What is 8/54 plus 6/21? (Answer: 82/189)

Exact Answer

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Problem: What is 8/54 plus 6/21?
Formula / Expression: 8/54 + 6/21
Final Answer: 82/189
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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 8/54 by 7, and multiply the numerator and denominator of 6/21 by 18 so both fractions share the common base 378.
Working: 8 × 7/54 × 7 = 56/378 and 6 × 18/21 × 18 = 108/378

Step 3: Add the Numerators
Now add the numerators (56 + 108 = 164) and keep the common denominator 378 unchanged.
Working: 56 + 108/378 = 164/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 164 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 164 ÷ 2/378 ÷ 2 = 82/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 82 by denominator 189 produces a repeating decimal (approximately 0.433862, or 43.3862%).
Working: 82 ÷ 189 = 0.433862 (43.3862%)

Key Values:
- Simplified Fraction: 82/189
- Mixed Number Form: 82/189
- Decimal Value: 0.433862
- Percentage: 43.3862%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-54-plus-6-21/
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8/54 + 6/21 = 82/189

Simplified Fraction

82/189

Mixed Number

Proper (82/189)

Decimal Value

0.433862

Percentage

43.3862%

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Step-by-Step Solution: 8/54 + 6/21

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 8/54 by 7, and multiply the numerator and denominator of 6/21 by 18 so both fractions share the common base 378.

8 × 7/54 × 7 = 56/378 and 6 × 18/21 × 18 = 108/378

Step 3

Add the Numerators

Now add the numerators (56 + 108 = 164) and keep the common denominator 378 unchanged.

56 + 108/378 = 164/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 164 and 378, which is 2. Divide both the numerator and denominator by 2.

164 ÷ 2/378 ÷ 2 = 82/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 82 by denominator 189 produces a repeating decimal (approximately 0.433862, or 43.3862%).

82 ÷ 189 = 0.433862 (43.3862%)

Visual Representation

The diagram below illustrates 8/54 plus 6/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`82/189`
Mixed Number Form	`82/189`
Decimal Form	`0.433862`
Percentage	`43.3862%`

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Frequently Asked Questions

What is 8/54 plus 6/21 as a fraction?

8/54 + 6/21 in simplest fraction form is 82/189.

What is 8/54 plus 6/21 as a decimal?

8/54 + 6/21 converted to a decimal is 0.433862.

What is 8/54 plus 6/21 as a percentage?

8/54 + 6/21 expressed as a percentage is 43.3862%.

Does 8/54 plus 6/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.433862...) because the denominator contains prime factors other than 2 and 5.