What is 1/54 plus 5/21? (Answer: 97/378)

Exact Answer

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Problem: What is 1/54 plus 5/21?
Formula / Expression: 1/54 + 5/21
Final Answer: 97/378
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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 1/54 by 7, and multiply the numerator and denominator of 5/21 by 18 so both fractions share the common base 378.
Working: 1 × 7/54 × 7 = 7/378 and 5 × 18/21 × 18 = 90/378

Step 3: Add the Numerators
Now add the numerators (7 + 90 = 97) and keep the common denominator 378 unchanged.
Working: 7 + 90/378 = 97/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 97 and 378 is 1, confirming that 97/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 97/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 378 produces a repeating decimal (approximately 0.256614, or 25.6614%).
Working: 97 ÷ 378 = 0.256614 (25.6614%)

Key Values:
- Simplified Fraction: 97/378
- Mixed Number Form: 97/378
- Decimal Value: 0.256614
- Percentage: 25.6614%

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Solved with FractionsCalc:
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1/54 + 5/21 = 97/378

Simplified Fraction

97/378

Mixed Number

Proper (97/378)

Decimal Value

0.256614

Percentage

25.6614%

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Step-by-Step Solution: 1/54 + 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 1/54 by 7, and multiply the numerator and denominator of 5/21 by 18 so both fractions share the common base 378.

1 × 7/54 × 7 = 7/378 and 5 × 18/21 × 18 = 90/378

Step 3

Add the Numerators

Now add the numerators (7 + 90 = 97) and keep the common denominator 378 unchanged.

7 + 90/378 = 97/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 97 and 378 is 1, confirming that 97/378 cannot be reduced further—it is already in its simplest irreducible form.

97/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 378 produces a repeating decimal (approximately 0.256614, or 25.6614%).

97 ÷ 378 = 0.256614 (25.6614%)

Visual Representation

The diagram below illustrates 1/54 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/378`
Mixed Number Form	`97/378`
Decimal Form	`0.256614`
Percentage	`25.6614%`

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Frequently Asked Questions

What is 1/54 plus 5/21 as a fraction?

1/54 + 5/21 in simplest fraction form is 97/378.

What is 1/54 plus 5/21 as a decimal?

1/54 + 5/21 converted to a decimal is 0.256614.

What is 1/54 plus 5/21 as a percentage?

1/54 + 5/21 expressed as a percentage is 25.6614%.

Does 1/54 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.256614...) because the denominator contains prime factors other than 2 and 5.