What is 4/12 plus 4/9? (Answer: 7/9)

Exact Answer

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Problem: What is 4/12 plus 4/9?
Formula / Expression: 4/12 + 4/9
Final Answer: 7/9
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Step-by-Step Solution:

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

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

Step 3: Add the Numerators
Now add the numerators (12 + 16 = 28) and keep the common denominator 36 unchanged.
Working: 12 + 16/36 = 28/36

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 28 and 36, which is 4. Divide both the numerator and denominator by 4.
Working: 28 ÷ 4/36 ÷ 4 = 7/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).
Working: 7 ÷ 9 = 0.777778 (77.7778%)

Key Values:
- Simplified Fraction: 7/9
- Mixed Number Form: 7/9
- Decimal Value: 0.777778
- Percentage: 77.7778%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-12-plus-4-9/
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4/12 + 4/9 = 7/9

Simplified Fraction

7/9

Mixed Number

Proper (7/9)

Decimal Value

0.777778

Percentage

77.7778%

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Step-by-Step Solution: 4/12 + 4/9

Step 1

Find the Least Common Denominator (LCD)

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

LCD(12, 9) = 36

Step 2

Convert to Equivalent Fractions with Common Denominator 36

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

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

Step 3

Add the Numerators

Now add the numerators (12 + 16 = 28) and keep the common denominator 36 unchanged.

12 + 16/36 = 28/36

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 28 and 36, which is 4. Divide both the numerator and denominator by 4.

28 ÷ 4/36 ÷ 4 = 7/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).

7 ÷ 9 = 0.777778 (77.7778%)

Visual Representation

The diagram below illustrates 4/12 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/9`
Mixed Number Form	`7/9`
Decimal Form	`0.777778`
Percentage	`77.7778%`

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Frequently Asked Questions

What is 4/12 plus 4/9 as a fraction?

4/12 + 4/9 in simplest fraction form is 7/9.

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

4/12 + 4/9 converted to a decimal is 0.777778.

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

4/12 + 4/9 expressed as a percentage is 77.7778%.

Does 4/12 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.777778...) because the denominator contains prime factors other than 2 and 5.