2x - 2), 2 x + 2x -2x,2 x - 2, 4 x, 3 x)

### Step 13: The equation needs to be expressed as a quadratic equation.

Setting the equation equal to zero is what we want to do at this point.We subtract 12 from the other side to get 2x - 14.Some values can equal 0.2x - 14 is the simplest form of the equation.Even when some values are 0, it will help to mirror the form of the quadratic equation.

### Step 14: Plug the numbers from the equation into the formula.

The formula will help us figure out the value of x at this point.Don't be intimidated by the length of the formula.You plug the values from your equation into the appropriate spots before you solve it.x is equal to (b - 4ac)/2a.2x + 14 + 2 + b + 0 + c + -14 is an equation.