What is 4/9 plus 8/12? (Answer: 10/9)

Exact Answer

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Problem: What is 4/9 plus 8/12?
Formula / Expression: 4/9 + 8/12
Final Answer: 1 1/9 (10/9)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).
Working: LCD(9, 12) = 36

Step 2: Convert to Equivalent Fractions with Common Denominator 36
Multiply the numerator and denominator of 4/9 by 4, and multiply the numerator and denominator of 8/12 by 3 so both fractions share the common base 36.
Working: 4 × 4/9 × 4 = 16/36 and 8 × 3/12 × 3 = 24/36

Step 3: Add the Numerators
Now add the numerators (16 + 24 = 40) and keep the common denominator 36 unchanged.
Working: 16 + 24/36 = 40/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 40 and 36, which is 4. Divide both the numerator and denominator by 4.
Working: 40 ÷ 4/36 ÷ 4 = 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:
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4/9 + 8/12 = 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 + 8/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 36 (which is smaller than their product 9 × 12 = 108, keeping the calculation simpler).

LCD(9, 12) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

Multiply the numerator and denominator of 4/9 by 4, and multiply the numerator and denominator of 8/12 by 3 so both fractions share the common base 36.

4 × 4/9 × 4 = 16/36 and 8 × 3/12 × 3 = 24/36

Step 3

Add the Numerators

Now add the numerators (16 + 24 = 40) and keep the common denominator 36 unchanged.

16 + 24/36 = 40/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 40 and 36, which is 4. Divide both the numerator and denominator by 4.

40 ÷ 4/36 ÷ 4 = 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 8/12 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 8/12 as a fraction?

4/9 + 8/12 in simplest fraction form is 10/9 (or 1 1/9 as a mixed number).

What is 4/9 plus 8/12 as a decimal?

4/9 + 8/12 converted to a decimal is 1.111111.

What is 4/9 plus 8/12 as a percentage?

4/9 + 8/12 expressed as a percentage is 111.1111%.

How do you write 4/9 plus 8/12 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 8/12 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.