What is 2/54 plus 8/21? (Answer: 79/189)

Exact Answer

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Problem: What is 2/54 plus 8/21?
Formula / Expression: 2/54 + 8/21
Final Answer: 79/189
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 378
Multiply the numerator and denominator of 2/54 by 7, and multiply the numerator and denominator of 8/21 by 18 so both fractions share the common base 378.
Working: 2 × 7/54 × 7 = 14/378 and 8 × 18/21 × 18 = 144/378

Step 3: Add the Numerators
Now add the numerators (14 + 144 = 158) and keep the common denominator 378 unchanged.
Working: 14 + 144/378 = 158/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 158 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 158 ÷ 2/378 ÷ 2 = 79/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 189 produces a repeating decimal (approximately 0.417989, or 41.7989%).
Working: 79 ÷ 189 = 0.417989 (41.7989%)

Key Values:
- Simplified Fraction: 79/189
- Mixed Number Form: 79/189
- Decimal Value: 0.417989
- Percentage: 41.7989%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-54-plus-8-21/
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2/54 + 8/21 = 79/189

Simplified Fraction

79/189

Mixed Number

Proper (79/189)

Decimal Value

0.417989

Percentage

41.7989%

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Step-by-Step Solution: 2/54 + 8/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(54, 21) = 378

Step 2

Convert to Equivalent Fractions with Common Denominator 378

Multiply the numerator and denominator of 2/54 by 7, and multiply the numerator and denominator of 8/21 by 18 so both fractions share the common base 378.

2 × 7/54 × 7 = 14/378 and 8 × 18/21 × 18 = 144/378

Step 3

Add the Numerators

Now add the numerators (14 + 144 = 158) and keep the common denominator 378 unchanged.

14 + 144/378 = 158/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 158 and 378, which is 2. Divide both the numerator and denominator by 2.

158 ÷ 2/378 ÷ 2 = 79/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 189 produces a repeating decimal (approximately 0.417989, or 41.7989%).

79 ÷ 189 = 0.417989 (41.7989%)

Visual Representation

The diagram below illustrates 2/54 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/189`
Mixed Number Form	`79/189`
Decimal Form	`0.417989`
Percentage	`41.7989%`

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Frequently Asked Questions

What is 2/54 plus 8/21 as a fraction?

2/54 + 8/21 in simplest fraction form is 79/189.

What is 2/54 plus 8/21 as a decimal?

2/54 + 8/21 converted to a decimal is 0.417989.

What is 2/54 plus 8/21 as a percentage?

2/54 + 8/21 expressed as a percentage is 41.7989%.

Does 2/54 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.417989...) because the denominator contains prime factors other than 2 and 5.