What is 14/25 plus 12/21? (Answer: 198/175)

Exact Answer

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Problem: What is 14/25 plus 12/21?
Formula / Expression: 14/25 + 12/21
Final Answer: 1 23/175 (198/175)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.
Working: LCD(25, 21) = 525

Step 2: Convert to Equivalent Fractions with Common Denominator 525
Multiply the numerator and denominator of 14/25 by 21, and multiply the numerator and denominator of 12/21 by 25 so both fractions share the common base 525.
Working: 14 × 21/25 × 21 = 294/525 and 12 × 25/21 × 25 = 300/525

Step 3: Add the Numerators
Now add the numerators (294 + 300 = 594) and keep the common denominator 525 unchanged.
Working: 294 + 300/525 = 594/525

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 594 and 525, which is 3. Divide both the numerator and denominator by 3.
Working: 594 ÷ 3/525 ÷ 3 = 198/175

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (198) is greater than the denominator (175), divide 198 by 175: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/175.
Working: 198/175 = 1 23/175

Step 6: Decimal & Percentage Representation
Dividing the numerator 198 by denominator 175 produces a repeating decimal (approximately 1.131429, or 113.1429%).
Working: 198 ÷ 175 = 1.131429 (113.1429%)

Key Values:
- Simplified Fraction: 198/175
- Mixed Number Form: 1 23/175
- Decimal Value: 1.131429
- Percentage: 113.1429%

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14/25 + 12/21 = 198/175

Simplified Fraction

198/175

Mixed Number

1 23/175

Decimal Value

1.131429

Percentage

113.1429%

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Step-by-Step Solution: 14/25 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 25 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 25 × 21 = 525.

LCD(25, 21) = 525

Step 2

Convert to Equivalent Fractions with Common Denominator 525

Multiply the numerator and denominator of 14/25 by 21, and multiply the numerator and denominator of 12/21 by 25 so both fractions share the common base 525.

14 × 21/25 × 21 = 294/525 and 12 × 25/21 × 25 = 300/525

Step 3

Add the Numerators

Now add the numerators (294 + 300 = 594) and keep the common denominator 525 unchanged.

294 + 300/525 = 594/525

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 594 and 525, which is 3. Divide both the numerator and denominator by 3.

594 ÷ 3/525 ÷ 3 = 198/175

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (198) is greater than the denominator (175), divide 198 by 175: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/175.

198/175 = 123/175

Step 6

Decimal & Percentage Representation

Dividing the numerator 198 by denominator 175 produces a repeating decimal (approximately 1.131429, or 113.1429%).

198 ÷ 175 = 1.131429 (113.1429%)

Visual Representation

The diagram below illustrates 14/25 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`198/175`
Mixed Number Form	`1 23/175`
Decimal Form	`1.131429`
Percentage	`113.1429%`

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Frequently Asked Questions

What is 14/25 plus 12/21 as a fraction?

14/25 + 12/21 in simplest fraction form is 198/175 (or 1 23/175 as a mixed number).

What is 14/25 plus 12/21 as a decimal?

14/25 + 12/21 converted to a decimal is 1.131429.

What is 14/25 plus 12/21 as a percentage?

14/25 + 12/21 expressed as a percentage is 113.1429%.

How do you write 14/25 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 198/175 can be written as the mixed number 1 23/175.

Does 14/25 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.131429...) because the denominator contains prime factors other than 2 and 5.