What is 3/10 plus 3/9? (Answer: 19/30)

Exact Answer

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Problem: What is 3/10 plus 3/9?
Formula / Expression: 3/10 + 3/9
Final Answer: 19/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.
Working: LCD(10, 9) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 3/10 by 9, and multiply the numerator and denominator of 3/9 by 10 so both fractions share the common base 90.
Working: 3 × 9/10 × 9 = 27/90 and 3 × 10/9 × 10 = 30/90

Step 3: Add the Numerators
Now add the numerators (27 + 30 = 57) and keep the common denominator 90 unchanged.
Working: 27 + 30/90 = 57/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 90, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/90 ÷ 3 = 19/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).
Working: 19 ÷ 30 = 0.633333 (63.3333%)

Key Values:
- Simplified Fraction: 19/30
- Mixed Number Form: 19/30
- Decimal Value: 0.633333
- Percentage: 63.3333%

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Solved with FractionsCalc:
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3/10 + 3/9 = 19/30

Simplified Fraction

19/30

Mixed Number

Proper (19/30)

Decimal Value

0.633333

Percentage

63.3333%

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Step-by-Step Solution: 3/10 + 3/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 9 = 90.

LCD(10, 9) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 3/10 by 9, and multiply the numerator and denominator of 3/9 by 10 so both fractions share the common base 90.

3 × 9/10 × 9 = 27/90 and 3 × 10/9 × 10 = 30/90

Step 3

Add the Numerators

Now add the numerators (27 + 30 = 57) and keep the common denominator 90 unchanged.

27 + 30/90 = 57/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 90, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/90 ÷ 3 = 19/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 30 produces a repeating decimal (approximately 0.633333, or 63.3333%).

19 ÷ 30 = 0.633333 (63.3333%)

Visual Representation

The diagram below illustrates 3/10 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/30`
Mixed Number Form	`19/30`
Decimal Form	`0.633333`
Percentage	`63.3333%`

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Frequently Asked Questions

What is 3/10 plus 3/9 as a fraction?

3/10 + 3/9 in simplest fraction form is 19/30.

What is 3/10 plus 3/9 as a decimal?

3/10 + 3/9 converted to a decimal is 0.633333.

What is 3/10 plus 3/9 as a percentage?

3/10 + 3/9 expressed as a percentage is 63.3333%.

Does 3/10 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.633333...) because the denominator contains prime factors other than 2 and 5.