What is 7/21 plus 18/54? (Answer: 2/3)

Exact Answer

==================================================
Problem: What is 7/21 plus 18/54?
Formula / Expression: 7/21 + 18/54
Final Answer: 2/3
==================================================

Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 54 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 21 × 54 = 1134, keeping the calculation simpler).
Working: LCD(21, 54) = 378

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 7/21 by 18, and multiply the numerator and denominator of 18/54 by 7 so both fractions share the common base 378.
Working: 7 × 18/21 × 18 = 126/378 and 18 × 7/54 × 7 = 126/378

Step 3: Add the Numerators
Now add the numerators (126 + 126 = 252) and keep the common denominator 378 unchanged.
Working: 126 + 126/378 = 252/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 252 and 378, which is 126. Divide both the numerator and denominator by 126.
Working: 252 ÷ 126/378 ÷ 126 = 2/3

Step 5: Decimal & Percentage Representation
Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).
Working: 2 ÷ 3 = 0.666667 (66.6667%)

Key Values:
- Simplified Fraction: 2/3
- Mixed Number Form: 2/3
- Decimal Value: 0.666667
- Percentage: 66.6667%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-21-plus-18-54/
==================================================

7/21 + 18/54 = 2/3

Simplified Fraction

2/3

Mixed Number

Proper (2/3)

Decimal Value

0.666667

Percentage

66.6667%

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: 7/21 + 18/54

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 54 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 378 (which is smaller than their product 21 × 54 = 1134, keeping the calculation simpler).

LCD(21, 54) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 7/21 by 18, and multiply the numerator and denominator of 18/54 by 7 so both fractions share the common base 378.

7 × 18/21 × 18 = 126/378 and 18 × 7/54 × 7 = 126/378

Step 3

Add the Numerators

Now add the numerators (126 + 126 = 252) and keep the common denominator 378 unchanged.

126 + 126/378 = 252/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 252 and 378, which is 126. Divide both the numerator and denominator by 126.

252 ÷ 126/378 ÷ 126 = 2/3

Step 5

Decimal & Percentage Representation

Dividing the numerator 2 by denominator 3 produces a repeating decimal (approximately 0.666667, or 66.6667%).

2 ÷ 3 = 0.666667 (66.6667%)

Visual Representation

The diagram below illustrates 7/21 plus 18/54 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`2/3`
Mixed Number Form	`2/3`
Decimal Form	`0.666667`
Percentage	`66.6667%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

What is 7/21 plus 18/54 as a fraction?

7/21 + 18/54 in simplest fraction form is 2/3.

What is 7/21 plus 18/54 as a decimal?

7/21 + 18/54 converted to a decimal is 0.666667.

What is 7/21 plus 18/54 as a percentage?

7/21 + 18/54 expressed as a percentage is 66.6667%.

Does 7/21 plus 18/54 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.666667...) because the denominator contains prime factors other than 2 and 5.