What is 3/9 plus 9/16? (Answer: 43/48)

Exact Answer

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Problem: What is 3/9 plus 9/16?
Formula / Expression: 3/9 + 9/16
Final Answer: 43/48
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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 9/16 by 9 so both fractions share the common base 144.
Working: 3 × 16/9 × 16 = 48/144 and 9 × 9/16 × 9 = 81/144

Step 3: Add the Numerators
Now add the numerators (48 + 81 = 129) and keep the common denominator 144 unchanged.
Working: 48 + 81/144 = 129/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 129 and 144, which is 3. Divide both the numerator and denominator by 3.
Working: 129 ÷ 3/144 ÷ 3 = 43/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 48 produces a repeating decimal (approximately 0.895833, or 89.5833%).
Working: 43 ÷ 48 = 0.895833 (89.5833%)

Key Values:
- Simplified Fraction: 43/48
- Mixed Number Form: 43/48
- Decimal Value: 0.895833
- Percentage: 89.5833%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-9-16/
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3/9 + 9/16 = 43/48

Simplified Fraction

43/48

Mixed Number

Proper (43/48)

Decimal Value

0.895833

Percentage

89.5833%

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

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 9/16 by 9 so both fractions share the common base 144.

3 × 16/9 × 16 = 48/144 and 9 × 9/16 × 9 = 81/144

Step 3

Add the Numerators

Now add the numerators (48 + 81 = 129) and keep the common denominator 144 unchanged.

48 + 81/144 = 129/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 129 and 144, which is 3. Divide both the numerator and denominator by 3.

129 ÷ 3/144 ÷ 3 = 43/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 48 produces a repeating decimal (approximately 0.895833, or 89.5833%).

43 ÷ 48 = 0.895833 (89.5833%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/48`
Mixed Number Form	`43/48`
Decimal Form	`0.895833`
Percentage	`89.5833%`

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Frequently Asked Questions

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

3/9 + 9/16 in simplest fraction form is 43/48.

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

3/9 + 9/16 converted to a decimal is 0.895833.

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

3/9 + 9/16 expressed as a percentage is 89.5833%.

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

It results in a repeating decimal (approximately 0.895833...) because the denominator contains prime factors other than 2 and 5.