What is 2/6 plus 7/10? (Answer: 31/30)

Exact Answer

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Problem: What is 2/6 plus 7/10?
Formula / Expression: 2/6 + 7/10
Final Answer: 1 1/30 (31/30)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 2/6 by 5, and multiply the numerator and denominator of 7/10 by 3 so both fractions share the common base 30.
Working: 2 × 5/6 × 5 = 10/30 and 7 × 3/10 × 3 = 21/30

Step 3: Add the Numerators
Now add the numerators (10 + 21 = 31) and keep the common denominator 30 unchanged.
Working: 10 + 21/30 = 31/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 31 and 30 is 1, confirming that 31/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 31/30

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (31) is greater than the denominator (30), divide 31 by 30: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/30.
Working: 31/30 = 1 1/30

Step 6: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 30 produces a repeating decimal (approximately 1.033333, or 103.3333%).
Working: 31 ÷ 30 = 1.033333 (103.3333%)

Key Values:
- Simplified Fraction: 31/30
- Mixed Number Form: 1 1/30
- Decimal Value: 1.033333
- Percentage: 103.3333%

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Solved with FractionsCalc:
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2/6 + 7/10 = 31/30

Simplified Fraction

31/30

Mixed Number

1 1/30

Decimal Value

1.033333

Percentage

103.3333%

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Step-by-Step Solution: 2/6 + 7/10

Step 1

Find the Least Common Denominator (LCD)

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

LCD(6, 10) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

Multiply the numerator and denominator of 2/6 by 5, and multiply the numerator and denominator of 7/10 by 3 so both fractions share the common base 30.

2 × 5/6 × 5 = 10/30 and 7 × 3/10 × 3 = 21/30

Step 3

Add the Numerators

Now add the numerators (10 + 21 = 31) and keep the common denominator 30 unchanged.

10 + 21/30 = 31/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 31 and 30 is 1, confirming that 31/30 cannot be reduced further—it is already in its simplest irreducible form.

31/30

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (31) is greater than the denominator (30), divide 31 by 30: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/30.

31/30 = 11/30

Step 6

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 30 produces a repeating decimal (approximately 1.033333, or 103.3333%).

31 ÷ 30 = 1.033333 (103.3333%)

Visual Representation

The diagram below illustrates 2/6 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/30`
Mixed Number Form	`1 1/30`
Decimal Form	`1.033333`
Percentage	`103.3333%`

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Frequently Asked Questions

What is 2/6 plus 7/10 as a fraction?

2/6 + 7/10 in simplest fraction form is 31/30 (or 1 1/30 as a mixed number).

What is 2/6 plus 7/10 as a decimal?

2/6 + 7/10 converted to a decimal is 1.033333.

What is 2/6 plus 7/10 as a percentage?

2/6 + 7/10 expressed as a percentage is 103.3333%.

How do you write 2/6 plus 7/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 31/30 can be written as the mixed number 1 1/30.

Does 2/6 plus 7/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.033333...) because the denominator contains prime factors other than 2 and 5.