What is 4/9 plus 2/3? (Answer: 10/9)

Exact Answer

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Problem: What is 4/9 plus 2/3?
Formula / Expression: 4/9 + 2/3
Final Answer: 1 1/9 (10/9)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.
Working: LCD(9, 3) = 9

Step 2: Convert to Equivalent Fractions with Common Denominator 9
Multiply the numerator and denominator of 4/9 by 1, and multiply the numerator and denominator of 2/3 by 3 so both fractions share the common base 9.
Working: 4 × 1/9 × 1 = 4/9 and 2 × 3/3 × 3 = 6/9

Step 3: Add the Numerators
Now add the numerators (4 + 6 = 10) and keep the common denominator 9 unchanged.
Working: 4 + 6/9 = 10/9

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 10 and 9 is 1, confirming that 10/9 cannot be reduced further—it is already in its simplest irreducible form.
Working: 10/9

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (10) is greater than the denominator (9), divide 10 by 9: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/9.
Working: 10/9 = 1 1/9

Step 6: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 9 produces a repeating decimal (approximately 1.111111, or 111.1111%).
Working: 10 ÷ 9 = 1.111111 (111.1111%)

Key Values:
- Simplified Fraction: 10/9
- Mixed Number Form: 1 1/9
- Decimal Value: 1.111111
- Percentage: 111.1111%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-9-plus-2-3/
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4/9 + 2/3 = 10/9

Simplified Fraction

10/9

Mixed Number

1 1/9

Decimal Value

1.111111

Percentage

111.1111%

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Step-by-Step Solution: 4/9 + 2/3

Step 1

Find the Least Common Denominator (LCD)

Notice that 9 is an exact multiple of 3 (3 × 3 = 9). The Least Common Denominator (LCD) is simply 9, meaning we only need to scale one fraction.

LCD(9, 3) = 9

Step 2

Convert to Equivalent Fractions with Common Denominator 9

Multiply the numerator and denominator of 4/9 by 1, and multiply the numerator and denominator of 2/3 by 3 so both fractions share the common base 9.

4 × 1/9 × 1 = 4/9 and 2 × 3/3 × 3 = 6/9

Step 3

Add the Numerators

Now add the numerators (4 + 6 = 10) and keep the common denominator 9 unchanged.

4 + 6/9 = 10/9

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 10 and 9 is 1, confirming that 10/9 cannot be reduced further—it is already in its simplest irreducible form.

10/9

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (10) is greater than the denominator (9), divide 10 by 9: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/9.

10/9 = 11/9

Step 6

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 9 produces a repeating decimal (approximately 1.111111, or 111.1111%).

10 ÷ 9 = 1.111111 (111.1111%)

Visual Representation

The diagram below illustrates 4/9 plus 2/3 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/9`
Mixed Number Form	`1 1/9`
Decimal Form	`1.111111`
Percentage	`111.1111%`

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Frequently Asked Questions

What is 4/9 plus 2/3 as a fraction?

4/9 + 2/3 in simplest fraction form is 10/9 (or 1 1/9 as a mixed number).

What is 4/9 plus 2/3 as a decimal?

4/9 + 2/3 converted to a decimal is 1.111111.

What is 4/9 plus 2/3 as a percentage?

4/9 + 2/3 expressed as a percentage is 111.1111%.

How do you write 4/9 plus 2/3 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 10/9 can be written as the mixed number 1 1/9.

Does 4/9 plus 2/3 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.111111...) because the denominator contains prime factors other than 2 and 5.