What is 15/32 plus 12/21? (Answer: 233/224)

Exact Answer

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Problem: What is 15/32 plus 12/21?
Formula / Expression: 15/32 + 12/21
Final Answer: 1 9/224 (233/224)
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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 15/32 by 21, and multiply the numerator and denominator of 12/21 by 32 so both fractions share the common base 672.
Working: 15 × 21/32 × 21 = 315/672 and 12 × 32/21 × 32 = 384/672

Step 3: Add the Numerators
Now add the numerators (315 + 384 = 699) and keep the common denominator 672 unchanged.
Working: 315 + 384/672 = 699/672

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 699 and 672, which is 3. Divide both the numerator and denominator by 3.
Working: 699 ÷ 3/672 ÷ 3 = 233/224

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (233) is greater than the denominator (224), divide 233 by 224: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/224.
Working: 233/224 = 1 9/224

Step 6: Decimal & Percentage Representation
Dividing the numerator 233 by denominator 224 produces a repeating decimal (approximately 1.040179, or 104.0179%).
Working: 233 ÷ 224 = 1.040179 (104.0179%)

Key Values:
- Simplified Fraction: 233/224
- Mixed Number Form: 1 9/224
- Decimal Value: 1.040179
- Percentage: 104.0179%

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Solved with FractionsCalc:
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15/32 + 12/21 = 233/224

Simplified Fraction

233/224

Mixed Number

1 9/224

Decimal Value

1.040179

Percentage

104.0179%

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Step-by-Step Solution: 15/32 + 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 15/32 by 21, and multiply the numerator and denominator of 12/21 by 32 so both fractions share the common base 672.

15 × 21/32 × 21 = 315/672 and 12 × 32/21 × 32 = 384/672

Step 3

Add the Numerators

Now add the numerators (315 + 384 = 699) and keep the common denominator 672 unchanged.

315 + 384/672 = 699/672

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 699 and 672, which is 3. Divide both the numerator and denominator by 3.

699 ÷ 3/672 ÷ 3 = 233/224

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (233) is greater than the denominator (224), divide 233 by 224: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/224.

233/224 = 19/224

Step 6

Decimal & Percentage Representation

Dividing the numerator 233 by denominator 224 produces a repeating decimal (approximately 1.040179, or 104.0179%).

233 ÷ 224 = 1.040179 (104.0179%)

Visual Representation

The diagram below illustrates 15/32 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`233/224`
Mixed Number Form	`1 9/224`
Decimal Form	`1.040179`
Percentage	`104.0179%`

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Frequently Asked Questions

What is 15/32 plus 12/21 as a fraction?

15/32 + 12/21 in simplest fraction form is 233/224 (or 1 9/224 as a mixed number).

What is 15/32 plus 12/21 as a decimal?

15/32 + 12/21 converted to a decimal is 1.040179.

What is 15/32 plus 12/21 as a percentage?

15/32 + 12/21 expressed as a percentage is 104.0179%.

How do you write 15/32 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 233/224 can be written as the mixed number 1 9/224.

Does 15/32 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.040179...) because the denominator contains prime factors other than 2 and 5.