What is 4/9 plus 9/16? (Answer: 145/144)

Exact Answer

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Problem: What is 4/9 plus 9/16?
Formula / Expression: 4/9 + 9/16
Final Answer: 1 1/144 (145/144)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.
Working: LCD(9, 16) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 4/9 by 16, and multiply the numerator and denominator of 9/16 by 9 so both fractions share the common base 144.
Working: 4 × 16/9 × 16 = 64/144 and 9 × 9/16 × 9 = 81/144

Step 3: Add the Numerators
Now add the numerators (64 + 81 = 145) and keep the common denominator 144 unchanged.
Working: 64 + 81/144 = 145/144

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 145 and 144 is 1, confirming that 145/144 cannot be reduced further—it is already in its simplest irreducible form.
Working: 145/144

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (145) is greater than the denominator (144), divide 145 by 144: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/144.
Working: 145/144 = 1 1/144

Step 6: Decimal & Percentage Representation
Dividing the numerator 145 by denominator 144 produces a repeating decimal (approximately 1.006944, or 100.6944%).
Working: 145 ÷ 144 = 1.006944 (100.6944%)

Key Values:
- Simplified Fraction: 145/144
- Mixed Number Form: 1 1/144
- Decimal Value: 1.006944
- Percentage: 100.6944%

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Solved with FractionsCalc:
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4/9 + 9/16 = 145/144

Simplified Fraction

145/144

Mixed Number

1 1/144

Decimal Value

1.006944

Percentage

100.6944%

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Step-by-Step Solution: 4/9 + 9/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 16 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 16 = 144.

LCD(9, 16) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 4/9 by 16, and multiply the numerator and denominator of 9/16 by 9 so both fractions share the common base 144.

4 × 16/9 × 16 = 64/144 and 9 × 9/16 × 9 = 81/144

Step 3

Add the Numerators

Now add the numerators (64 + 81 = 145) and keep the common denominator 144 unchanged.

64 + 81/144 = 145/144

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 145 and 144 is 1, confirming that 145/144 cannot be reduced further—it is already in its simplest irreducible form.

145/144

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (145) is greater than the denominator (144), divide 145 by 144: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/144.

145/144 = 11/144

Step 6

Decimal & Percentage Representation

Dividing the numerator 145 by denominator 144 produces a repeating decimal (approximately 1.006944, or 100.6944%).

145 ÷ 144 = 1.006944 (100.6944%)

Visual Representation

The diagram below illustrates 4/9 plus 9/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`145/144`
Mixed Number Form	`1 1/144`
Decimal Form	`1.006944`
Percentage	`100.6944%`

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Frequently Asked Questions

What is 4/9 plus 9/16 as a fraction?

4/9 + 9/16 in simplest fraction form is 145/144 (or 1 1/144 as a mixed number).

What is 4/9 plus 9/16 as a decimal?

4/9 + 9/16 converted to a decimal is 1.006944.

What is 4/9 plus 9/16 as a percentage?

4/9 + 9/16 expressed as a percentage is 100.6944%.

How do you write 4/9 plus 9/16 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 145/144 can be written as the mixed number 1 1/144.

Does 4/9 plus 9/16 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.006944...) because the denominator contains prime factors other than 2 and 5.