What is 3/21 plus 8/54? (Answer: 55/189)

Exact Answer

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Problem: What is 3/21 plus 8/54?
Formula / Expression: 3/21 + 8/54
Final Answer: 55/189
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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 3/21 by 18, and multiply the numerator and denominator of 8/54 by 7 so both fractions share the common base 378.
Working: 3 × 18/21 × 18 = 54/378 and 8 × 7/54 × 7 = 56/378

Step 3: Add the Numerators
Now add the numerators (54 + 56 = 110) and keep the common denominator 378 unchanged.
Working: 54 + 56/378 = 110/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 110 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 110 ÷ 2/378 ÷ 2 = 55/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 189 produces a repeating decimal (approximately 0.291005, or 29.1005%).
Working: 55 ÷ 189 = 0.291005 (29.1005%)

Key Values:
- Simplified Fraction: 55/189
- Mixed Number Form: 55/189
- Decimal Value: 0.291005
- Percentage: 29.1005%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-8-54/
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3/21 + 8/54 = 55/189

Simplified Fraction

55/189

Mixed Number

Proper (55/189)

Decimal Value

0.291005

Percentage

29.1005%

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Step-by-Step Solution: 3/21 + 8/54

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 3/21 by 18, and multiply the numerator and denominator of 8/54 by 7 so both fractions share the common base 378.

3 × 18/21 × 18 = 54/378 and 8 × 7/54 × 7 = 56/378

Step 3

Add the Numerators

Now add the numerators (54 + 56 = 110) and keep the common denominator 378 unchanged.

54 + 56/378 = 110/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 110 and 378, which is 2. Divide both the numerator and denominator by 2.

110 ÷ 2/378 ÷ 2 = 55/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 189 produces a repeating decimal (approximately 0.291005, or 29.1005%).

55 ÷ 189 = 0.291005 (29.1005%)

Visual Representation

The diagram below illustrates 3/21 plus 8/54 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/189`
Mixed Number Form	`55/189`
Decimal Form	`0.291005`
Percentage	`29.1005%`

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Frequently Asked Questions

What is 3/21 plus 8/54 as a fraction?

3/21 + 8/54 in simplest fraction form is 55/189.

What is 3/21 plus 8/54 as a decimal?

3/21 + 8/54 converted to a decimal is 0.291005.

What is 3/21 plus 8/54 as a percentage?

3/21 + 8/54 expressed as a percentage is 29.1005%.

Does 3/21 plus 8/54 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.291005...) because the denominator contains prime factors other than 2 and 5.