What is 4/16 plus 3/9? (Answer: 7/12)

Exact Answer

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Problem: What is 4/16 plus 3/9?
Formula / Expression: 4/16 + 3/9
Final Answer: 7/12
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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 3/9 by 16 so both fractions share the common base 144.
Working: 4 × 9/16 × 9 = 36/144 and 3 × 16/9 × 16 = 48/144

Step 3: Add the Numerators
Now add the numerators (36 + 48 = 84) and keep the common denominator 144 unchanged.
Working: 36 + 48/144 = 84/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 144, which is 12. Divide both the numerator and denominator by 12.
Working: 84 ÷ 12/144 ÷ 12 = 7/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).
Working: 7 ÷ 12 = 0.583333 (58.3333%)

Key Values:
- Simplified Fraction: 7/12
- Mixed Number Form: 7/12
- Decimal Value: 0.583333
- Percentage: 58.3333%

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Solved with FractionsCalc:
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4/16 + 3/9 = 7/12

Simplified Fraction

7/12

Mixed Number

Proper (7/12)

Decimal Value

0.583333

Percentage

58.3333%

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Step-by-Step Solution: 4/16 + 3/9

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 3/9 by 16 so both fractions share the common base 144.

4 × 9/16 × 9 = 36/144 and 3 × 16/9 × 16 = 48/144

Step 3

Add the Numerators

Now add the numerators (36 + 48 = 84) and keep the common denominator 144 unchanged.

36 + 48/144 = 84/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 144, which is 12. Divide both the numerator and denominator by 12.

84 ÷ 12/144 ÷ 12 = 7/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).

7 ÷ 12 = 0.583333 (58.3333%)

Visual Representation

The diagram below illustrates 4/16 plus 3/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/12`
Mixed Number Form	`7/12`
Decimal Form	`0.583333`
Percentage	`58.3333%`

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Frequently Asked Questions

What is 4/16 plus 3/9 as a fraction?

4/16 + 3/9 in simplest fraction form is 7/12.

What is 4/16 plus 3/9 as a decimal?

4/16 + 3/9 converted to a decimal is 0.583333.

What is 4/16 plus 3/9 as a percentage?

4/16 + 3/9 expressed as a percentage is 58.3333%.

Does 4/16 plus 3/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.583333...) because the denominator contains prime factors other than 2 and 5.