What is 2/9 plus 7/21? (Answer: 5/9)

Exact Answer

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Problem: What is 2/9 plus 7/21?
Formula / Expression: 2/9 + 7/21
Final Answer: 5/9
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 2/9 by 7, and multiply the numerator and denominator of 7/21 by 3 so both fractions share the common base 63.
Working: 2 × 7/9 × 7 = 14/63 and 7 × 3/21 × 3 = 21/63

Step 3: Add the Numerators
Now add the numerators (14 + 21 = 35) and keep the common denominator 63 unchanged.
Working: 14 + 21/63 = 35/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 35 and 63, which is 7. Divide both the numerator and denominator by 7.
Working: 35 ÷ 7/63 ÷ 7 = 5/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).
Working: 5 ÷ 9 = 0.555556 (55.5556%)

Key Values:
- Simplified Fraction: 5/9
- Mixed Number Form: 5/9
- Decimal Value: 0.555556
- Percentage: 55.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-7-21/
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2/9 + 7/21 = 5/9

Simplified Fraction

5/9

Mixed Number

Proper (5/9)

Decimal Value

0.555556

Percentage

55.5556%

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Step-by-Step Solution: 2/9 + 7/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

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

2 × 7/9 × 7 = 14/63 and 7 × 3/21 × 3 = 21/63

Step 3

Add the Numerators

Now add the numerators (14 + 21 = 35) and keep the common denominator 63 unchanged.

14 + 21/63 = 35/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 35 and 63, which is 7. Divide both the numerator and denominator by 7.

35 ÷ 7/63 ÷ 7 = 5/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).

5 ÷ 9 = 0.555556 (55.5556%)

Visual Representation

The diagram below illustrates 2/9 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/9`
Mixed Number Form	`5/9`
Decimal Form	`0.555556`
Percentage	`55.5556%`

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Frequently Asked Questions

What is 2/9 plus 7/21 as a fraction?

2/9 + 7/21 in simplest fraction form is 5/9.

What is 2/9 plus 7/21 as a decimal?

2/9 + 7/21 converted to a decimal is 0.555556.

What is 2/9 plus 7/21 as a percentage?

2/9 + 7/21 expressed as a percentage is 55.5556%.

Does 2/9 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.555556...) because the denominator contains prime factors other than 2 and 5.