What is 2/9 plus 4/16? (Answer: 17/36)

Exact Answer

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Problem: What is 2/9 plus 4/16?
Formula / Expression: 2/9 + 4/16
Final Answer: 17/36
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.
Working: LCD(9, 16) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 2/9 by 16, and multiply the numerator and denominator of 4/16 by 9 so both fractions share the common base 144.
Working: 2 × 16/9 × 16 = 32/144 and 4 × 9/16 × 9 = 36/144

Step 3: Add the Numerators
Now add the numerators (32 + 36 = 68) and keep the common denominator 144 unchanged.
Working: 32 + 36/144 = 68/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 68 and 144, which is 4. Divide both the numerator and denominator by 4.
Working: 68 ÷ 4/144 ÷ 4 = 17/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 36 produces a repeating decimal (approximately 0.472222, or 47.2222%).
Working: 17 ÷ 36 = 0.472222 (47.2222%)

Key Values:
- Simplified Fraction: 17/36
- Mixed Number Form: 17/36
- Decimal Value: 0.472222
- Percentage: 47.2222%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-9-plus-4-16/
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2/9 + 4/16 = 17/36

Simplified Fraction

17/36

Mixed Number

Proper (17/36)

Decimal Value

0.472222

Percentage

47.2222%

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Step-by-Step Solution: 2/9 + 4/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.

LCD(9, 16) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 2/9 by 16, and multiply the numerator and denominator of 4/16 by 9 so both fractions share the common base 144.

2 × 16/9 × 16 = 32/144 and 4 × 9/16 × 9 = 36/144

Step 3

Add the Numerators

Now add the numerators (32 + 36 = 68) and keep the common denominator 144 unchanged.

32 + 36/144 = 68/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 68 and 144, which is 4. Divide both the numerator and denominator by 4.

68 ÷ 4/144 ÷ 4 = 17/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 36 produces a repeating decimal (approximately 0.472222, or 47.2222%).

17 ÷ 36 = 0.472222 (47.2222%)

Visual Representation

The diagram below illustrates 2/9 plus 4/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/36`
Mixed Number Form	`17/36`
Decimal Form	`0.472222`
Percentage	`47.2222%`

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Frequently Asked Questions

What is 2/9 plus 4/16 as a fraction?

2/9 + 4/16 in simplest fraction form is 17/36.

What is 2/9 plus 4/16 as a decimal?

2/9 + 4/16 converted to a decimal is 0.472222.

What is 2/9 plus 4/16 as a percentage?

2/9 + 4/16 expressed as a percentage is 47.2222%.

Does 2/9 plus 4/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.472222...) because the denominator contains prime factors other than 2 and 5.