What is 1/27 plus 9/21? (Answer: 88/189)

Exact Answer

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Problem: What is 1/27 plus 9/21?
Formula / Expression: 1/27 + 9/21
Final Answer: 88/189
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 189
Multiply the numerator and denominator of 1/27 by 7, and multiply the numerator and denominator of 9/21 by 9 so both fractions share the common base 189.
Working: 1 × 7/27 × 7 = 7/189 and 9 × 9/21 × 9 = 81/189

Step 3: Add the Numerators
Now add the numerators (7 + 81 = 88) and keep the common denominator 189 unchanged.
Working: 7 + 81/189 = 88/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 88 and 189 is 1, confirming that 88/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 88/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 88 by denominator 189 produces a repeating decimal (approximately 0.465608, or 46.5608%).
Working: 88 ÷ 189 = 0.465608 (46.5608%)

Key Values:
- Simplified Fraction: 88/189
- Mixed Number Form: 88/189
- Decimal Value: 0.465608
- Percentage: 46.5608%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-27-plus-9-21/
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1/27 + 9/21 = 88/189

Simplified Fraction

88/189

Mixed Number

Proper (88/189)

Decimal Value

0.465608

Percentage

46.5608%

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Step-by-Step Solution: 1/27 + 9/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(27, 21) = 189

Step 2

Convert to Equivalent Fractions with Common Denominator 189

Multiply the numerator and denominator of 1/27 by 7, and multiply the numerator and denominator of 9/21 by 9 so both fractions share the common base 189.

1 × 7/27 × 7 = 7/189 and 9 × 9/21 × 9 = 81/189

Step 3

Add the Numerators

Now add the numerators (7 + 81 = 88) and keep the common denominator 189 unchanged.

7 + 81/189 = 88/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 88 and 189 is 1, confirming that 88/189 cannot be reduced further—it is already in its simplest irreducible form.

88/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 88 by denominator 189 produces a repeating decimal (approximately 0.465608, or 46.5608%).

88 ÷ 189 = 0.465608 (46.5608%)

Visual Representation

The diagram below illustrates 1/27 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`88/189`
Mixed Number Form	`88/189`
Decimal Form	`0.465608`
Percentage	`46.5608%`

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Frequently Asked Questions

What is 1/27 plus 9/21 as a fraction?

1/27 + 9/21 in simplest fraction form is 88/189.

What is 1/27 plus 9/21 as a decimal?

1/27 + 9/21 converted to a decimal is 0.465608.

What is 1/27 plus 9/21 as a percentage?

1/27 + 9/21 expressed as a percentage is 46.5608%.

Does 1/27 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.465608...) because the denominator contains prime factors other than 2 and 5.