What is 4/9 plus 3/4? (Answer: 43/36)

Exact Answer

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Problem: What is 4/9 plus 3/4?
Formula / Expression: 4/9 + 3/4
Final Answer: 1 7/36 (43/36)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 4 = 36.
Working: LCD(9, 4) = 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 3/4 by 9 so both fractions share the common base 36.
Working: 4 × 4/9 × 4 = 16/36 and 3 × 9/4 × 9 = 27/36

Step 3: Add the Numerators
Now add the numerators (16 + 27 = 43) and keep the common denominator 36 unchanged.
Working: 16 + 27/36 = 43/36

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 43 and 36 is 1, confirming that 43/36 cannot be reduced further—it is already in its simplest irreducible form.
Working: 43/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (43) is greater than the denominator (36), divide 43 by 36: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/36.
Working: 43/36 = 1 7/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 36 produces a repeating decimal (approximately 1.194444, or 119.4444%).
Working: 43 ÷ 36 = 1.194444 (119.4444%)

Key Values:
- Simplified Fraction: 43/36
- Mixed Number Form: 1 7/36
- Decimal Value: 1.194444
- Percentage: 119.4444%

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Solved with FractionsCalc:
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4/9 + 3/4 = 43/36

Simplified Fraction

43/36

Mixed Number

1 7/36

Decimal Value

1.194444

Percentage

119.4444%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 4 = 36.

LCD(9, 4) = 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 3/4 by 9 so both fractions share the common base 36.

4 × 4/9 × 4 = 16/36 and 3 × 9/4 × 9 = 27/36

Step 3

Add the Numerators

Now add the numerators (16 + 27 = 43) and keep the common denominator 36 unchanged.

16 + 27/36 = 43/36

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 43 and 36 is 1, confirming that 43/36 cannot be reduced further—it is already in its simplest irreducible form.

43/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (43) is greater than the denominator (36), divide 43 by 36: it goes in 1 whole time(s) with a remainder of 7, giving the mixed number 1 7/36.

43/36 = 17/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 36 produces a repeating decimal (approximately 1.194444, or 119.4444%).

43 ÷ 36 = 1.194444 (119.4444%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/36`
Mixed Number Form	`1 7/36`
Decimal Form	`1.194444`
Percentage	`119.4444%`

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Frequently Asked Questions

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

4/9 + 3/4 in simplest fraction form is 43/36 (or 1 7/36 as a mixed number).

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

4/9 + 3/4 converted to a decimal is 1.194444.

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

4/9 + 3/4 expressed as a percentage is 119.4444%.

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

Because the numerator is greater than the denominator, the improper fraction 43/36 can be written as the mixed number 1 7/36.

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

It results in a repeating decimal (approximately 1.194444...) because the denominator contains prime factors other than 2 and 5.