What is 3/9 plus 9/21? (Answer: 16/21)

Exact Answer

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Problem: What is 3/9 plus 9/21?
Formula / Expression: 3/9 + 9/21
Final Answer: 16/21
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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 3/9 by 7, and multiply the numerator and denominator of 9/21 by 3 so both fractions share the common base 63.
Working: 3 × 7/9 × 7 = 21/63 and 9 × 3/21 × 3 = 27/63

Step 3: Add the Numerators
Now add the numerators (21 + 27 = 48) and keep the common denominator 63 unchanged.
Working: 21 + 27/63 = 48/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 48 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 48 ÷ 3/63 ÷ 3 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-9-21/
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3/9 + 9/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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

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

3 × 7/9 × 7 = 21/63 and 9 × 3/21 × 3 = 27/63

Step 3

Add the Numerators

Now add the numerators (21 + 27 = 48) and keep the common denominator 63 unchanged.

21 + 27/63 = 48/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 48 and 63, which is 3. Divide both the numerator and denominator by 3.

48 ÷ 3/63 ÷ 3 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

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

3/9 + 9/21 in simplest fraction form is 16/21.

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

3/9 + 9/21 converted to a decimal is 0.761905.

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

3/9 + 9/21 expressed as a percentage is 76.1905%.

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

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.