What is 7/27 plus 7/21? (Answer: 16/27)

Exact Answer

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Problem: What is 7/27 plus 7/21?
Formula / Expression: 7/27 + 7/21
Final Answer: 16/27
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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 7/27 by 7, and multiply the numerator and denominator of 7/21 by 9 so both fractions share the common base 189.
Working: 7 × 7/27 × 7 = 49/189 and 7 × 9/21 × 9 = 63/189

Step 3: Add the Numerators
Now add the numerators (49 + 63 = 112) and keep the common denominator 189 unchanged.
Working: 49 + 63/189 = 112/189

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 112 and 189, which is 7. Divide both the numerator and denominator by 7.
Working: 112 ÷ 7/189 ÷ 7 = 16/27

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 27 produces a repeating decimal (approximately 0.592593, or 59.2593%).
Working: 16 ÷ 27 = 0.592593 (59.2593%)

Key Values:
- Simplified Fraction: 16/27
- Mixed Number Form: 16/27
- Decimal Value: 0.592593
- Percentage: 59.2593%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-7-27-plus-7-21/
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7/27 + 7/21 = 16/27

Simplified Fraction

16/27

Mixed Number

Proper (16/27)

Decimal Value

0.592593

Percentage

59.2593%

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

7 × 7/27 × 7 = 49/189 and 7 × 9/21 × 9 = 63/189

Step 3

Add the Numerators

Now add the numerators (49 + 63 = 112) and keep the common denominator 189 unchanged.

49 + 63/189 = 112/189

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 112 and 189, which is 7. Divide both the numerator and denominator by 7.

112 ÷ 7/189 ÷ 7 = 16/27

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 27 produces a repeating decimal (approximately 0.592593, or 59.2593%).

16 ÷ 27 = 0.592593 (59.2593%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/27`
Mixed Number Form	`16/27`
Decimal Form	`0.592593`
Percentage	`59.2593%`

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Frequently Asked Questions

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

7/27 + 7/21 in simplest fraction form is 16/27.

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

7/27 + 7/21 converted to a decimal is 0.592593.

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

7/27 + 7/21 expressed as a percentage is 59.2593%.

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

It results in a repeating decimal (approximately 0.592593...) because the denominator contains prime factors other than 2 and 5.