What is 2/3 plus 8/10? (Answer: 22/15)

Exact Answer

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Problem: What is 2/3 plus 8/10?
Formula / Expression: 2/3 + 8/10
Final Answer: 1 7/15 (22/15)
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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 8/10 by 3 so both fractions share the common base 30.
Working: 2 × 10/3 × 10 = 20/30 and 8 × 3/10 × 3 = 24/30

Step 3: Add the Numerators
Now add the numerators (20 + 24 = 44) and keep the common denominator 30 unchanged.
Working: 20 + 24/30 = 44/30

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 44 and 30, which is 2. Divide both the numerator and denominator by 2.
Working: 44 ÷ 2/30 ÷ 2 = 22/15

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (22) is greater than the denominator (15), divide 22 by 15: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/15.
Working: 22/15 = 1 7/15

Step 6: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 15 produces a repeating decimal (approximately 1.466667, or 146.6667%).
Working: 22 ÷ 15 = 1.466667 (146.6667%)

Key Values:
- Simplified Fraction: 22/15
- Mixed Number Form: 1 7/15
- Decimal Value: 1.466667
- Percentage: 146.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-3-plus-8-10/
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2/3 + 8/10 = 22/15

Simplified Fraction

22/15

Mixed Number

1 7/15

Decimal Value

1.466667

Percentage

146.6667%

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Step-by-Step Solution: 2/3 + 8/10

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 8/10 by 3 so both fractions share the common base 30.

2 × 10/3 × 10 = 20/30 and 8 × 3/10 × 3 = 24/30

Step 3

Add the Numerators

Now add the numerators (20 + 24 = 44) and keep the common denominator 30 unchanged.

20 + 24/30 = 44/30

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 44 and 30, which is 2. Divide both the numerator and denominator by 2.

44 ÷ 2/30 ÷ 2 = 22/15

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (22) is greater than the denominator (15), divide 22 by 15: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/15.

22/15 = 17/15

Step 6

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 15 produces a repeating decimal (approximately 1.466667, or 146.6667%).

22 ÷ 15 = 1.466667 (146.6667%)

Visual Representation

The diagram below illustrates 2/3 plus 8/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/15`
Mixed Number Form	`1 7/15`
Decimal Form	`1.466667`
Percentage	`146.6667%`

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Frequently Asked Questions

What is 2/3 plus 8/10 as a fraction?

2/3 + 8/10 in simplest fraction form is 22/15 (or 1 7/15 as a mixed number).

What is 2/3 plus 8/10 as a decimal?

2/3 + 8/10 converted to a decimal is 1.466667.

What is 2/3 plus 8/10 as a percentage?

2/3 + 8/10 expressed as a percentage is 146.6667%.

How do you write 2/3 plus 8/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 22/15 can be written as the mixed number 1 7/15.

Does 2/3 plus 8/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.466667...) because the denominator contains prime factors other than 2 and 5.