What is 2/18 plus 2/16? (Answer: 17/72)

Exact Answer

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Problem: What is 2/18 plus 2/16?
Formula / Expression: 2/18 + 2/16
Final Answer: 17/72
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 18 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 144 (which is smaller than their product 18 × 16 = 288, keeping the calculation simpler).
Working: LCD(18, 16) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 2/18 by 8, and multiply the numerator and denominator of 2/16 by 9 so both fractions share the common base 144.
Working: 2 × 8/18 × 8 = 16/144 and 2 × 9/16 × 9 = 18/144

Step 3: Add the Numerators
Now add the numerators (16 + 18 = 34) and keep the common denominator 144 unchanged.
Working: 16 + 18/144 = 34/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 144, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/144 ÷ 2 = 17/72

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 72 produces a repeating decimal (approximately 0.236111, or 23.6111%).
Working: 17 ÷ 72 = 0.236111 (23.6111%)

Key Values:
- Simplified Fraction: 17/72
- Mixed Number Form: 17/72
- Decimal Value: 0.236111
- Percentage: 23.6111%

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Solved with FractionsCalc:
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2/18 + 2/16 = 17/72

Simplified Fraction

17/72

Mixed Number

Proper (17/72)

Decimal Value

0.236111

Percentage

23.6111%

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Step-by-Step Solution: 2/18 + 2/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 18 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 144 (which is smaller than their product 18 × 16 = 288, keeping the calculation simpler).

LCD(18, 16) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 2/18 by 8, and multiply the numerator and denominator of 2/16 by 9 so both fractions share the common base 144.

2 × 8/18 × 8 = 16/144 and 2 × 9/16 × 9 = 18/144

Step 3

Add the Numerators

Now add the numerators (16 + 18 = 34) and keep the common denominator 144 unchanged.

16 + 18/144 = 34/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 144, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/144 ÷ 2 = 17/72

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 72 produces a repeating decimal (approximately 0.236111, or 23.6111%).

17 ÷ 72 = 0.236111 (23.6111%)

Visual Representation

The diagram below illustrates 2/18 plus 2/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/72`
Mixed Number Form	`17/72`
Decimal Form	`0.236111`
Percentage	`23.6111%`

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Frequently Asked Questions

What is 2/18 plus 2/16 as a fraction?

2/18 + 2/16 in simplest fraction form is 17/72.

What is 2/18 plus 2/16 as a decimal?

2/18 + 2/16 converted to a decimal is 0.236111.

What is 2/18 plus 2/16 as a percentage?

2/18 + 2/16 expressed as a percentage is 23.6111%.

Does 2/18 plus 2/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.236111...) because the denominator contains prime factors other than 2 and 5.