What is 4/21 plus 2/4? (Answer: 29/42)

Exact Answer

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Problem: What is 4/21 plus 2/4?
Formula / Expression: 4/21 + 2/4
Final Answer: 29/42
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 4 = 84.
Working: LCD(21, 4) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 4/21 by 4, and multiply the numerator and denominator of 2/4 by 21 so both fractions share the common base 84.
Working: 4 × 4/21 × 4 = 16/84 and 2 × 21/4 × 21 = 42/84

Step 3: Add the Numerators
Now add the numerators (16 + 42 = 58) and keep the common denominator 84 unchanged.
Working: 16 + 42/84 = 58/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 58 and 84, which is 2. Divide both the numerator and denominator by 2.
Working: 58 ÷ 2/84 ÷ 2 = 29/42

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 42 produces a repeating decimal (approximately 0.690476, or 69.0476%).
Working: 29 ÷ 42 = 0.690476 (69.0476%)

Key Values:
- Simplified Fraction: 29/42
- Mixed Number Form: 29/42
- Decimal Value: 0.690476
- Percentage: 69.0476%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-2-4/
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4/21 + 2/4 = 29/42

Simplified Fraction

29/42

Mixed Number

Proper (29/42)

Decimal Value

0.690476

Percentage

69.0476%

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Step-by-Step Solution: 4/21 + 2/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 4 = 84.

LCD(21, 4) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 4/21 by 4, and multiply the numerator and denominator of 2/4 by 21 so both fractions share the common base 84.

4 × 4/21 × 4 = 16/84 and 2 × 21/4 × 21 = 42/84

Step 3

Add the Numerators

Now add the numerators (16 + 42 = 58) and keep the common denominator 84 unchanged.

16 + 42/84 = 58/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 58 and 84, which is 2. Divide both the numerator and denominator by 2.

58 ÷ 2/84 ÷ 2 = 29/42

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 42 produces a repeating decimal (approximately 0.690476, or 69.0476%).

29 ÷ 42 = 0.690476 (69.0476%)

Visual Representation

The diagram below illustrates 4/21 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/42`
Mixed Number Form	`29/42`
Decimal Form	`0.690476`
Percentage	`69.0476%`

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Frequently Asked Questions

What is 4/21 plus 2/4 as a fraction?

4/21 + 2/4 in simplest fraction form is 29/42.

What is 4/21 plus 2/4 as a decimal?

4/21 + 2/4 converted to a decimal is 0.690476.

What is 4/21 plus 2/4 as a percentage?

4/21 + 2/4 expressed as a percentage is 69.0476%.

Does 4/21 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.690476...) because the denominator contains prime factors other than 2 and 5.