What is 2/10 plus 4/12? (Answer: 8/15)

Exact Answer

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Problem: What is 2/10 plus 4/12?
Formula / Expression: 2/10 + 4/12
Final Answer: 8/15
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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 4/12 by 5 so both fractions share the common base 60.
Working: 2 × 6/10 × 6 = 12/60 and 4 × 5/12 × 5 = 20/60

Step 3: Add the Numerators
Now add the numerators (12 + 20 = 32) and keep the common denominator 60 unchanged.
Working: 12 + 20/60 = 32/60

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 32 and 60, which is 4. Divide both the numerator and denominator by 4.
Working: 32 ÷ 4/60 ÷ 4 = 8/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 15 produces a repeating decimal (approximately 0.533333, or 53.3333%).
Working: 8 ÷ 15 = 0.533333 (53.3333%)

Key Values:
- Simplified Fraction: 8/15
- Mixed Number Form: 8/15
- Decimal Value: 0.533333
- Percentage: 53.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-10-plus-4-12/
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2/10 + 4/12 = 8/15

Simplified Fraction

8/15

Mixed Number

Proper (8/15)

Decimal Value

0.533333

Percentage

53.3333%

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Step-by-Step Solution: 2/10 + 4/12

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 4/12 by 5 so both fractions share the common base 60.

2 × 6/10 × 6 = 12/60 and 4 × 5/12 × 5 = 20/60

Step 3

Add the Numerators

Now add the numerators (12 + 20 = 32) and keep the common denominator 60 unchanged.

12 + 20/60 = 32/60

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 32 and 60, which is 4. Divide both the numerator and denominator by 4.

32 ÷ 4/60 ÷ 4 = 8/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 15 produces a repeating decimal (approximately 0.533333, or 53.3333%).

8 ÷ 15 = 0.533333 (53.3333%)

Visual Representation

The diagram below illustrates 2/10 plus 4/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/15`
Mixed Number Form	`8/15`
Decimal Form	`0.533333`
Percentage	`53.3333%`

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Frequently Asked Questions

What is 2/10 plus 4/12 as a fraction?

2/10 + 4/12 in simplest fraction form is 8/15.

What is 2/10 plus 4/12 as a decimal?

2/10 + 4/12 converted to a decimal is 0.533333.

What is 2/10 plus 4/12 as a percentage?

2/10 + 4/12 expressed as a percentage is 53.3333%.

Does 2/10 plus 4/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.533333...) because the denominator contains prime factors other than 2 and 5.