What is 4/21 plus 12/62? (Answer: 250/651)

Exact Answer

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Problem: What is 4/21 plus 12/62?
Formula / Expression: 4/21 + 12/62
Final Answer: 250/651
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 62 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 62 = 1302.
Working: LCD(21, 62) = 1302

Step 2: Convert to Equivalent Fractions with Common Denominator 1302
Multiply the numerator and denominator of 4/21 by 62, and multiply the numerator and denominator of 12/62 by 21 so both fractions share the common base 1302.
Working: 4 × 62/21 × 62 = 248/1302 and 12 × 21/62 × 21 = 252/1302

Step 3: Add the Numerators
Now add the numerators (248 + 252 = 500) and keep the common denominator 1302 unchanged.
Working: 248 + 252/1302 = 500/1302

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 500 and 1302, which is 2. Divide both the numerator and denominator by 2.
Working: 500 ÷ 2/1302 ÷ 2 = 250/651

Step 5: Decimal & Percentage Representation
Dividing the numerator 250 by denominator 651 produces a repeating decimal (approximately 0.384025, or 38.4025%).
Working: 250 ÷ 651 = 0.384025 (38.4025%)

Key Values:
- Simplified Fraction: 250/651
- Mixed Number Form: 250/651
- Decimal Value: 0.384025
- Percentage: 38.4025%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-12-62/
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4/21 + 12/62 = 250/651

Simplified Fraction

250/651

Mixed Number

Proper (250/651)

Decimal Value

0.384025

Percentage

38.4025%

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Step-by-Step Solution: 4/21 + 12/62

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 62 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 62 = 1302.

LCD(21, 62) = 1302

Step 2

Convert to Equivalent Fractions with Common Denominator 1302

Multiply the numerator and denominator of 4/21 by 62, and multiply the numerator and denominator of 12/62 by 21 so both fractions share the common base 1302.

4 × 62/21 × 62 = 248/1302 and 12 × 21/62 × 21 = 252/1302

Step 3

Add the Numerators

Now add the numerators (248 + 252 = 500) and keep the common denominator 1302 unchanged.

248 + 252/1302 = 500/1302

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 500 and 1302, which is 2. Divide both the numerator and denominator by 2.

500 ÷ 2/1302 ÷ 2 = 250/651

Step 5

Decimal & Percentage Representation

Dividing the numerator 250 by denominator 651 produces a repeating decimal (approximately 0.384025, or 38.4025%).

250 ÷ 651 = 0.384025 (38.4025%)

Visual Representation

The diagram below illustrates 4/21 plus 12/62 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`250/651`
Mixed Number Form	`250/651`
Decimal Form	`0.384025`
Percentage	`38.4025%`

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Frequently Asked Questions

What is 4/21 plus 12/62 as a fraction?

4/21 + 12/62 in simplest fraction form is 250/651.

What is 4/21 plus 12/62 as a decimal?

4/21 + 12/62 converted to a decimal is 0.384025.

What is 4/21 plus 12/62 as a percentage?

4/21 + 12/62 expressed as a percentage is 38.4025%.

Does 4/21 plus 12/62 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.384025...) because the denominator contains prime factors other than 2 and 5.