What is 14/30 plus 12/21? (Answer: 109/105)

Exact Answer

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Problem: What is 14/30 plus 12/21?
Formula / Expression: 14/30 + 12/21
Final Answer: 1 4/105 (109/105)
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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 14/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.
Working: 14 × 7/30 × 7 = 98/210 and 12 × 10/21 × 10 = 120/210

Step 3: Add the Numerators
Now add the numerators (98 + 120 = 218) and keep the common denominator 210 unchanged.
Working: 98 + 120/210 = 218/210

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 218 and 210, which is 2. Divide both the numerator and denominator by 2.
Working: 218 ÷ 2/210 ÷ 2 = 109/105

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (109) is greater than the denominator (105), divide 109 by 105: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/105.
Working: 109/105 = 1 4/105

Step 6: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 105 produces a repeating decimal (approximately 1.038095, or 103.8095%).
Working: 109 ÷ 105 = 1.038095 (103.8095%)

Key Values:
- Simplified Fraction: 109/105
- Mixed Number Form: 1 4/105
- Decimal Value: 1.038095
- Percentage: 103.8095%

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14/30 + 12/21 = 109/105

Simplified Fraction

109/105

Mixed Number

1 4/105

Decimal Value

1.038095

Percentage

103.8095%

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Step-by-Step Solution: 14/30 + 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 14/30 by 7, and multiply the numerator and denominator of 12/21 by 10 so both fractions share the common base 210.

14 × 7/30 × 7 = 98/210 and 12 × 10/21 × 10 = 120/210

Step 3

Add the Numerators

Now add the numerators (98 + 120 = 218) and keep the common denominator 210 unchanged.

98 + 120/210 = 218/210

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 218 and 210, which is 2. Divide both the numerator and denominator by 2.

218 ÷ 2/210 ÷ 2 = 109/105

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (109) is greater than the denominator (105), divide 109 by 105: it goes in 1 whole time(s) with a remainder of 4, giving the mixed number 1 4/105.

109/105 = 14/105

Step 6

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 105 produces a repeating decimal (approximately 1.038095, or 103.8095%).

109 ÷ 105 = 1.038095 (103.8095%)

Visual Representation

The diagram below illustrates 14/30 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/105`
Mixed Number Form	`1 4/105`
Decimal Form	`1.038095`
Percentage	`103.8095%`

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Frequently Asked Questions

What is 14/30 plus 12/21 as a fraction?

14/30 + 12/21 in simplest fraction form is 109/105 (or 1 4/105 as a mixed number).

What is 14/30 plus 12/21 as a decimal?

14/30 + 12/21 converted to a decimal is 1.038095.

What is 14/30 plus 12/21 as a percentage?

14/30 + 12/21 expressed as a percentage is 103.8095%.

How do you write 14/30 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 109/105 can be written as the mixed number 1 4/105.

Does 14/30 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.038095...) because the denominator contains prime factors other than 2 and 5.