What is 2/10 plus 7/16? (Answer: 51/80)

Exact Answer

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Problem: What is 2/10 plus 7/16?
Formula / Expression: 2/10 + 7/16
Final Answer: 51/80
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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 7/16 by 5 so both fractions share the common base 80.
Working: 2 × 8/10 × 8 = 16/80 and 7 × 5/16 × 5 = 35/80

Step 3: Add the Numerators
Now add the numerators (16 + 35 = 51) and keep the common denominator 80 unchanged.
Working: 16 + 35/80 = 51/80

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 51 and 80 is 1, confirming that 51/80 cannot be reduced further—it is already in its simplest irreducible form.
Working: 51/80

Step 5: Decimal & Percentage Representation
Dividing the numerator 51 by denominator 80 yields an exact terminating decimal of 0.6375 (or 63.75%).
Working: 51 ÷ 80 = 0.6375 (63.75%)

Key Values:
- Simplified Fraction: 51/80
- Mixed Number Form: 51/80
- Decimal Value: 0.6375
- Percentage: 63.75%

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Solved with FractionsCalc:
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2/10 + 7/16 = 51/80

Simplified Fraction

51/80

Mixed Number

Proper (51/80)

Decimal Value

0.6375

Percentage

63.75%

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Step-by-Step Solution: 2/10 + 7/16

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 7/16 by 5 so both fractions share the common base 80.

2 × 8/10 × 8 = 16/80 and 7 × 5/16 × 5 = 35/80

Step 3

Add the Numerators

Now add the numerators (16 + 35 = 51) and keep the common denominator 80 unchanged.

16 + 35/80 = 51/80

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 51 and 80 is 1, confirming that 51/80 cannot be reduced further—it is already in its simplest irreducible form.

51/80

Step 5

Decimal & Percentage Representation

Dividing the numerator 51 by denominator 80 yields an exact terminating decimal of 0.6375 (or 63.75%).

51 ÷ 80 = 0.6375 (63.75%)

Visual Representation

The diagram below illustrates 2/10 plus 7/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`51/80`
Mixed Number Form	`51/80`
Decimal Form	`0.6375`
Percentage	`63.75%`

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Frequently Asked Questions

What is 2/10 plus 7/16 as a fraction?

2/10 + 7/16 in simplest fraction form is 51/80.

What is 2/10 plus 7/16 as a decimal?

2/10 + 7/16 converted to a decimal is 0.6375.

What is 2/10 plus 7/16 as a percentage?

2/10 + 7/16 expressed as a percentage is 63.75%.

Does 2/10 plus 7/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.6375) because the denominator in simplest terms contains only prime factors 2 and/or 5.