Solve the Proportion 7/10 = 21/x (Answer: x = 30)

Exact Answer

==================================================
Problem: Solve the Proportion 7/10 = 21/x
Formula / Expression: 7/10 = 21/x → x = 30
Final Answer: x = 30
==================================================

Step-by-Step Solution:

Step 1: Set Up the Proportion Equation
Write the proportion equating the two ratios:
7 / 10 = 21 / x
Working: 7/10 = 21/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: (7) × (x) = (10) × (21).
Working: (7) × (x) = (10) × (21)

Step 3: Isolate the Unknown Variable x
Combine known numbers to obtain a simple one-step linear equation:
7 × x = 210.
Working: 7x = 210

Step 4: Divide to Solve for x
Divide both sides of the equation by 7:
x = 210 ÷ 7 = 30.
Working: x = 210 / 7 = 30

Step 5: Verify Proportion and Scale Multiplier
Check your work: Substituting x = 30 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.
Working: Check: (7 ÷ 10) = (21 ÷ 30)

Key Values:
- Solved Value (x): x = 30
- Equation: 7/10 = 21/x
- Cross Product: 210
- Scale Multiplier: 3x

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/solve-proportion-7-10-equals-21-x/
==================================================

710 = 21x → x = 30

Solved Value (x)

x = 30

Equation

7/10 = 21/x

Cross Product

210

Scale Multiplier

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

Step-by-Step Solution: 7/10 = 21/x → x = 30

Step 1

Set Up the Proportion Equation

Write the proportion equating the two ratios:
7 / 10 = 21 / x

7/10 = 21/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: (7) × (x) = (10) × (21).

(7) × (x) = (10) × (21)

Step 3

Isolate the Unknown Variable x

Combine known numbers to obtain a simple one-step linear equation:
7 × x = 210.

7x = 210

Step 4

Divide to Solve for x

Divide both sides of the equation by 7:
x = 210 ÷ 7 = 30.

x = 210 / 7 = 30

Step 5

Verify Proportion and Scale Multiplier

Check your work: Substituting x = 30 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.

Check: (7 ÷ 10) = (21 ÷ 30)

Visual Representation

The diagram below illustrates Solve proportion 7/10 = 21/x visually:

Summary & Alternative Representations

Property / Format	Value
Solved Value (x)	`x = 30`
Equation	`7/10 = 21/x`
Cross Product	`210`
Scale Multiplier	`3x`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

How do you solve for x in the proportion 7/10 = 21/x?

Cross-multiply diagonally: multiply the known diagonal pair (10 × 21 = 210) and then divide by the coefficient paired with x (7), resulting in x = 30.

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.