Solve the Proportion 2/5 = 6/x (Answer: x = 15)

Exact Answer

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Problem: Solve the Proportion 2/5 = 6/x
Formula / Expression: 2/5 = 6/x → x = 15
Final Answer: x = 15
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Step-by-Step Solution:

Step 1: Set Up the Proportion Equation
Write the proportion equating the two ratios:
2 / 5 = 6 / x
Working: 2/5 = 6/x

Step 2: Apply the Cross-Multiplication Property
In any true proportion A/B = C/D, the cross products are always equal: A × D = B × C.
Multiplying diagonally: (2) × (x) = (5) × (6).
Working: (2) × (x) = (5) × (6)

Step 3: Isolate the Unknown Variable x
Combine known numbers to obtain a simple one-step linear equation:
2 × x = 30.
Working: 2x = 30

Step 4: Divide to Solve for x
Divide both sides of the equation by 2:
x = 30 ÷ 2 = 15.
Working: x = 30 / 2 = 15

Step 5: Verify Proportion and Scale Multiplier
Check your work: Substituting x = 15 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.
Working: Check: (2 ÷ 5) = (6 ÷ 15)

Key Values:
- Solved Value (x): x = 15
- Equation: 2/5 = 6/x
- Cross Product: 30
- Scale Multiplier: 3x

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Solved with FractionsCalc:
https://fractionscalc.com/solve-proportion-2-5-equals-6-x/
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25 = 6x → x = 15

Solved Value (x)

x = 15

Equation

2/5 = 6/x

Cross Product

Scale Multiplier

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Step-by-Step Solution: 2/5 = 6/x → x = 15

Step 1

Set Up the Proportion Equation

Write the proportion equating the two ratios:
2 / 5 = 6 / x

2/5 = 6/x

Step 2

Apply the Cross-Multiplication Property

In any true proportion A/B = C/D, the cross products are always equal: A × D = B × C.
Multiplying diagonally: (2) × (x) = (5) × (6).

(2) × (x) = (5) × (6)

Step 3

Isolate the Unknown Variable x

Combine known numbers to obtain a simple one-step linear equation:
2 × x = 30.

2x = 30

Step 4

Divide to Solve for x

Divide both sides of the equation by 2:
x = 30 ÷ 2 = 15.

x = 30 / 2 = 15

Step 5

Verify Proportion and Scale Multiplier

Check your work: Substituting x = 15 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.

Check: (2 ÷ 5) = (6 ÷ 15)

Visual Representation

The diagram below illustrates Solve proportion 2/5 = 6/x visually:

Summary & Alternative Representations

Property / Format	Value
Solved Value (x)	`x = 15`
Equation	`2/5 = 6/x`
Cross Product	`30`
Scale Multiplier	`3x`

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Frequently Asked Questions

How do you solve for x in the proportion 2/5 = 6/x?

Cross-multiply diagonally: multiply the known diagonal pair (5 × 6 = 30) and then divide by the coefficient paired with x (2), resulting in x = 15.

What is the cross multiplication rule for proportions?

For any proportion A/B = C/D, the product of the extremes (A × D) is always equal to the product of the means (B × C).

Can a proportion have decimal answers?

Yes! If the cross-product is not evenly divisible by the coefficient, the result can be written as an exact decimal or as a simplified fraction / mixed number.