What is 2/5 plus 10/16? (Answer: 41/40)

Exact Answer

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Problem: What is 2/5 plus 10/16?
Formula / Expression: 2/5 + 10/16
Final Answer: 1 1/40 (41/40)
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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 10/16 by 5 so both fractions share the common base 80.
Working: 2 × 16/5 × 16 = 32/80 and 10 × 5/16 × 5 = 50/80

Step 3: Add the Numerators
Now add the numerators (32 + 50 = 82) and keep the common denominator 80 unchanged.
Working: 32 + 50/80 = 82/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 82 and 80, which is 2. Divide both the numerator and denominator by 2.
Working: 82 ÷ 2/80 ÷ 2 = 41/40

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (41) is greater than the denominator (40), divide 41 by 40: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/40.
Working: 41/40 = 1 1/40

Step 6: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 40 yields an exact terminating decimal of 1.025 (or 102.5%).
Working: 41 ÷ 40 = 1.025 (102.5%)

Key Values:
- Simplified Fraction: 41/40
- Mixed Number Form: 1 1/40
- Decimal Value: 1.025
- Percentage: 102.5%

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Solved with FractionsCalc:
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2/5 + 10/16 = 41/40

Simplified Fraction

41/40

Mixed Number

1 1/40

Decimal Value

1.025

Percentage

102.5%

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Step-by-Step Solution: 2/5 + 10/16

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 10/16 by 5 so both fractions share the common base 80.

2 × 16/5 × 16 = 32/80 and 10 × 5/16 × 5 = 50/80

Step 3

Add the Numerators

Now add the numerators (32 + 50 = 82) and keep the common denominator 80 unchanged.

32 + 50/80 = 82/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 82 and 80, which is 2. Divide both the numerator and denominator by 2.

82 ÷ 2/80 ÷ 2 = 41/40

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (41) is greater than the denominator (40), divide 41 by 40: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/40.

41/40 = 11/40

Step 6

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 40 yields an exact terminating decimal of 1.025 (or 102.5%).

41 ÷ 40 = 1.025 (102.5%)

Visual Representation

The diagram below illustrates 2/5 plus 10/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/40`
Mixed Number Form	`1 1/40`
Decimal Form	`1.025`
Percentage	`102.5%`

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Frequently Asked Questions

What is 2/5 plus 10/16 as a fraction?

2/5 + 10/16 in simplest fraction form is 41/40 (or 1 1/40 as a mixed number).

What is 2/5 plus 10/16 as a decimal?

2/5 + 10/16 converted to a decimal is 1.025.

What is 2/5 plus 10/16 as a percentage?

2/5 + 10/16 expressed as a percentage is 102.5%.

How do you write 2/5 plus 10/16 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 41/40 can be written as the mixed number 1 1/40.

Does 2/5 plus 10/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.025) because the denominator in simplest terms contains only prime factors 2 and/or 5.