What is 13/54 plus 9/21? (Answer: 253/378)

Exact Answer

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Problem: What is 13/54 plus 9/21?
Formula / Expression: 13/54 + 9/21
Final Answer: 253/378
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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 13/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 13 × 7/54 × 7 = 91/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (91 + 162 = 253) and keep the common denominator 378 unchanged.
Working: 91 + 162/378 = 253/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 253 and 378 is 1, confirming that 253/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 253/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 253 by denominator 378 produces a repeating decimal (approximately 0.669312, or 66.9312%).
Working: 253 ÷ 378 = 0.669312 (66.9312%)

Key Values:
- Simplified Fraction: 253/378
- Mixed Number Form: 253/378
- Decimal Value: 0.669312
- Percentage: 66.9312%

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Solved with FractionsCalc:
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13/54 + 9/21 = 253/378

Simplified Fraction

253/378

Mixed Number

Proper (253/378)

Decimal Value

0.669312

Percentage

66.9312%

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Step-by-Step Solution: 13/54 + 9/21

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 13/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

13 × 7/54 × 7 = 91/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (91 + 162 = 253) and keep the common denominator 378 unchanged.

91 + 162/378 = 253/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 253 and 378 is 1, confirming that 253/378 cannot be reduced further—it is already in its simplest irreducible form.

253/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 253 by denominator 378 produces a repeating decimal (approximately 0.669312, or 66.9312%).

253 ÷ 378 = 0.669312 (66.9312%)

Visual Representation

The diagram below illustrates 13/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`253/378`
Mixed Number Form	`253/378`
Decimal Form	`0.669312`
Percentage	`66.9312%`

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Frequently Asked Questions

What is 13/54 plus 9/21 as a fraction?

13/54 + 9/21 in simplest fraction form is 253/378.

What is 13/54 plus 9/21 as a decimal?

13/54 + 9/21 converted to a decimal is 0.669312.

What is 13/54 plus 9/21 as a percentage?

13/54 + 9/21 expressed as a percentage is 66.9312%.

Does 13/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.669312...) because the denominator contains prime factors other than 2 and 5.