What is 1/2 plus 3/5? (Answer: 11/10)

Exact Answer

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Problem: What is 1/2 plus 3/5?
Formula / Expression: 1/2 + 3/5
Final Answer: 1 1/10 (11/10)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 2 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 5 = 10.
Working: LCD(2, 5) = 10

Step 2: Convert to Equivalent Fractions with Common Denominator 10
Multiply the numerator and denominator of 1/2 by 5, and multiply the numerator and denominator of 3/5 by 2 so both fractions share the common base 10.
Working: 1 × 5/2 × 5 = 5/10 and 3 × 2/5 × 2 = 6/10

Step 3: Add the Numerators
Now add the numerators (5 + 6 = 11) and keep the common denominator 10 unchanged.
Working: 5 + 6/10 = 11/10

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 11 and 10 is 1, confirming that 11/10 cannot be reduced further—it is already in its simplest irreducible form.
Working: 11/10

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (11) is greater than the denominator (10), divide 11 by 10: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/10.
Working: 11/10 = 1 1/10

Step 6: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 10 yields an exact terminating decimal of 1.1 (or 110%).
Working: 11 ÷ 10 = 1.1 (110%)

Key Values:
- Simplified Fraction: 11/10
- Mixed Number Form: 1 1/10
- Decimal Value: 1.1
- Percentage: 110%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-2-plus-3-5/
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1/2 + 3/5 = 11/10

Simplified Fraction

11/10

Mixed Number

1 1/10

Decimal Value

1.1

Percentage

110%

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Step-by-Step Solution: 1/2 + 3/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 2 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 2 × 5 = 10.

LCD(2, 5) = 10

Step 2

Convert to Equivalent Fractions with Common Denominator 10

Multiply the numerator and denominator of 1/2 by 5, and multiply the numerator and denominator of 3/5 by 2 so both fractions share the common base 10.

1 × 5/2 × 5 = 5/10 and 3 × 2/5 × 2 = 6/10

Step 3

Add the Numerators

Now add the numerators (5 + 6 = 11) and keep the common denominator 10 unchanged.

5 + 6/10 = 11/10

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 11 and 10 is 1, confirming that 11/10 cannot be reduced further—it is already in its simplest irreducible form.

11/10

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (11) is greater than the denominator (10), divide 11 by 10: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/10.

11/10 = 11/10

Step 6

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 10 yields an exact terminating decimal of 1.1 (or 110%).

11 ÷ 10 = 1.1 (110%)

Visual Representation

The diagram below illustrates 1/2 plus 3/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/10`
Mixed Number Form	`1 1/10`
Decimal Form	`1.1`
Percentage	`110%`

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Frequently Asked Questions

What is 1/2 plus 3/5 as a fraction?

1/2 + 3/5 in simplest fraction form is 11/10 (or 1 1/10 as a mixed number).

What is 1/2 plus 3/5 as a decimal?

1/2 + 3/5 converted to a decimal is 1.1.

What is 1/2 plus 3/5 as a percentage?

1/2 + 3/5 expressed as a percentage is 110%.

How do you write 1/2 plus 3/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 11/10 can be written as the mixed number 1 1/10.

Does 1/2 plus 3/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.1) because the denominator in simplest terms contains only prime factors 2 and/or 5.