What is 16/32 plus 12/21? (Answer: 15/14)

Exact Answer

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Problem: What is 16/32 plus 12/21?
Formula / Expression: 16/32 + 12/21
Final Answer: 1 1/14 (15/14)
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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 16/32 by 21, and multiply the numerator and denominator of 12/21 by 32 so both fractions share the common base 672.
Working: 16 × 21/32 × 21 = 336/672 and 12 × 32/21 × 32 = 384/672

Step 3: Add the Numerators
Now add the numerators (336 + 384 = 720) and keep the common denominator 672 unchanged.
Working: 336 + 384/672 = 720/672

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 720 and 672, which is 48. Divide both the numerator and denominator by 48.
Working: 720 ÷ 48/672 ÷ 48 = 15/14

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.
Working: 15/14 = 1 1/14

Step 6: Decimal & Percentage Representation
Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).
Working: 15 ÷ 14 = 1.071429 (107.1429%)

Key Values:
- Simplified Fraction: 15/14
- Mixed Number Form: 1 1/14
- Decimal Value: 1.071429
- Percentage: 107.1429%

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Solved with FractionsCalc:
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16/32 + 12/21 = 15/14

Simplified Fraction

15/14

Mixed Number

1 1/14

Decimal Value

1.071429

Percentage

107.1429%

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Step-by-Step Solution: 16/32 + 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 16/32 by 21, and multiply the numerator and denominator of 12/21 by 32 so both fractions share the common base 672.

16 × 21/32 × 21 = 336/672 and 12 × 32/21 × 32 = 384/672

Step 3

Add the Numerators

Now add the numerators (336 + 384 = 720) and keep the common denominator 672 unchanged.

336 + 384/672 = 720/672

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 720 and 672, which is 48. Divide both the numerator and denominator by 48.

720 ÷ 48/672 ÷ 48 = 15/14

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (15) is greater than the denominator (14), divide 15 by 14: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/14.

15/14 = 11/14

Step 6

Decimal & Percentage Representation

Dividing the numerator 15 by denominator 14 produces a repeating decimal (approximately 1.071429, or 107.1429%).

15 ÷ 14 = 1.071429 (107.1429%)

Visual Representation

The diagram below illustrates 16/32 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`15/14`
Mixed Number Form	`1 1/14`
Decimal Form	`1.071429`
Percentage	`107.1429%`

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Frequently Asked Questions

What is 16/32 plus 12/21 as a fraction?

16/32 + 12/21 in simplest fraction form is 15/14 (or 1 1/14 as a mixed number).

What is 16/32 plus 12/21 as a decimal?

16/32 + 12/21 converted to a decimal is 1.071429.

What is 16/32 plus 12/21 as a percentage?

16/32 + 12/21 expressed as a percentage is 107.1429%.

How do you write 16/32 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 15/14 can be written as the mixed number 1 1/14.

Does 16/32 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.071429...) because the denominator contains prime factors other than 2 and 5.