What is 12/54 plus 9/21? (Answer: 41/63)

Exact Answer

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Problem: What is 12/54 plus 9/21?
Formula / Expression: 12/54 + 9/21
Final Answer: 41/63
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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 12/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 12 × 7/54 × 7 = 84/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (84 + 162 = 246) and keep the common denominator 378 unchanged.
Working: 84 + 162/378 = 246/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 246 and 378, which is 6. Divide both the numerator and denominator by 6.
Working: 246 ÷ 6/378 ÷ 6 = 41/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).
Working: 41 ÷ 63 = 0.650794 (65.0794%)

Key Values:
- Simplified Fraction: 41/63
- Mixed Number Form: 41/63
- Decimal Value: 0.650794
- Percentage: 65.0794%

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Solved with FractionsCalc:
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12/54 + 9/21 = 41/63

Simplified Fraction

41/63

Mixed Number

Proper (41/63)

Decimal Value

0.650794

Percentage

65.0794%

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Step-by-Step Solution: 12/54 + 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 12/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

12 × 7/54 × 7 = 84/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (84 + 162 = 246) and keep the common denominator 378 unchanged.

84 + 162/378 = 246/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 246 and 378, which is 6. Divide both the numerator and denominator by 6.

246 ÷ 6/378 ÷ 6 = 41/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 63 produces a repeating decimal (approximately 0.650794, or 65.0794%).

41 ÷ 63 = 0.650794 (65.0794%)

Visual Representation

The diagram below illustrates 12/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/63`
Mixed Number Form	`41/63`
Decimal Form	`0.650794`
Percentage	`65.0794%`

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Frequently Asked Questions

What is 12/54 plus 9/21 as a fraction?

12/54 + 9/21 in simplest fraction form is 41/63.

What is 12/54 plus 9/21 as a decimal?

12/54 + 9/21 converted to a decimal is 0.650794.

What is 12/54 plus 9/21 as a percentage?

12/54 + 9/21 expressed as a percentage is 65.0794%.

Does 12/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.650794...) because the denominator contains prime factors other than 2 and 5.