What is 16/50 plus 9/13? (Answer: 329/325)

Exact Answer

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Problem: What is 16/50 plus 9/13?
Formula / Expression: 16/50 + 9/13
Final Answer: 1 4/325 (329/325)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 50 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 13 = 650.
Working: LCD(50, 13) = 650

Step 2: Convert to Equivalent Fractions with Common Denominator 650
Multiply the numerator and denominator of 16/50 by 13, and multiply the numerator and denominator of 9/13 by 50 so both fractions share the common base 650.
Working: 16 × 13/50 × 13 = 208/650 and 9 × 50/13 × 50 = 450/650

Step 3: Add the Numerators
Now add the numerators (208 + 450 = 658) and keep the common denominator 650 unchanged.
Working: 208 + 450/650 = 658/650

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 658 and 650, which is 2. Divide both the numerator and denominator by 2.
Working: 658 ÷ 2/650 ÷ 2 = 329/325

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (329) is greater than the denominator (325), divide 329 by 325: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/325.
Working: 329/325 = 1 4/325

Step 6: Decimal & Percentage Representation
Dividing the numerator 329 by denominator 325 produces a repeating decimal (approximately 1.012308, or 101.2308%).
Working: 329 ÷ 325 = 1.012308 (101.2308%)

Key Values:
- Simplified Fraction: 329/325
- Mixed Number Form: 1 4/325
- Decimal Value: 1.012308
- Percentage: 101.2308%

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Solved with FractionsCalc:
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16/50 + 9/13 = 329/325

Simplified Fraction

329/325

Mixed Number

1 4/325

Decimal Value

1.012308

Percentage

101.2308%

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Step-by-Step Solution: 16/50 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 50 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 50 × 13 = 650.

LCD(50, 13) = 650

Step 2

Convert to Equivalent Fractions with Common Denominator 650

Multiply the numerator and denominator of 16/50 by 13, and multiply the numerator and denominator of 9/13 by 50 so both fractions share the common base 650.

16 × 13/50 × 13 = 208/650 and 9 × 50/13 × 50 = 450/650

Step 3

Add the Numerators

Now add the numerators (208 + 450 = 658) and keep the common denominator 650 unchanged.

208 + 450/650 = 658/650

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 658 and 650, which is 2. Divide both the numerator and denominator by 2.

658 ÷ 2/650 ÷ 2 = 329/325

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (329) is greater than the denominator (325), divide 329 by 325: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/325.

329/325 = 14/325

Step 6

Decimal & Percentage Representation

Dividing the numerator 329 by denominator 325 produces a repeating decimal (approximately 1.012308, or 101.2308%).

329 ÷ 325 = 1.012308 (101.2308%)

Visual Representation

The diagram below illustrates 16/50 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`329/325`
Mixed Number Form	`1 4/325`
Decimal Form	`1.012308`
Percentage	`101.2308%`

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Frequently Asked Questions

What is 16/50 plus 9/13 as a fraction?

16/50 + 9/13 in simplest fraction form is 329/325 (or 1 4/325 as a mixed number).

What is 16/50 plus 9/13 as a decimal?

16/50 + 9/13 converted to a decimal is 1.012308.

What is 16/50 plus 9/13 as a percentage?

16/50 + 9/13 expressed as a percentage is 101.2308%.

How do you write 16/50 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 329/325 can be written as the mixed number 1 4/325.

Does 16/50 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.012308...) because the denominator contains prime factors other than 2 and 5.