What is 6/54 plus 4/21? (Answer: 19/63)

Exact Answer

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Problem: What is 6/54 plus 4/21?
Formula / Expression: 6/54 + 4/21
Final Answer: 19/63
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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 6/54 by 7, and multiply the numerator and denominator of 4/21 by 18 so both fractions share the common base 378.
Working: 6 × 7/54 × 7 = 42/378 and 4 × 18/21 × 18 = 72/378

Step 3: Add the Numerators
Now add the numerators (42 + 72 = 114) and keep the common denominator 378 unchanged.
Working: 42 + 72/378 = 114/378

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 378, which is 6. Divide both the numerator and denominator by 6.
Working: 114 ÷ 6/378 ÷ 6 = 19/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 63 produces a repeating decimal (approximately 0.301587, or 30.1587%).
Working: 19 ÷ 63 = 0.301587 (30.1587%)

Key Values:
- Simplified Fraction: 19/63
- Mixed Number Form: 19/63
- Decimal Value: 0.301587
- Percentage: 30.1587%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-54-plus-4-21/
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6/54 + 4/21 = 19/63

Simplified Fraction

19/63

Mixed Number

Proper (19/63)

Decimal Value

0.301587

Percentage

30.1587%

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Step-by-Step Solution: 6/54 + 4/21

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 6/54 by 7, and multiply the numerator and denominator of 4/21 by 18 so both fractions share the common base 378.

6 × 7/54 × 7 = 42/378 and 4 × 18/21 × 18 = 72/378

Step 3

Add the Numerators

Now add the numerators (42 + 72 = 114) and keep the common denominator 378 unchanged.

42 + 72/378 = 114/378

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 378, which is 6. Divide both the numerator and denominator by 6.

114 ÷ 6/378 ÷ 6 = 19/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 63 produces a repeating decimal (approximately 0.301587, or 30.1587%).

19 ÷ 63 = 0.301587 (30.1587%)

Visual Representation

The diagram below illustrates 6/54 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/63`
Mixed Number Form	`19/63`
Decimal Form	`0.301587`
Percentage	`30.1587%`

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Frequently Asked Questions

What is 6/54 plus 4/21 as a fraction?

6/54 + 4/21 in simplest fraction form is 19/63.

What is 6/54 plus 4/21 as a decimal?

6/54 + 4/21 converted to a decimal is 0.301587.

What is 6/54 plus 4/21 as a percentage?

6/54 + 4/21 expressed as a percentage is 30.1587%.

Does 6/54 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.301587...) because the denominator contains prime factors other than 2 and 5.