What is 3/9 plus 8/16? (Answer: 5/6)

Exact Answer

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Problem: What is 3/9 plus 8/16?
Formula / Expression: 3/9 + 8/16
Final Answer: 5/6
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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 3/9 by 16, and multiply the numerator and denominator of 8/16 by 9 so both fractions share the common base 144.
Working: 3 × 16/9 × 16 = 48/144 and 8 × 9/16 × 9 = 72/144

Step 3: Add the Numerators
Now add the numerators (48 + 72 = 120) and keep the common denominator 144 unchanged.
Working: 48 + 72/144 = 120/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 144, which is 24. Divide both the numerator and denominator by 24.
Working: 120 ÷ 24/144 ÷ 24 = 5/6

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).
Working: 5 ÷ 6 = 0.833333 (83.3333%)

Key Values:
- Simplified Fraction: 5/6
- Mixed Number Form: 5/6
- Decimal Value: 0.833333
- Percentage: 83.3333%

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Solved with FractionsCalc:
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3/9 + 8/16 = 5/6

Simplified Fraction

5/6

Mixed Number

Proper (5/6)

Decimal Value

0.833333

Percentage

83.3333%

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Step-by-Step Solution: 3/9 + 8/16

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 3/9 by 16, and multiply the numerator and denominator of 8/16 by 9 so both fractions share the common base 144.

3 × 16/9 × 16 = 48/144 and 8 × 9/16 × 9 = 72/144

Step 3

Add the Numerators

Now add the numerators (48 + 72 = 120) and keep the common denominator 144 unchanged.

48 + 72/144 = 120/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 144, which is 24. Divide both the numerator and denominator by 24.

120 ÷ 24/144 ÷ 24 = 5/6

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 6 produces a repeating decimal (approximately 0.833333, or 83.3333%).

5 ÷ 6 = 0.833333 (83.3333%)

Visual Representation

The diagram below illustrates 3/9 plus 8/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/6`
Mixed Number Form	`5/6`
Decimal Form	`0.833333`
Percentage	`83.3333%`

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Frequently Asked Questions

What is 3/9 plus 8/16 as a fraction?

3/9 + 8/16 in simplest fraction form is 5/6.

What is 3/9 plus 8/16 as a decimal?

3/9 + 8/16 converted to a decimal is 0.833333.

What is 3/9 plus 8/16 as a percentage?

3/9 + 8/16 expressed as a percentage is 83.3333%.

Does 3/9 plus 8/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.833333...) because the denominator contains prime factors other than 2 and 5.