What is 2/5 plus 9/16? (Answer: 77/80)

Exact Answer

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Problem: What is 2/5 plus 9/16?
Formula / Expression: 2/5 + 9/16
Final Answer: 77/80
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 16 = 80.
Working: LCD(5, 16) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/5 by 16, and multiply the numerator and denominator of 9/16 by 5 so both fractions share the common base 80.
Working: 2 × 16/5 × 16 = 32/80 and 9 × 5/16 × 5 = 45/80

Step 3: Add the Numerators
Now add the numerators (32 + 45 = 77) and keep the common denominator 80 unchanged.
Working: 32 + 45/80 = 77/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 77 and 80 is 1, confirming that 77/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 77/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 77 by denominator 80 yields an exact terminating decimal of 0.9625 (or 96.25%).
Working: 77 ÷ 80 = 0.9625 (96.25%)

Key Values:
- Simplified Fraction: 77/80
- Mixed Number Form: 77/80
- Decimal Value: 0.9625
- Percentage: 96.25%

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Solved with FractionsCalc:
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2/5 + 9/16 = 77/80

Simplified Fraction

77/80

Mixed Number

Proper (77/80)

Decimal Value

0.9625

Percentage

96.25%

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Step-by-Step Solution: 2/5 + 9/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 16 = 80.

LCD(5, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 2/5 by 16, and multiply the numerator and denominator of 9/16 by 5 so both fractions share the common base 80.

2 × 16/5 × 16 = 32/80 and 9 × 5/16 × 5 = 45/80

Step 3

Add the Numerators

Now add the numerators (32 + 45 = 77) and keep the common denominator 80 unchanged.

32 + 45/80 = 77/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 77 and 80 is 1, confirming that 77/80 cannot be reduced further—it is already in its simplest irreducible form.

77/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 77 by denominator 80 yields an exact terminating decimal of 0.9625 (or 96.25%).

77 ÷ 80 = 0.9625 (96.25%)

Visual Representation

The diagram below illustrates 2/5 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`77/80`
Mixed Number Form	`77/80`
Decimal Form	`0.9625`
Percentage	`96.25%`

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Frequently Asked Questions

What is 2/5 plus 9/16 as a fraction?

2/5 + 9/16 in simplest fraction form is 77/80.

What is 2/5 plus 9/16 as a decimal?

2/5 + 9/16 converted to a decimal is 0.9625.

What is 2/5 plus 9/16 as a percentage?

2/5 + 9/16 expressed as a percentage is 96.25%.

Does 2/5 plus 9/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.9625) because the denominator in simplest terms contains only prime factors 2 and/or 5.