Solve the Proportion 5/x = 15/21 (Answer: x = 7)

Exact Answer

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Problem: Solve the Proportion 5/x = 15/21
Formula / Expression: 5/x = 15/21 → x = 7
Final Answer: x = 7
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Step-by-Step Solution:

Step 1: Set Up the Proportion Equation
Write the proportion equating the two ratios:
5 / x = 15 / 21
Working: 5/x = 15/21

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: (5) × (21) = (x) × (15).
Working: (5) × (21) = (x) × (15)

Step 3: Isolate the Unknown Variable x
Combine known numbers to obtain a simple one-step linear equation:
15 × x = 105.
Working: 15x = 105

Step 4: Divide to Solve for x
Divide both sides of the equation by 15:
x = 105 ÷ 15 = 7.
Working: x = 105 / 15 = 7

Step 5: Verify Proportion and Scale Multiplier
Check your work: Substituting x = 7 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.
Working: Check: (5 ÷ 7) = (15 ÷ 21)

Key Values:
- Solved Value (x): x = 7
- Equation: 5/x = 15/21
- Cross Product: 105
- Scale Multiplier: 3x

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Solved with FractionsCalc:
https://fractionscalc.com/solve-proportion-5-x-equals-15-21/
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5x = 1521 → x = 7

Solved Value (x)

x = 7

Equation

5/x = 15/21

Cross Product

105

Scale Multiplier

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Step-by-Step Solution: 5/x = 15/21 → x = 7

Step 1

Set Up the Proportion Equation

Write the proportion equating the two ratios:
5 / x = 15 / 21

5/x = 15/21

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: (5) × (21) = (x) × (15).

(5) × (21) = (x) × (15)

Step 3

Isolate the Unknown Variable x

Combine known numbers to obtain a simple one-step linear equation:
15 × x = 105.

15x = 105

Step 4

Divide to Solve for x

Divide both sides of the equation by 15:
x = 105 ÷ 15 = 7.

x = 105 / 15 = 7

Step 5

Verify Proportion and Scale Multiplier

Check your work: Substituting x = 7 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.

Check: (5 ÷ 7) = (15 ÷ 21)

Visual Representation

The diagram below illustrates Solve proportion 5/x = 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Solved Value (x)	`x = 7`
Equation	`5/x = 15/21`
Cross Product	`105`
Scale Multiplier	`3x`

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Frequently Asked Questions

How do you solve for x in the proportion 5/x = 15/21?

Cross-multiply diagonally: multiply the known diagonal pair (5 × 21 = 105) and then divide by the coefficient paired with x (15), resulting in x = 7.

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.