What is 3/5 plus 3/4? (Answer: 27/20)

Exact Answer

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Problem: What is 3/5 plus 3/4?
Formula / Expression: 3/5 + 3/4
Final Answer: 1 7/20 (27/20)
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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 3/5 by 4, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.
Working: 3 × 4/5 × 4 = 12/20 and 3 × 5/4 × 5 = 15/20

Step 3: Add the Numerators
Now add the numerators (12 + 15 = 27) and keep the common denominator 20 unchanged.
Working: 12 + 15/20 = 27/20

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 27 and 20 is 1, confirming that 27/20 cannot be reduced further—it is already in its simplest irreducible form.
Working: 27/20

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (27) is greater than the denominator (20), divide 27 by 20: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/20.
Working: 27/20 = 1 7/20

Step 6: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 20 yields an exact terminating decimal of 1.35 (or 135%).
Working: 27 ÷ 20 = 1.35 (135%)

Key Values:
- Simplified Fraction: 27/20
- Mixed Number Form: 1 7/20
- Decimal Value: 1.35
- Percentage: 135%

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3/5 + 3/4 = 27/20

Simplified Fraction

27/20

Mixed Number

1 7/20

Decimal Value

1.35

Percentage

135%

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Step-by-Step Solution: 3/5 + 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 3/5 by 4, and multiply the numerator and denominator of 3/4 by 5 so both fractions share the common base 20.

3 × 4/5 × 4 = 12/20 and 3 × 5/4 × 5 = 15/20

Step 3

Add the Numerators

Now add the numerators (12 + 15 = 27) and keep the common denominator 20 unchanged.

12 + 15/20 = 27/20

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 27 and 20 is 1, confirming that 27/20 cannot be reduced further—it is already in its simplest irreducible form.

27/20

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (27) is greater than the denominator (20), divide 27 by 20: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/20.

27/20 = 17/20

Step 6

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 20 yields an exact terminating decimal of 1.35 (or 135%).

27 ÷ 20 = 1.35 (135%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/20`
Mixed Number Form	`1 7/20`
Decimal Form	`1.35`
Percentage	`135%`

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Frequently Asked Questions

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

3/5 + 3/4 in simplest fraction form is 27/20 (or 1 7/20 as a mixed number).

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

3/5 + 3/4 converted to a decimal is 1.35.

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

3/5 + 3/4 expressed as a percentage is 135%.

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

Because the numerator is greater than the denominator, the improper fraction 27/20 can be written as the mixed number 1 7/20.

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

It results in an exact terminating decimal (1.35) because the denominator in simplest terms contains only prime factors 2 and/or 5.