What is 2/10 plus 9/16? (Answer: 61/80)

Exact Answer

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Problem: What is 2/10 plus 9/16?
Formula / Expression: 2/10 + 9/16
Final Answer: 61/80
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 10 × 16 = 160, keeping the calculation simpler).
Working: LCD(10, 16) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/10 by 8, and multiply the numerator and denominator of 9/16 by 5 so both fractions share the common base 80.
Working: 2 × 8/10 × 8 = 16/80 and 9 × 5/16 × 5 = 45/80

Step 3: Add the Numerators
Now add the numerators (16 + 45 = 61) and keep the common denominator 80 unchanged.
Working: 16 + 45/80 = 61/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 61 and 80 is 1, confirming that 61/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 61/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 61 by denominator 80 yields an exact terminating decimal of 0.7625 (or 76.25%).
Working: 61 ÷ 80 = 0.7625 (76.25%)

Key Values:
- Simplified Fraction: 61/80
- Mixed Number Form: 61/80
- Decimal Value: 0.7625
- Percentage: 76.25%

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Solved with FractionsCalc:
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2/10 + 9/16 = 61/80

Simplified Fraction

61/80

Mixed Number

Proper (61/80)

Decimal Value

0.7625

Percentage

76.25%

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Step-by-Step Solution: 2/10 + 9/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 16 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 10 × 16 = 160, keeping the calculation simpler).

LCD(10, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 2/10 by 8, and multiply the numerator and denominator of 9/16 by 5 so both fractions share the common base 80.

2 × 8/10 × 8 = 16/80 and 9 × 5/16 × 5 = 45/80

Step 3

Add the Numerators

Now add the numerators (16 + 45 = 61) and keep the common denominator 80 unchanged.

16 + 45/80 = 61/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 61 and 80 is 1, confirming that 61/80 cannot be reduced further—it is already in its simplest irreducible form.

61/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 61 by denominator 80 yields an exact terminating decimal of 0.7625 (or 76.25%).

61 ÷ 80 = 0.7625 (76.25%)

Visual Representation

The diagram below illustrates 2/10 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`61/80`
Mixed Number Form	`61/80`
Decimal Form	`0.7625`
Percentage	`76.25%`

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Frequently Asked Questions

What is 2/10 plus 9/16 as a fraction?

2/10 + 9/16 in simplest fraction form is 61/80.

What is 2/10 plus 9/16 as a decimal?

2/10 + 9/16 converted to a decimal is 0.7625.

What is 2/10 plus 9/16 as a percentage?

2/10 + 9/16 expressed as a percentage is 76.25%.

Does 2/10 plus 9/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.7625) because the denominator in simplest terms contains only prime factors 2 and/or 5.