What is 2/10 plus 9/12? (Answer: 19/20)

Exact Answer

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Problem: What is 2/10 plus 9/12?
Formula / Expression: 2/10 + 9/12
Final Answer: 19/20
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 12 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 10 × 12 = 120, keeping the calculation simpler).
Working: LCD(10, 12) = 60

Step 2: Convert to Equivalent Fractions with Common Denominator 60
Multiply the numerator and denominator of 2/10 by 6, and multiply the numerator and denominator of 9/12 by 5 so both fractions share the common base 60.
Working: 2 × 6/10 × 6 = 12/60 and 9 × 5/12 × 5 = 45/60

Step 3: Add the Numerators
Now add the numerators (12 + 45 = 57) and keep the common denominator 60 unchanged.
Working: 12 + 45/60 = 57/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 60, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/60 ÷ 3 = 19/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 20 yields an exact terminating decimal of 0.95 (or 95%).
Working: 19 ÷ 20 = 0.95 (95%)

Key Values:
- Simplified Fraction: 19/20
- Mixed Number Form: 19/20
- Decimal Value: 0.95
- Percentage: 95%

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Solved with FractionsCalc:
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2/10 + 9/12 = 19/20

Simplified Fraction

19/20

Mixed Number

Proper (19/20)

Decimal Value

0.95

Percentage

95%

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Step-by-Step Solution: 2/10 + 9/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 12 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 60 (which is smaller than their product 10 × 12 = 120, keeping the calculation simpler).

LCD(10, 12) = 60

Step 2

Convert to Equivalent Fractions with Common Denominator 60

Multiply the numerator and denominator of 2/10 by 6, and multiply the numerator and denominator of 9/12 by 5 so both fractions share the common base 60.

2 × 6/10 × 6 = 12/60 and 9 × 5/12 × 5 = 45/60

Step 3

Add the Numerators

Now add the numerators (12 + 45 = 57) and keep the common denominator 60 unchanged.

12 + 45/60 = 57/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 60, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/60 ÷ 3 = 19/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 20 yields an exact terminating decimal of 0.95 (or 95%).

19 ÷ 20 = 0.95 (95%)

Visual Representation

The diagram below illustrates 2/10 plus 9/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/20`
Mixed Number Form	`19/20`
Decimal Form	`0.95`
Percentage	`95%`

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Frequently Asked Questions

What is 2/10 plus 9/12 as a fraction?

2/10 + 9/12 in simplest fraction form is 19/20.

What is 2/10 plus 9/12 as a decimal?

2/10 + 9/12 converted to a decimal is 0.95.

What is 2/10 plus 9/12 as a percentage?

2/10 + 9/12 expressed as a percentage is 95%.

Does 2/10 plus 9/12 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.95) because the denominator in simplest terms contains only prime factors 2 and/or 5.