What is 2/5 plus 9/12? (Answer: 23/20)

Exact Answer

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Problem: What is 2/5 plus 9/12?
Formula / Expression: 2/5 + 9/12
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 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 2/5 by 12, and multiply the numerator and denominator of 9/12 by 5 so both fractions share the common base 60.
Working: 2 × 12/5 × 12 = 24/60 and 9 × 5/12 × 5 = 45/60

Step 3: Add the Numerators
Now add the numerators (24 + 45 = 69) and keep the common denominator 60 unchanged.
Working: 24 + 45/60 = 69/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 60, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/60 ÷ 3 = 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 + 9/12 = 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 + 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 2/5 by 12, and multiply the numerator and denominator of 9/12 by 5 so both fractions share the common base 60.

2 × 12/5 × 12 = 24/60 and 9 × 5/12 × 5 = 45/60

Step 3

Add the Numerators

Now add the numerators (24 + 45 = 69) and keep the common denominator 60 unchanged.

24 + 45/60 = 69/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 60, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/60 ÷ 3 = 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 9/12 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 9/12 as a fraction?

2/5 + 9/12 in simplest fraction form is 23/20 (or 1 3/20 as a mixed number).

What is 2/5 plus 9/12 as a decimal?

2/5 + 9/12 converted to a decimal is 1.15.

What is 2/5 plus 9/12 as a percentage?

2/5 + 9/12 expressed as a percentage is 115%.

How do you write 2/5 plus 9/12 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 9/12 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.