What is 1/27 plus 7/21? (Answer: 10/27)

Exact Answer

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Problem: What is 1/27 plus 7/21?
Formula / Expression: 1/27 + 7/21
Final Answer: 10/27
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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 7/21 by 9 so both fractions share the common base 189.
Working: 1 × 7/27 × 7 = 7/189 and 7 × 9/21 × 9 = 63/189

Step 3: Add the Numerators
Now add the numerators (7 + 63 = 70) and keep the common denominator 189 unchanged.
Working: 7 + 63/189 = 70/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 70 and 189, which is 7. Divide both the numerator and denominator by 7.
Working: 70 ÷ 7/189 ÷ 7 = 10/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 27 produces a repeating decimal (approximately 0.37037, or 37.037%).
Working: 10 ÷ 27 = 0.37037 (37.037%)

Key Values:
- Simplified Fraction: 10/27
- Mixed Number Form: 10/27
- Decimal Value: 0.37037
- Percentage: 37.037%

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Solved with FractionsCalc:
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1/27 + 7/21 = 10/27

Simplified Fraction

10/27

Mixed Number

Proper (10/27)

Decimal Value

0.37037

Percentage

37.037%

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Step-by-Step Solution: 1/27 + 7/21

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 7/21 by 9 so both fractions share the common base 189.

1 × 7/27 × 7 = 7/189 and 7 × 9/21 × 9 = 63/189

Step 3

Add the Numerators

Now add the numerators (7 + 63 = 70) and keep the common denominator 189 unchanged.

7 + 63/189 = 70/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 70 and 189, which is 7. Divide both the numerator and denominator by 7.

70 ÷ 7/189 ÷ 7 = 10/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 27 produces a repeating decimal (approximately 0.37037, or 37.037%).

10 ÷ 27 = 0.37037 (37.037%)

Visual Representation

The diagram below illustrates 1/27 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/27`
Mixed Number Form	`10/27`
Decimal Form	`0.37037`
Percentage	`37.037%`

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Frequently Asked Questions

What is 1/27 plus 7/21 as a fraction?

1/27 + 7/21 in simplest fraction form is 10/27.

What is 1/27 plus 7/21 as a decimal?

1/27 + 7/21 converted to a decimal is 0.37037.

What is 1/27 plus 7/21 as a percentage?

1/27 + 7/21 expressed as a percentage is 37.037%.

Does 1/27 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.37037...) because the denominator contains prime factors other than 2 and 5.