What is 14/54 plus 7/21? (Answer: 16/27)

Exact Answer

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Problem: What is 14/54 plus 7/21?
Formula / Expression: 14/54 + 7/21
Final Answer: 16/27
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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 14/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.
Working: 14 × 7/54 × 7 = 98/378 and 7 × 18/21 × 18 = 126/378

Step 3: Add the Numerators
Now add the numerators (98 + 126 = 224) and keep the common denominator 378 unchanged.
Working: 98 + 126/378 = 224/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 224 and 378, which is 14. Divide both the numerator and denominator by 14.
Working: 224 ÷ 14/378 ÷ 14 = 16/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 27 produces a repeating decimal (approximately 0.592593, or 59.2593%).
Working: 16 ÷ 27 = 0.592593 (59.2593%)

Key Values:
- Simplified Fraction: 16/27
- Mixed Number Form: 16/27
- Decimal Value: 0.592593
- Percentage: 59.2593%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-14-54-plus-7-21/
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14/54 + 7/21 = 16/27

Simplified Fraction

16/27

Mixed Number

Proper (16/27)

Decimal Value

0.592593

Percentage

59.2593%

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Step-by-Step Solution: 14/54 + 7/21

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 14/54 by 7, and multiply the numerator and denominator of 7/21 by 18 so both fractions share the common base 378.

14 × 7/54 × 7 = 98/378 and 7 × 18/21 × 18 = 126/378

Step 3

Add the Numerators

Now add the numerators (98 + 126 = 224) and keep the common denominator 378 unchanged.

98 + 126/378 = 224/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 224 and 378, which is 14. Divide both the numerator and denominator by 14.

224 ÷ 14/378 ÷ 14 = 16/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 27 produces a repeating decimal (approximately 0.592593, or 59.2593%).

16 ÷ 27 = 0.592593 (59.2593%)

Visual Representation

The diagram below illustrates 14/54 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/27`
Mixed Number Form	`16/27`
Decimal Form	`0.592593`
Percentage	`59.2593%`

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Frequently Asked Questions

What is 14/54 plus 7/21 as a fraction?

14/54 + 7/21 in simplest fraction form is 16/27.

What is 14/54 plus 7/21 as a decimal?

14/54 + 7/21 converted to a decimal is 0.592593.

What is 14/54 plus 7/21 as a percentage?

14/54 + 7/21 expressed as a percentage is 59.2593%.

Does 14/54 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.592593...) because the denominator contains prime factors other than 2 and 5.