What is 5/21 plus 7/27? (Answer: 94/189)

Exact Answer

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Problem: What is 5/21 plus 7/27?
Formula / Expression: 5/21 + 7/27
Final Answer: 94/189
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 27 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 21 × 27 = 567, keeping the calculation simpler).
Working: LCD(21, 27) = 189

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 5/21 by 9, and multiply the numerator and denominator of 7/27 by 7 so both fractions share the common base 189.
Working: 5 × 9/21 × 9 = 45/189 and 7 × 7/27 × 7 = 49/189

Step 3: Add the Numerators
Now add the numerators (45 + 49 = 94) and keep the common denominator 189 unchanged.
Working: 45 + 49/189 = 94/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 94 and 189 is 1, confirming that 94/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 94/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 94 by denominator 189 produces a repeating decimal (approximately 0.497354, or 49.7354%).
Working: 94 ÷ 189 = 0.497354 (49.7354%)

Key Values:
- Simplified Fraction: 94/189
- Mixed Number Form: 94/189
- Decimal Value: 0.497354
- Percentage: 49.7354%

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Solved with FractionsCalc:
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5/21 + 7/27 = 94/189

Simplified Fraction

94/189

Mixed Number

Proper (94/189)

Decimal Value

0.497354

Percentage

49.7354%

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Step-by-Step Solution: 5/21 + 7/27

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 27 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 189 (which is smaller than their product 21 × 27 = 567, keeping the calculation simpler).

LCD(21, 27) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 5/21 by 9, and multiply the numerator and denominator of 7/27 by 7 so both fractions share the common base 189.

5 × 9/21 × 9 = 45/189 and 7 × 7/27 × 7 = 49/189

Step 3

Add the Numerators

Now add the numerators (45 + 49 = 94) and keep the common denominator 189 unchanged.

45 + 49/189 = 94/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 94 and 189 is 1, confirming that 94/189 cannot be reduced further—it is already in its simplest irreducible form.

94/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 94 by denominator 189 produces a repeating decimal (approximately 0.497354, or 49.7354%).

94 ÷ 189 = 0.497354 (49.7354%)

Visual Representation

The diagram below illustrates 5/21 plus 7/27 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`94/189`
Mixed Number Form	`94/189`
Decimal Form	`0.497354`
Percentage	`49.7354%`

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Frequently Asked Questions

What is 5/21 plus 7/27 as a fraction?

5/21 + 7/27 in simplest fraction form is 94/189.

What is 5/21 plus 7/27 as a decimal?

5/21 + 7/27 converted to a decimal is 0.497354.

What is 5/21 plus 7/27 as a percentage?

5/21 + 7/27 expressed as a percentage is 49.7354%.

Does 5/21 plus 7/27 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.497354...) because the denominator contains prime factors other than 2 and 5.