What is 8/54 plus 5/21? (Answer: 73/189)

Exact Answer

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Problem: What is 8/54 plus 5/21?
Formula / Expression: 8/54 + 5/21
Final Answer: 73/189
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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 5/21 by 18 so both fractions share the common base 378.
Working: 8 × 7/54 × 7 = 56/378 and 5 × 18/21 × 18 = 90/378

Step 3: Add the Numerators
Now add the numerators (56 + 90 = 146) and keep the common denominator 378 unchanged.
Working: 56 + 90/378 = 146/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 146 and 378, which is 2. Divide both the numerator and denominator by 2.
Working: 146 ÷ 2/378 ÷ 2 = 73/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 189 produces a repeating decimal (approximately 0.386243, or 38.6243%).
Working: 73 ÷ 189 = 0.386243 (38.6243%)

Key Values:
- Simplified Fraction: 73/189
- Mixed Number Form: 73/189
- Decimal Value: 0.386243
- Percentage: 38.6243%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-54-plus-5-21/
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8/54 + 5/21 = 73/189

Simplified Fraction

73/189

Mixed Number

Proper (73/189)

Decimal Value

0.386243

Percentage

38.6243%

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Step-by-Step Solution: 8/54 + 5/21

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 5/21 by 18 so both fractions share the common base 378.

8 × 7/54 × 7 = 56/378 and 5 × 18/21 × 18 = 90/378

Step 3

Add the Numerators

Now add the numerators (56 + 90 = 146) and keep the common denominator 378 unchanged.

56 + 90/378 = 146/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 146 and 378, which is 2. Divide both the numerator and denominator by 2.

146 ÷ 2/378 ÷ 2 = 73/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 189 produces a repeating decimal (approximately 0.386243, or 38.6243%).

73 ÷ 189 = 0.386243 (38.6243%)

Visual Representation

The diagram below illustrates 8/54 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/189`
Mixed Number Form	`73/189`
Decimal Form	`0.386243`
Percentage	`38.6243%`

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Frequently Asked Questions

What is 8/54 plus 5/21 as a fraction?

8/54 + 5/21 in simplest fraction form is 73/189.

What is 8/54 plus 5/21 as a decimal?

8/54 + 5/21 converted to a decimal is 0.386243.

What is 8/54 plus 5/21 as a percentage?

8/54 + 5/21 expressed as a percentage is 38.6243%.

Does 8/54 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.386243...) because the denominator contains prime factors other than 2 and 5.