What is 10/32 plus 9/13? (Answer: 209/208)

Exact Answer

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Problem: What is 10/32 plus 9/13?
Formula / Expression: 10/32 + 9/13
Final Answer: 1 1/208 (209/208)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.
Working: LCD(32, 13) = 416

Step 2: Convert to Equivalent Fractions with Common Denominator 416
Multiply the numerator and denominator of 10/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.
Working: 10 × 13/32 × 13 = 130/416 and 9 × 32/13 × 32 = 288/416

Step 3: Add the Numerators
Now add the numerators (130 + 288 = 418) and keep the common denominator 416 unchanged.
Working: 130 + 288/416 = 418/416

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 418 and 416, which is 2. Divide both the numerator and denominator by 2.
Working: 418 ÷ 2/416 ÷ 2 = 209/208

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (209) is greater than the denominator (208), divide 209 by 208: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/208.
Working: 209/208 = 1 1/208

Step 6: Decimal & Percentage Representation
Dividing the numerator 209 by denominator 208 produces a repeating decimal (approximately 1.004808, or 100.4808%).
Working: 209 ÷ 208 = 1.004808 (100.4808%)

Key Values:
- Simplified Fraction: 209/208
- Mixed Number Form: 1 1/208
- Decimal Value: 1.004808
- Percentage: 100.4808%

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10/32 + 9/13 = 209/208

Simplified Fraction

209/208

Mixed Number

1 1/208

Decimal Value

1.004808

Percentage

100.4808%

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Step-by-Step Solution: 10/32 + 9/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 13 = 416.

LCD(32, 13) = 416

Step 2

Convert to Equivalent Fractions with Common Denominator 416

Multiply the numerator and denominator of 10/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.

10 × 13/32 × 13 = 130/416 and 9 × 32/13 × 32 = 288/416

Step 3

Add the Numerators

Now add the numerators (130 + 288 = 418) and keep the common denominator 416 unchanged.

130 + 288/416 = 418/416

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 418 and 416, which is 2. Divide both the numerator and denominator by 2.

418 ÷ 2/416 ÷ 2 = 209/208

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (209) is greater than the denominator (208), divide 209 by 208: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/208.

209/208 = 11/208

Step 6

Decimal & Percentage Representation

Dividing the numerator 209 by denominator 208 produces a repeating decimal (approximately 1.004808, or 100.4808%).

209 ÷ 208 = 1.004808 (100.4808%)

Visual Representation

The diagram below illustrates 10/32 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`209/208`
Mixed Number Form	`1 1/208`
Decimal Form	`1.004808`
Percentage	`100.4808%`

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Frequently Asked Questions

What is 10/32 plus 9/13 as a fraction?

10/32 + 9/13 in simplest fraction form is 209/208 (or 1 1/208 as a mixed number).

What is 10/32 plus 9/13 as a decimal?

10/32 + 9/13 converted to a decimal is 1.004808.

What is 10/32 plus 9/13 as a percentage?

10/32 + 9/13 expressed as a percentage is 100.4808%.

How do you write 10/32 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 209/208 can be written as the mixed number 1 1/208.

Does 10/32 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.004808...) because the denominator contains prime factors other than 2 and 5.