What is 7/27 plus 10/21? (Answer: 139/189)

Exact Answer

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Problem: What is 7/27 plus 10/21?
Formula / Expression: 7/27 + 10/21
Final Answer: 139/189
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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 7/27 by 7, and multiply the numerator and denominator of 10/21 by 9 so both fractions share the common base 189.
Working: 7 × 7/27 × 7 = 49/189 and 10 × 9/21 × 9 = 90/189

Step 3: Add the Numerators
Now add the numerators (49 + 90 = 139) and keep the common denominator 189 unchanged.
Working: 49 + 90/189 = 139/189

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 189 is 1, confirming that 139/189 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/189

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 189 produces a repeating decimal (approximately 0.73545, or 73.545%).
Working: 139 ÷ 189 = 0.73545 (73.545%)

Key Values:
- Simplified Fraction: 139/189
- Mixed Number Form: 139/189
- Decimal Value: 0.73545
- Percentage: 73.545%

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Solved with FractionsCalc:
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7/27 + 10/21 = 139/189

Simplified Fraction

139/189

Mixed Number

Proper (139/189)

Decimal Value

0.73545

Percentage

73.545%

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Step-by-Step Solution: 7/27 + 10/21

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 7/27 by 7, and multiply the numerator and denominator of 10/21 by 9 so both fractions share the common base 189.

7 × 7/27 × 7 = 49/189 and 10 × 9/21 × 9 = 90/189

Step 3

Add the Numerators

Now add the numerators (49 + 90 = 139) and keep the common denominator 189 unchanged.

49 + 90/189 = 139/189

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 189 is 1, confirming that 139/189 cannot be reduced further—it is already in its simplest irreducible form.

139/189

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 189 produces a repeating decimal (approximately 0.73545, or 73.545%).

139 ÷ 189 = 0.73545 (73.545%)

Visual Representation

The diagram below illustrates 7/27 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/189`
Mixed Number Form	`139/189`
Decimal Form	`0.73545`
Percentage	`73.545%`

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Frequently Asked Questions

What is 7/27 plus 10/21 as a fraction?

7/27 + 10/21 in simplest fraction form is 139/189.

What is 7/27 plus 10/21 as a decimal?

7/27 + 10/21 converted to a decimal is 0.73545.

What is 7/27 plus 10/21 as a percentage?

7/27 + 10/21 expressed as a percentage is 73.545%.

Does 7/27 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.73545...) because the denominator contains prime factors other than 2 and 5.