What is 8/27 plus 7/21? (Answer: 17/27)

Exact Answer

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Problem: What is 8/27 plus 7/21?
Formula / Expression: 8/27 + 7/21
Final Answer: 17/27
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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 8/27 by 7, and multiply the numerator and denominator of 7/21 by 9 so both fractions share the common base 189.
Working: 8 × 7/27 × 7 = 56/189 and 7 × 9/21 × 9 = 63/189

Step 3: Add the Numerators
Now add the numerators (56 + 63 = 119) and keep the common denominator 189 unchanged.
Working: 56 + 63/189 = 119/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 119 and 189, which is 7. Divide both the numerator and denominator by 7.
Working: 119 ÷ 7/189 ÷ 7 = 17/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 27 produces a repeating decimal (approximately 0.62963, or 62.963%).
Working: 17 ÷ 27 = 0.62963 (62.963%)

Key Values:
- Simplified Fraction: 17/27
- Mixed Number Form: 17/27
- Decimal Value: 0.62963
- Percentage: 62.963%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-27-plus-7-21/
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8/27 + 7/21 = 17/27

Simplified Fraction

17/27

Mixed Number

Proper (17/27)

Decimal Value

0.62963

Percentage

62.963%

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Step-by-Step Solution: 8/27 + 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 8/27 by 7, and multiply the numerator and denominator of 7/21 by 9 so both fractions share the common base 189.

8 × 7/27 × 7 = 56/189 and 7 × 9/21 × 9 = 63/189

Step 3

Add the Numerators

Now add the numerators (56 + 63 = 119) and keep the common denominator 189 unchanged.

56 + 63/189 = 119/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 119 and 189, which is 7. Divide both the numerator and denominator by 7.

119 ÷ 7/189 ÷ 7 = 17/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 27 produces a repeating decimal (approximately 0.62963, or 62.963%).

17 ÷ 27 = 0.62963 (62.963%)

Visual Representation

The diagram below illustrates 8/27 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/27`
Mixed Number Form	`17/27`
Decimal Form	`0.62963`
Percentage	`62.963%`

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Frequently Asked Questions

What is 8/27 plus 7/21 as a fraction?

8/27 + 7/21 in simplest fraction form is 17/27.

What is 8/27 plus 7/21 as a decimal?

8/27 + 7/21 converted to a decimal is 0.62963.

What is 8/27 plus 7/21 as a percentage?

8/27 + 7/21 expressed as a percentage is 62.963%.

Does 8/27 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.62963...) because the denominator contains prime factors other than 2 and 5.