What is 2/3 plus 7/10? (Answer: 41/30)

Exact Answer

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Problem: What is 2/3 plus 7/10?
Formula / Expression: 2/3 + 7/10
Final Answer: 1 11/30 (41/30)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 3 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 10 = 30.
Working: LCD(3, 10) = 30

Step 2: Convert to Equivalent Fractions with Common Denominator 30
Multiply the numerator and denominator of 2/3 by 10, and multiply the numerator and denominator of 7/10 by 3 so both fractions share the common base 30.
Working: 2 × 10/3 × 10 = 20/30 and 7 × 3/10 × 3 = 21/30

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 30 unchanged.
Working: 20 + 21/30 = 41/30

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 30 is 1, confirming that 41/30 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/30

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (41) is greater than the denominator (30), divide 41 by 30: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/30.
Working: 41/30 = 1 11/30

Step 6: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 30 produces a repeating decimal (approximately 1.366667, or 136.6667%).
Working: 41 ÷ 30 = 1.366667 (136.6667%)

Key Values:
- Simplified Fraction: 41/30
- Mixed Number Form: 1 11/30
- Decimal Value: 1.366667
- Percentage: 136.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-plus-7-10/
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2/3 + 7/10 = 41/30

Simplified Fraction

41/30

Mixed Number

1 11/30

Decimal Value

1.366667

Percentage

136.6667%

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Step-by-Step Solution: 2/3 + 7/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 10 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 10 = 30.

LCD(3, 10) = 30

Step 2

Convert to Equivalent Fractions with Common Denominator 30

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

2 × 10/3 × 10 = 20/30 and 7 × 3/10 × 3 = 21/30

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 30 unchanged.

20 + 21/30 = 41/30

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 30 is 1, confirming that 41/30 cannot be reduced further—it is already in its simplest irreducible form.

41/30

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (41) is greater than the denominator (30), divide 41 by 30: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/30.

41/30 = 111/30

Step 6

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 30 produces a repeating decimal (approximately 1.366667, or 136.6667%).

41 ÷ 30 = 1.366667 (136.6667%)

Visual Representation

The diagram below illustrates 2/3 plus 7/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/30`
Mixed Number Form	`1 11/30`
Decimal Form	`1.366667`
Percentage	`136.6667%`

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Frequently Asked Questions

What is 2/3 plus 7/10 as a fraction?

2/3 + 7/10 in simplest fraction form is 41/30 (or 1 11/30 as a mixed number).

What is 2/3 plus 7/10 as a decimal?

2/3 + 7/10 converted to a decimal is 1.366667.

What is 2/3 plus 7/10 as a percentage?

2/3 + 7/10 expressed as a percentage is 136.6667%.

How do you write 2/3 plus 7/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 41/30 can be written as the mixed number 1 11/30.

Does 2/3 plus 7/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.366667...) because the denominator contains prime factors other than 2 and 5.