What is 2/5 plus 3/4? (Answer: 23/20)

Exact Answer

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Problem: What is 2/5 plus 3/4?
Formula / Expression: 2/5 + 3/4
Final Answer: 1 3/20 (23/20)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 5 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 4 = 20.
Working: LCD(5, 4) = 20

Step 2: Convert to Equivalent Fractions with Common Denominator 20
Multiply the numerator and denominator of 2/5 by 4, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.
Working: 2 × 4/5 × 4 = 8/20 and 3 × 5/4 × 5 = 15/20

Step 3: Add the Numerators
Now add the numerators (8 + 15 = 23) and keep the common denominator 20 unchanged.
Working: 8 + 15/20 = 23/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 20 is 1, confirming that 23/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/20

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (23) is greater than the denominator (20), divide 23 by 20: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/20.
Working: 23/20 = 1 3/20

Step 6: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 20 yields an exact terminating decimal of 1.15 (or 115%).
Working: 23 ÷ 20 = 1.15 (115%)

Key Values:
- Simplified Fraction: 23/20
- Mixed Number Form: 1 3/20
- Decimal Value: 1.15
- Percentage: 115%

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Solved with FractionsCalc:
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2/5 + 3/4 = 23/20

Simplified Fraction

23/20

Mixed Number

1 3/20

Decimal Value

1.15

Percentage

115%

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Step-by-Step Solution: 2/5 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 4 = 20.

LCD(5, 4) = 20

Step 2

Convert to Equivalent Fractions with Common Denominator 20

Multiply the numerator and denominator of 2/5 by 4, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.

2 × 4/5 × 4 = 8/20 and 3 × 5/4 × 5 = 15/20

Step 3

Add the Numerators

Now add the numerators (8 + 15 = 23) and keep the common denominator 20 unchanged.

8 + 15/20 = 23/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 20 is 1, confirming that 23/20 cannot be reduced further—it is already in its simplest irreducible form.

23/20

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (23) is greater than the denominator (20), divide 23 by 20: it goes in 1 whole time(s) with a remainder of 3, giving the mixed number 1 3/20.

23/20 = 13/20

Step 6

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 20 yields an exact terminating decimal of 1.15 (or 115%).

23 ÷ 20 = 1.15 (115%)

Visual Representation

The diagram below illustrates 2/5 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/20`
Mixed Number Form	`1 3/20`
Decimal Form	`1.15`
Percentage	`115%`

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Frequently Asked Questions

What is 2/5 plus 3/4 as a fraction?

2/5 + 3/4 in simplest fraction form is 23/20 (or 1 3/20 as a mixed number).

What is 2/5 plus 3/4 as a decimal?

2/5 + 3/4 converted to a decimal is 1.15.

What is 2/5 plus 3/4 as a percentage?

2/5 + 3/4 expressed as a percentage is 115%.

How do you write 2/5 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 23/20 can be written as the mixed number 1 3/20.

Does 2/5 plus 3/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.15) because the denominator in simplest terms contains only prime factors 2 and/or 5.