What is 21/32 plus 9/13? (Answer: 561/416)

Exact Answer

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Problem: What is 21/32 plus 9/13?
Formula / Expression: 21/32 + 9/13
Final Answer: 1 145/416 (561/416)
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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 21/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.
Working: 21 × 13/32 × 13 = 273/416 and 9 × 32/13 × 32 = 288/416

Step 3: Add the Numerators
Now add the numerators (273 + 288 = 561) and keep the common denominator 416 unchanged.
Working: 273 + 288/416 = 561/416

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 561 and 416 is 1, confirming that 561/416 cannot be reduced further—it is already in its simplest irreducible form.
Working: 561/416

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (561) is greater than the denominator (416), divide 561 by 416: it goes in 1 whole time(s) with a remainder of 145, giving the mixed number 1 145/416.
Working: 561/416 = 1 145/416

Step 6: Decimal & Percentage Representation
Dividing the numerator 561 by denominator 416 produces a repeating decimal (approximately 1.348558, or 134.8558%).
Working: 561 ÷ 416 = 1.348558 (134.8558%)

Key Values:
- Simplified Fraction: 561/416
- Mixed Number Form: 1 145/416
- Decimal Value: 1.348558
- Percentage: 134.8558%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-21-32-plus-9-13/
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21/32 + 9/13 = 561/416

Simplified Fraction

561/416

Mixed Number

1 145/416

Decimal Value

1.348558

Percentage

134.8558%

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Step-by-Step Solution: 21/32 + 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 21/32 by 13, and multiply the numerator and denominator of 9/13 by 32 so both fractions share the common base 416.

21 × 13/32 × 13 = 273/416 and 9 × 32/13 × 32 = 288/416

Step 3

Add the Numerators

Now add the numerators (273 + 288 = 561) and keep the common denominator 416 unchanged.

273 + 288/416 = 561/416

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 561 and 416 is 1, confirming that 561/416 cannot be reduced further—it is already in its simplest irreducible form.

561/416

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (561) is greater than the denominator (416), divide 561 by 416: it goes in 1 whole time(s) with a remainder of 145, giving the mixed number 1 145/416.

561/416 = 1145/416

Step 6

Decimal & Percentage Representation

Dividing the numerator 561 by denominator 416 produces a repeating decimal (approximately 1.348558, or 134.8558%).

561 ÷ 416 = 1.348558 (134.8558%)

Visual Representation

The diagram below illustrates 21/32 plus 9/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`561/416`
Mixed Number Form	`1 145/416`
Decimal Form	`1.348558`
Percentage	`134.8558%`

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Frequently Asked Questions

What is 21/32 plus 9/13 as a fraction?

21/32 + 9/13 in simplest fraction form is 561/416 (or 1 145/416 as a mixed number).

What is 21/32 plus 9/13 as a decimal?

21/32 + 9/13 converted to a decimal is 1.348558.

What is 21/32 plus 9/13 as a percentage?

21/32 + 9/13 expressed as a percentage is 134.8558%.

How do you write 21/32 plus 9/13 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 561/416 can be written as the mixed number 1 145/416.

Does 21/32 plus 9/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.348558...) because the denominator contains prime factors other than 2 and 5.