What is 2/21 plus 3/9? (Answer: 3/7)

Exact Answer

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Problem: What is 2/21 plus 3/9?
Formula / Expression: 2/21 + 3/9
Final Answer: 3/7
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
Working: LCD(21, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/21 by 3, and multiply the numerator and denominator of 3/9 by 7 so both fractions share the common base 63.
Working: 2 × 3/21 × 3 = 6/63 and 3 × 7/9 × 7 = 21/63

Step 3: Add the Numerators
Now add the numerators (6 + 21 = 27) and keep the common denominator 63 unchanged.
Working: 6 + 21/63 = 27/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 27 and 63, which is 9. Divide both the numerator and denominator by 9.
Working: 27 ÷ 9/63 ÷ 9 = 3/7

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).
Working: 3 ÷ 7 = 0.428571 (42.8571%)

Key Values:
- Simplified Fraction: 3/7
- Mixed Number Form: 3/7
- Decimal Value: 0.428571
- Percentage: 42.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-3-9/
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2/21 + 3/9 = 3/7

Simplified Fraction

3/7

Mixed Number

Proper (3/7)

Decimal Value

0.428571

Percentage

42.8571%

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Step-by-Step Solution: 2/21 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 2/21 by 3, and multiply the numerator and denominator of 3/9 by 7 so both fractions share the common base 63.

2 × 3/21 × 3 = 6/63 and 3 × 7/9 × 7 = 21/63

Step 3

Add the Numerators

Now add the numerators (6 + 21 = 27) and keep the common denominator 63 unchanged.

6 + 21/63 = 27/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 27 and 63, which is 9. Divide both the numerator and denominator by 9.

27 ÷ 9/63 ÷ 9 = 3/7

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 7 produces a repeating decimal (approximately 0.428571, or 42.8571%).

3 ÷ 7 = 0.428571 (42.8571%)

Visual Representation

The diagram below illustrates 2/21 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/7`
Mixed Number Form	`3/7`
Decimal Form	`0.428571`
Percentage	`42.8571%`

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Frequently Asked Questions

What is 2/21 plus 3/9 as a fraction?

2/21 + 3/9 in simplest fraction form is 3/7.

What is 2/21 plus 3/9 as a decimal?

2/21 + 3/9 converted to a decimal is 0.428571.

What is 2/21 plus 3/9 as a percentage?

2/21 + 3/9 expressed as a percentage is 42.8571%.

Does 2/21 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.428571...) because the denominator contains prime factors other than 2 and 5.