What is 23/54 plus 9/21? (Answer: 323/378)

Exact Answer

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Problem: What is 23/54 plus 9/21?
Formula / Expression: 23/54 + 9/21
Final Answer: 323/378
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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 23/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.
Working: 23 × 7/54 × 7 = 161/378 and 9 × 18/21 × 18 = 162/378

Step 3: Add the Numerators
Now add the numerators (161 + 162 = 323) and keep the common denominator 378 unchanged.
Working: 161 + 162/378 = 323/378

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 323 and 378 is 1, confirming that 323/378 cannot be reduced further—it is already in its simplest irreducible form.
Working: 323/378

Step 5: Decimal & Percentage Representation
Dividing the numerator 323 by denominator 378 produces a repeating decimal (approximately 0.854497, or 85.4497%).
Working: 323 ÷ 378 = 0.854497 (85.4497%)

Key Values:
- Simplified Fraction: 323/378
- Mixed Number Form: 323/378
- Decimal Value: 0.854497
- Percentage: 85.4497%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-23-54-plus-9-21/
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23/54 + 9/21 = 323/378

Simplified Fraction

323/378

Mixed Number

Proper (323/378)

Decimal Value

0.854497

Percentage

85.4497%

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Step-by-Step Solution: 23/54 + 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 23/54 by 7, and multiply the numerator and denominator of 9/21 by 18 so both fractions share the common base 378.

23 × 7/54 × 7 = 161/378 and 9 × 18/21 × 18 = 162/378

Step 3

Add the Numerators

Now add the numerators (161 + 162 = 323) and keep the common denominator 378 unchanged.

161 + 162/378 = 323/378

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 323 and 378 is 1, confirming that 323/378 cannot be reduced further—it is already in its simplest irreducible form.

323/378

Step 5

Decimal & Percentage Representation

Dividing the numerator 323 by denominator 378 produces a repeating decimal (approximately 0.854497, or 85.4497%).

323 ÷ 378 = 0.854497 (85.4497%)

Visual Representation

The diagram below illustrates 23/54 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`323/378`
Mixed Number Form	`323/378`
Decimal Form	`0.854497`
Percentage	`85.4497%`

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Frequently Asked Questions

What is 23/54 plus 9/21 as a fraction?

23/54 + 9/21 in simplest fraction form is 323/378.

What is 23/54 plus 9/21 as a decimal?

23/54 + 9/21 converted to a decimal is 0.854497.

What is 23/54 plus 9/21 as a percentage?

23/54 + 9/21 expressed as a percentage is 85.4497%.

Does 23/54 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.854497...) because the denominator contains prime factors other than 2 and 5.