What is 2/3 plus 4/5? (Answer: 22/15)

Exact Answer

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Problem: What is 2/3 plus 4/5?
Formula / Expression: 2/3 + 4/5
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 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 5 = 15.
Working: LCD(3, 5) = 15

Step 2: Convert to Equivalent Fractions with Common Denominator 15
Multiply the numerator and denominator of 2/3 by 5, and multiply the numerator and denominator of 4/5 by 3 so both fractions share the common base 15.
Working: 2 × 5/3 × 5 = 10/15 and 4 × 3/5 × 3 = 12/15

Step 3: Add the Numerators
Now add the numerators (10 + 12 = 22) and keep the common denominator 15 unchanged.
Working: 10 + 12/15 = 22/15

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 22 and 15 is 1, confirming that 22/15 cannot be reduced further—it is already in its simplest irreducible form.
Working: 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-4-5/
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2/3 + 4/5 = 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 + 4/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 3 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 3 × 5 = 15.

LCD(3, 5) = 15

Step 2

Convert to Equivalent Fractions with Common Denominator 15

Multiply the numerator and denominator of 2/3 by 5, and multiply the numerator and denominator of 4/5 by 3 so both fractions share the common base 15.

2 × 5/3 × 5 = 10/15 and 4 × 3/5 × 3 = 12/15

Step 3

Add the Numerators

Now add the numerators (10 + 12 = 22) and keep the common denominator 15 unchanged.

10 + 12/15 = 22/15

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 22 and 15 is 1, confirming that 22/15 cannot be reduced further—it is already in its simplest irreducible form.

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 4/5 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 4/5 as a fraction?

2/3 + 4/5 in simplest fraction form is 22/15 (or 1 7/15 as a mixed number).

What is 2/3 plus 4/5 as a decimal?

2/3 + 4/5 converted to a decimal is 1.466667.

What is 2/3 plus 4/5 as a percentage?

2/3 + 4/5 expressed as a percentage is 146.6667%.

How do you write 2/3 plus 4/5 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 4/5 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.