What is 13/32 plus 12/21? (Answer: 219/224)

Exact Answer

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Problem: What is 13/32 plus 12/21?
Formula / Expression: 13/32 + 12/21
Final Answer: 219/224
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 32 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 21 = 672.
Working: LCD(32, 21) = 672

Step 2: Convert to Equivalent Fractions with Common Denominator 672
Multiply the numerator and denominator of 13/32 by 21, and multiply the numerator and denominator of 12/21 by 32 so both fractions share the common base 672.
Working: 13 × 21/32 × 21 = 273/672 and 12 × 32/21 × 32 = 384/672

Step 3: Add the Numerators
Now add the numerators (273 + 384 = 657) and keep the common denominator 672 unchanged.
Working: 273 + 384/672 = 657/672

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 657 and 672, which is 3. Divide both the numerator and denominator by 3.
Working: 657 ÷ 3/672 ÷ 3 = 219/224

Step 5: Decimal & Percentage Representation
Dividing the numerator 219 by denominator 224 produces a repeating decimal (approximately 0.977679, or 97.7679%).
Working: 219 ÷ 224 = 0.977679 (97.7679%)

Key Values:
- Simplified Fraction: 219/224
- Mixed Number Form: 219/224
- Decimal Value: 0.977679
- Percentage: 97.7679%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-13-32-plus-12-21/
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13/32 + 12/21 = 219/224

Simplified Fraction

219/224

Mixed Number

Proper (219/224)

Decimal Value

0.977679

Percentage

97.7679%

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Step-by-Step Solution: 13/32 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 32 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 32 × 21 = 672.

LCD(32, 21) = 672

Step 2

Convert to Equivalent Fractions with Common Denominator 672

Multiply the numerator and denominator of 13/32 by 21, and multiply the numerator and denominator of 12/21 by 32 so both fractions share the common base 672.

13 × 21/32 × 21 = 273/672 and 12 × 32/21 × 32 = 384/672

Step 3

Add the Numerators

Now add the numerators (273 + 384 = 657) and keep the common denominator 672 unchanged.

273 + 384/672 = 657/672

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 657 and 672, which is 3. Divide both the numerator and denominator by 3.

657 ÷ 3/672 ÷ 3 = 219/224

Step 5

Decimal & Percentage Representation

Dividing the numerator 219 by denominator 224 produces a repeating decimal (approximately 0.977679, or 97.7679%).

219 ÷ 224 = 0.977679 (97.7679%)

Visual Representation

The diagram below illustrates 13/32 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`219/224`
Mixed Number Form	`219/224`
Decimal Form	`0.977679`
Percentage	`97.7679%`

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Frequently Asked Questions

What is 13/32 plus 12/21 as a fraction?

13/32 + 12/21 in simplest fraction form is 219/224.

What is 13/32 plus 12/21 as a decimal?

13/32 + 12/21 converted to a decimal is 0.977679.

What is 13/32 plus 12/21 as a percentage?

13/32 + 12/21 expressed as a percentage is 97.7679%.

Does 13/32 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.977679...) because the denominator contains prime factors other than 2 and 5.