What is 3/5 plus 9/12? (Answer: 27/20)

Exact Answer

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Problem: What is 3/5 plus 9/12?
Formula / Expression: 3/5 + 9/12
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 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 12 = 60.
Working: LCD(5, 12) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 3/5 by 12, and multiply the numerator and denominator of 9/12 by 5 so both fractions share the common base 60.
Working: 3 × 12/5 × 12 = 36/60 and 9 × 5/12 × 5 = 45/60

Step 3: Add the Numerators
Now add the numerators (36 + 45 = 81) and keep the common denominator 60 unchanged.
Working: 36 + 45/60 = 81/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 81 and 60, which is 3. Divide both the numerator and denominator by 3.
Working: 81 ÷ 3/60 ÷ 3 = 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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Solved with FractionsCalc:
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3/5 + 9/12 = 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 + 9/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 5 and 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 5 × 12 = 60.

LCD(5, 12) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 3/5 by 12, and multiply the numerator and denominator of 9/12 by 5 so both fractions share the common base 60.

3 × 12/5 × 12 = 36/60 and 9 × 5/12 × 5 = 45/60

Step 3

Add the Numerators

Now add the numerators (36 + 45 = 81) and keep the common denominator 60 unchanged.

36 + 45/60 = 81/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 81 and 60, which is 3. Divide both the numerator and denominator by 3.

81 ÷ 3/60 ÷ 3 = 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 9/12 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 9/12 as a fraction?

3/5 + 9/12 in simplest fraction form is 27/20 (or 1 7/20 as a mixed number).

What is 3/5 plus 9/12 as a decimal?

3/5 + 9/12 converted to a decimal is 1.35.

What is 3/5 plus 9/12 as a percentage?

3/5 + 9/12 expressed as a percentage is 135%.

How do you write 3/5 plus 9/12 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 9/12 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.