What is 5/16 plus 3/9? (Answer: 31/48)

Exact Answer

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Problem: What is 5/16 plus 3/9?
Formula / Expression: 5/16 + 3/9
Final Answer: 31/48
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 5/16 by 9, and multiply the numerator and denominator of 3/9 by 16 so both fractions share the common base 144.
Working: 5 × 9/16 × 9 = 45/144 and 3 × 16/9 × 16 = 48/144

Step 3: Add the Numerators
Now add the numerators (45 + 48 = 93) and keep the common denominator 144 unchanged.
Working: 45 + 48/144 = 93/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 144, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/144 ÷ 3 = 31/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 48 produces a repeating decimal (approximately 0.645833, or 64.5833%).
Working: 31 ÷ 48 = 0.645833 (64.5833%)

Key Values:
- Simplified Fraction: 31/48
- Mixed Number Form: 31/48
- Decimal Value: 0.645833
- Percentage: 64.5833%

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Solved with FractionsCalc:
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5/16 + 3/9 = 31/48

Simplified Fraction

31/48

Mixed Number

Proper (31/48)

Decimal Value

0.645833

Percentage

64.5833%

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Step-by-Step Solution: 5/16 + 3/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(16, 9) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 5/16 by 9, and multiply the numerator and denominator of 3/9 by 16 so both fractions share the common base 144.

5 × 9/16 × 9 = 45/144 and 3 × 16/9 × 16 = 48/144

Step 3

Add the Numerators

Now add the numerators (45 + 48 = 93) and keep the common denominator 144 unchanged.

45 + 48/144 = 93/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 144, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/144 ÷ 3 = 31/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 48 produces a repeating decimal (approximately 0.645833, or 64.5833%).

31 ÷ 48 = 0.645833 (64.5833%)

Visual Representation

The diagram below illustrates 5/16 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/48`
Mixed Number Form	`31/48`
Decimal Form	`0.645833`
Percentage	`64.5833%`

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Frequently Asked Questions

What is 5/16 plus 3/9 as a fraction?

5/16 + 3/9 in simplest fraction form is 31/48.

What is 5/16 plus 3/9 as a decimal?

5/16 + 3/9 converted to a decimal is 0.645833.

What is 5/16 plus 3/9 as a percentage?

5/16 + 3/9 expressed as a percentage is 64.5833%.

Does 5/16 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.645833...) because the denominator contains prime factors other than 2 and 5.