What is 3/10 plus 5/6? (Answer: 17/15)

Exact Answer

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Problem: What is 3/10 plus 5/6?
Formula / Expression: 3/10 + 5/6
Final Answer: 1 2/15 (17/15)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 30 (which is smaller than their product 10 × 6 = 60, keeping the calculation simpler).
Working: LCD(10, 6) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 3/10 by 3, and multiply the numerator and denominator of 5/6 by 5 so both fractions share the common base 30.
Working: 3 × 3/10 × 3 = 9/30 and 5 × 5/6 × 5 = 25/30

Step 3: Add the Numerators
Now add the numerators (9 + 25 = 34) and keep the common denominator 30 unchanged.
Working: 9 + 25/30 = 34/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 34 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 34 ÷ 2/30 ÷ 2 = 17/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.
Working: 17/15 = 1 2/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).
Working: 17 ÷ 15 = 1.133333 (113.3333%)

Key Values:
- Simplified Fraction: 17/15
- Mixed Number Form: 1 2/15
- Decimal Value: 1.133333
- Percentage: 113.3333%

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Solved with FractionsCalc:
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3/10 + 5/6 = 17/15

Simplified Fraction

17/15

Mixed Number

1 2/15

Decimal Value

1.133333

Percentage

113.3333%

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Step-by-Step Solution: 3/10 + 5/6

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 6 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 30 (which is smaller than their product 10 × 6 = 60, keeping the calculation simpler).

LCD(10, 6) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 3/10 by 3, and multiply the numerator and denominator of 5/6 by 5 so both fractions share the common base 30.

3 × 3/10 × 3 = 9/30 and 5 × 5/6 × 5 = 25/30

Step 3

Add the Numerators

Now add the numerators (9 + 25 = 34) and keep the common denominator 30 unchanged.

9 + 25/30 = 34/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 34 and 30, which is 2. Divide both the numerator and denominator by 2.

34 ÷ 2/30 ÷ 2 = 17/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (17) is greater than the denominator (15), divide 17 by 15: it goes in 1 whole time(s) with a remainder of 2, giving the mixed number 1 2/15.

17/15 = 12/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 15 produces a repeating decimal (approximately 1.133333, or 113.3333%).

17 ÷ 15 = 1.133333 (113.3333%)

Visual Representation

The diagram below illustrates 3/10 plus 5/6 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/15`
Mixed Number Form	`1 2/15`
Decimal Form	`1.133333`
Percentage	`113.3333%`

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Frequently Asked Questions

What is 3/10 plus 5/6 as a fraction?

3/10 + 5/6 in simplest fraction form is 17/15 (or 1 2/15 as a mixed number).

What is 3/10 plus 5/6 as a decimal?

3/10 + 5/6 converted to a decimal is 1.133333.

What is 3/10 plus 5/6 as a percentage?

3/10 + 5/6 expressed as a percentage is 113.3333%.

How do you write 3/10 plus 5/6 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 17/15 can be written as the mixed number 1 2/15.

Does 3/10 plus 5/6 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.133333...) because the denominator contains prime factors other than 2 and 5.