What is 9/12 plus 4/5? (Answer: 31/20)

Exact Answer

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Problem: What is 9/12 plus 4/5?
Formula / Expression: 9/12 + 4/5
Final Answer: 1 11/20 (31/20)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 9/12 by 5, and multiply the numerator and denominator of 4/5 by 12 so both fractions share the common base 60.
Working: 9 × 5/12 × 5 = 45/60 and 4 × 12/5 × 12 = 48/60

Step 3: Add the Numerators
Now add the numerators (45 + 48 = 93) and keep the common denominator 60 unchanged.
Working: 45 + 48/60 = 93/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 93 and 60, which is 3. Divide both the numerator and denominator by 3.
Working: 93 ÷ 3/60 ÷ 3 = 31/20

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (20), divide 31 by 20: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/20.
Working: 31/20 = 1 11/20

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 20 yields an exact terminating decimal of 1.55 (or 155%).
Working: 31 ÷ 20 = 1.55 (155%)

Key Values:
- Simplified Fraction: 31/20
- Mixed Number Form: 1 11/20
- Decimal Value: 1.55
- Percentage: 155%

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Solved with FractionsCalc:
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9/12 + 4/5 = 31/20

Simplified Fraction

31/20

Mixed Number

1 11/20

Decimal Value

1.55

Percentage

155%

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Step-by-Step Solution: 9/12 + 4/5

Step 1

Find the Least Common Denominator (LCD)

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

LCD(12, 5) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 9/12 by 5, and multiply the numerator and denominator of 4/5 by 12 so both fractions share the common base 60.

9 × 5/12 × 5 = 45/60 and 4 × 12/5 × 12 = 48/60

Step 3

Add the Numerators

Now add the numerators (45 + 48 = 93) and keep the common denominator 60 unchanged.

45 + 48/60 = 93/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 93 and 60, which is 3. Divide both the numerator and denominator by 3.

93 ÷ 3/60 ÷ 3 = 31/20

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (20), divide 31 by 20: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/20.

31/20 = 111/20

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 20 yields an exact terminating decimal of 1.55 (or 155%).

31 ÷ 20 = 1.55 (155%)

Visual Representation

The diagram below illustrates 9/12 plus 4/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/20`
Mixed Number Form	`1 11/20`
Decimal Form	`1.55`
Percentage	`155%`

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Frequently Asked Questions

What is 9/12 plus 4/5 as a fraction?

9/12 + 4/5 in simplest fraction form is 31/20 (or 1 11/20 as a mixed number).

What is 9/12 plus 4/5 as a decimal?

9/12 + 4/5 converted to a decimal is 1.55.

What is 9/12 plus 4/5 as a percentage?

9/12 + 4/5 expressed as a percentage is 155%.

How do you write 9/12 plus 4/5 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/20 can be written as the mixed number 1 11/20.

Does 9/12 plus 4/5 result in a terminating or repeating decimal?

It results in an exact terminating decimal (1.55) because the denominator in simplest terms contains only prime factors 2 and/or 5.