What is 4/16 plus 4/9? (Answer: 25/36)

Exact Answer

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Problem: What is 4/16 plus 4/9?
Formula / Expression: 4/16 + 4/9
Final Answer: 25/36
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 4/16 by 9, and multiply the numerator and denominator of 4/9 by 16 so both fractions share the common base 144.
Working: 4 × 9/16 × 9 = 36/144 and 4 × 16/9 × 16 = 64/144

Step 3: Add the Numerators
Now add the numerators (36 + 64 = 100) and keep the common denominator 144 unchanged.
Working: 36 + 64/144 = 100/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 100 and 144, which is 4. Divide both the numerator and denominator by 4.
Working: 100 ÷ 4/144 ÷ 4 = 25/36

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 36 produces a repeating decimal (approximately 0.694444, or 69.4444%).
Working: 25 ÷ 36 = 0.694444 (69.4444%)

Key Values:
- Simplified Fraction: 25/36
- Mixed Number Form: 25/36
- Decimal Value: 0.694444
- Percentage: 69.4444%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-16-plus-4-9/
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4/16 + 4/9 = 25/36

Simplified Fraction

25/36

Mixed Number

Proper (25/36)

Decimal Value

0.694444

Percentage

69.4444%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(16, 9) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

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

4 × 9/16 × 9 = 36/144 and 4 × 16/9 × 16 = 64/144

Step 3

Add the Numerators

Now add the numerators (36 + 64 = 100) and keep the common denominator 144 unchanged.

36 + 64/144 = 100/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 100 and 144, which is 4. Divide both the numerator and denominator by 4.

100 ÷ 4/144 ÷ 4 = 25/36

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 36 produces a repeating decimal (approximately 0.694444, or 69.4444%).

25 ÷ 36 = 0.694444 (69.4444%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/36`
Mixed Number Form	`25/36`
Decimal Form	`0.694444`
Percentage	`69.4444%`

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Frequently Asked Questions

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

4/16 + 4/9 in simplest fraction form is 25/36.

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

4/16 + 4/9 converted to a decimal is 0.694444.

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

4/16 + 4/9 expressed as a percentage is 69.4444%.

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

It results in a repeating decimal (approximately 0.694444...) because the denominator contains prime factors other than 2 and 5.