What is 5/21 plus 13/54? (Answer: 181/378)

Exact Answer

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Problem: What is 5/21 plus 13/54?
Formula / Expression: 5/21 + 13/54
Final Answer: 181/378
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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 5/21 by 18, and multiply the numerator and denominator of 13/54 by 7 so both fractions share the common base 378.
Working: 5 × 18/21 × 18 = 90/378 and 13 × 7/54 × 7 = 91/378

Step 3: Add the Numerators
Now add the numerators (90 + 91 = 181) and keep the common denominator 378 unchanged.
Working: 90 + 91/378 = 181/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 181 and 378 is 1, confirming that 181/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 181/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 181 by denominator 378 produces a repeating decimal (approximately 0.478836, or 47.8836%).
Working: 181 ÷ 378 = 0.478836 (47.8836%)

Key Values:
- Simplified Fraction: 181/378
- Mixed Number Form: 181/378
- Decimal Value: 0.478836
- Percentage: 47.8836%

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Solved with FractionsCalc:
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5/21 + 13/54 = 181/378

Simplified Fraction

181/378

Mixed Number

Proper (181/378)

Decimal Value

0.478836

Percentage

47.8836%

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Step-by-Step Solution: 5/21 + 13/54

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 5/21 by 18, and multiply the numerator and denominator of 13/54 by 7 so both fractions share the common base 378.

5 × 18/21 × 18 = 90/378 and 13 × 7/54 × 7 = 91/378

Step 3

Add the Numerators

Now add the numerators (90 + 91 = 181) and keep the common denominator 378 unchanged.

90 + 91/378 = 181/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 181 and 378 is 1, confirming that 181/378 cannot be reduced further—it is already in its simplest irreducible form.

181/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 181 by denominator 378 produces a repeating decimal (approximately 0.478836, or 47.8836%).

181 ÷ 378 = 0.478836 (47.8836%)

Visual Representation

The diagram below illustrates 5/21 plus 13/54 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`181/378`
Mixed Number Form	`181/378`
Decimal Form	`0.478836`
Percentage	`47.8836%`

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Frequently Asked Questions

What is 5/21 plus 13/54 as a fraction?

5/21 + 13/54 in simplest fraction form is 181/378.

What is 5/21 plus 13/54 as a decimal?

5/21 + 13/54 converted to a decimal is 0.478836.

What is 5/21 plus 13/54 as a percentage?

5/21 + 13/54 expressed as a percentage is 47.8836%.

Does 5/21 plus 13/54 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.478836...) because the denominator contains prime factors other than 2 and 5.