What is 3/18 plus 2/10? (Answer: 11/30)

Exact Answer

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Problem: What is 3/18 plus 2/10?
Formula / Expression: 3/18 + 2/10
Final Answer: 11/30
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 18 × 10 = 180, keeping the calculation simpler).
Working: LCD(18, 10) = 90

Step 2: Convert to Equivalent Fractions with Common Denominator 90
Multiply the numerator and denominator of 3/18 by 5, and multiply the numerator and denominator of 2/10 by 9 so both fractions share the common base 90.
Working: 3 × 5/18 × 5 = 15/90 and 2 × 9/10 × 9 = 18/90

Step 3: Add the Numerators
Now add the numerators (15 + 18 = 33) and keep the common denominator 90 unchanged.
Working: 15 + 18/90 = 33/90

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 33 and 90, which is 3. Divide both the numerator and denominator by 3.
Working: 33 ÷ 3/90 ÷ 3 = 11/30

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 30 produces a repeating decimal (approximately 0.366667, or 36.6667%).
Working: 11 ÷ 30 = 0.366667 (36.6667%)

Key Values:
- Simplified Fraction: 11/30
- Mixed Number Form: 11/30
- Decimal Value: 0.366667
- Percentage: 36.6667%

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3/18 + 2/10 = 11/30

Simplified Fraction

11/30

Mixed Number

Proper (11/30)

Decimal Value

0.366667

Percentage

36.6667%

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Step-by-Step Solution: 3/18 + 2/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 90 (which is smaller than their product 18 × 10 = 180, keeping the calculation simpler).

LCD(18, 10) = 90

Step 2

Convert to Equivalent Fractions with Common Denominator 90

Multiply the numerator and denominator of 3/18 by 5, and multiply the numerator and denominator of 2/10 by 9 so both fractions share the common base 90.

3 × 5/18 × 5 = 15/90 and 2 × 9/10 × 9 = 18/90

Step 3

Add the Numerators

Now add the numerators (15 + 18 = 33) and keep the common denominator 90 unchanged.

15 + 18/90 = 33/90

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 33 and 90, which is 3. Divide both the numerator and denominator by 3.

33 ÷ 3/90 ÷ 3 = 11/30

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 30 produces a repeating decimal (approximately 0.366667, or 36.6667%).

11 ÷ 30 = 0.366667 (36.6667%)

Visual Representation

The diagram below illustrates 3/18 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/30`
Mixed Number Form	`11/30`
Decimal Form	`0.366667`
Percentage	`36.6667%`

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Frequently Asked Questions

What is 3/18 plus 2/10 as a fraction?

3/18 + 2/10 in simplest fraction form is 11/30.

What is 3/18 plus 2/10 as a decimal?

3/18 + 2/10 converted to a decimal is 0.366667.

What is 3/18 plus 2/10 as a percentage?

3/18 + 2/10 expressed as a percentage is 36.6667%.

Does 3/18 plus 2/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.366667...) because the denominator contains prime factors other than 2 and 5.