What is 16/30 plus 12/21? (Answer: 116/105)

Exact Answer

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Problem: What is 16/30 plus 12/21?
Formula / Expression: 16/30 + 12/21
Final Answer: 1 11/105 (116/105)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).
Working: LCD(30, 21) = 210

Step 2: Convert to Equivalent Fractions with Common Denominator 210
Multiply the numerator and denominator of 16/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.
Working: 16 × 7/30 × 7 = 112/210 and 12 × 10/21 × 10 = 120/210

Step 3: Add the Numerators
Now add the numerators (112 + 120 = 232) and keep the common denominator 210 unchanged.
Working: 112 + 120/210 = 232/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 232 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 232 ÷ 2/210 ÷ 2 = 116/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (116) is greater than the denominator (105), divide 116 by 105: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/105.
Working: 116/105 = 1 11/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 116 by denominator 105 produces a repeating decimal (approximately 1.104762, or 110.4762%).
Working: 116 ÷ 105 = 1.104762 (110.4762%)

Key Values:
- Simplified Fraction: 116/105
- Mixed Number Form: 1 11/105
- Decimal Value: 1.104762
- Percentage: 110.4762%

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Solved with FractionsCalc:
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16/30 + 12/21 = 116/105

Simplified Fraction

116/105

Mixed Number

1 11/105

Decimal Value

1.104762

Percentage

110.4762%

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Step-by-Step Solution: 16/30 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 30 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 210 (which is smaller than their product 30 × 21 = 630, keeping the calculation simpler).

LCD(30, 21) = 210

Step 2

Convert to Equivalent Fractions with Common Denominator 210

Multiply the numerator and denominator of 16/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.

16 × 7/30 × 7 = 112/210 and 12 × 10/21 × 10 = 120/210

Step 3

Add the Numerators

Now add the numerators (112 + 120 = 232) and keep the common denominator 210 unchanged.

112 + 120/210 = 232/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 232 and 210, which is 2. Divide both the numerator and denominator by 2.

232 ÷ 2/210 ÷ 2 = 116/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (116) is greater than the denominator (105), divide 116 by 105: it goes in 1 whole time(s) with a remainder of 11, giving the mixed number 1 11/105.

116/105 = 111/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 116 by denominator 105 produces a repeating decimal (approximately 1.104762, or 110.4762%).

116 ÷ 105 = 1.104762 (110.4762%)

Visual Representation

The diagram below illustrates 16/30 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`116/105`
Mixed Number Form	`1 11/105`
Decimal Form	`1.104762`
Percentage	`110.4762%`

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Frequently Asked Questions

What is 16/30 plus 12/21 as a fraction?

16/30 + 12/21 in simplest fraction form is 116/105 (or 1 11/105 as a mixed number).

What is 16/30 plus 12/21 as a decimal?

16/30 + 12/21 converted to a decimal is 1.104762.

What is 16/30 plus 12/21 as a percentage?

16/30 + 12/21 expressed as a percentage is 110.4762%.

How do you write 16/30 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 116/105 can be written as the mixed number 1 11/105.

Does 16/30 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.104762...) because the denominator contains prime factors other than 2 and 5.