What is 5/16 plus 4/9? (Answer: 109/144)

Exact Answer

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Problem: What is 5/16 plus 4/9?
Formula / Expression: 5/16 + 4/9
Final Answer: 109/144
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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 4/9 by 16 so both fractions share the common base 144.
Working: 5 × 9/16 × 9 = 45/144 and 4 × 16/9 × 16 = 64/144

Step 3: Add the Numerators
Now add the numerators (45 + 64 = 109) and keep the common denominator 144 unchanged.
Working: 45 + 64/144 = 109/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 109 and 144 is 1, confirming that 109/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 109/144

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 144 produces a repeating decimal (approximately 0.756944, or 75.6944%).
Working: 109 ÷ 144 = 0.756944 (75.6944%)

Key Values:
- Simplified Fraction: 109/144
- Mixed Number Form: 109/144
- Decimal Value: 0.756944
- Percentage: 75.6944%

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Solved with FractionsCalc:
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5/16 + 4/9 = 109/144

Simplified Fraction

109/144

Mixed Number

Proper (109/144)

Decimal Value

0.756944

Percentage

75.6944%

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Step-by-Step Solution: 5/16 + 4/9

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 4/9 by 16 so both fractions share the common base 144.

5 × 9/16 × 9 = 45/144 and 4 × 16/9 × 16 = 64/144

Step 3

Add the Numerators

Now add the numerators (45 + 64 = 109) and keep the common denominator 144 unchanged.

45 + 64/144 = 109/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 109 and 144 is 1, confirming that 109/144 cannot be reduced further—it is already in its simplest irreducible form.

109/144

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 144 produces a repeating decimal (approximately 0.756944, or 75.6944%).

109 ÷ 144 = 0.756944 (75.6944%)

Visual Representation

The diagram below illustrates 5/16 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/144`
Mixed Number Form	`109/144`
Decimal Form	`0.756944`
Percentage	`75.6944%`

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Frequently Asked Questions

What is 5/16 plus 4/9 as a fraction?

5/16 + 4/9 in simplest fraction form is 109/144.

What is 5/16 plus 4/9 as a decimal?

5/16 + 4/9 converted to a decimal is 0.756944.

What is 5/16 plus 4/9 as a percentage?

5/16 + 4/9 expressed as a percentage is 75.6944%.

Does 5/16 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.756944...) because the denominator contains prime factors other than 2 and 5.