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Fractions Solve for Unknown

Solve for One Unknown
Answer:
x = 15

Showing Work

By Comparison:
If
24 ÷ 8 = 3

Then we must have:
x ÷ 5 = 3

Solving for x,
x = 5 × 3

x = 15

By Cross Product:
(5/8) = (x/24)

The Cross Product:
(5 * 24) = (x * 8)

Solving for x:
(5 * 24) / 8 = x

Reducing:
15 = x

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Calculator Use

Solve equivalent and inequivalent fractions for one unknown value. This calculator will calculate 1 unknown variable to solve the proportion between 2 fractions. Some people refer to this as solving equivalent fractions but it also solves for inequalities.

Enter 3 values and 1 unknown. For example, enter X/45 = 1/15. This calculator will solve for X.

How to solve for variable X in fractions

We solve for X by cross multiplying and solving the equation for X

For Example: Given the equation 4/10 = X/15 solve for X.

Cross multiplying we get
4 * 15 = 10 * X

Solving the equation for X we get
X = (4 * 15) / 10

Simplifying we get
X = 6

Plugging 4 back into the original equation
4/10 = 6/15

Checking our answer, since multiplying anything by 1 doesn't change its value and 3/3 = 1 and 2/2 = 1,
4/10 * 3/3 = 12/30
6/15 * 2/2 = 12/30
since these are equal it is true that X = 4 in our equation.

Why does cross multiplying fractions work?

Cross multiplying works because we are really just multiplying both sides of the equation by 1. Since multiplying anything by 1 doesn't change its value we will have an equivalent equation.

For example, let's look at this equation:

\( \dfrac{a}{b} = \dfrac{c}{d} \)

If we multiply both sides by 1 using the denominators from the other side of the equation we get:

\( \dfrac{a}{b} \times \dfrac{d}{d} = \dfrac{c}{d} \times \dfrac{b}{b} \)

Note that this doesn't change anything, because multiplying anything by 1 doesn't change its value. So now we have:

\( \dfrac{a \times d}{b \times d} = \dfrac{b \times c}{b \times d} \)

If we said \( \frac{3}{4} = \frac{3}{4} \), or \( \frac{a}{4} = \frac{b}{4} \), you could then say 3 = 3 or a = b.

Since the denominators are also the same here, b × d, we can remove them and say that:

\( a \times d = b \times c \)

Which is the result of cross multiplying our original equation:

\( \dfrac{a}{b} = \dfrac{c}{d} \)

References/ Additional Reading

Cross Multiply from Math Is Fun at http://www.mathsisfun.com/

Cross-Multiplication from Ask Dr. Math at http://mathforum.org/

Cross Products from Ask Dr. Math at http://mathforum.org/



 

Cite this content, page or calculator as:

Furey, Edward "Fractions Solve for Unknown"; from http://www.calculatorsoup.com - Online Calculator Resource.

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