What is 3/21 plus 2/4? (Answer: 9/14)

Exact Answer

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Problem: What is 3/21 plus 2/4?
Formula / Expression: 3/21 + 2/4
Final Answer: 9/14
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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 3/21 by 4, and multiply the numerator and denominator of 2/4 by 21 so both fractions share the common base 84.
Working: 3 × 4/21 × 4 = 12/84 and 2 × 21/4 × 21 = 42/84

Step 3: Add the Numerators
Now add the numerators (12 + 42 = 54) and keep the common denominator 84 unchanged.
Working: 12 + 42/84 = 54/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 54 and 84, which is 6. Divide both the numerator and denominator by 6.
Working: 54 ÷ 6/84 ÷ 6 = 9/14

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 14 produces a repeating decimal (approximately 0.642857, or 64.2857%).
Working: 9 ÷ 14 = 0.642857 (64.2857%)

Key Values:
- Simplified Fraction: 9/14
- Mixed Number Form: 9/14
- Decimal Value: 0.642857
- Percentage: 64.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-21-plus-2-4/
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3/21 + 2/4 = 9/14

Simplified Fraction

9/14

Mixed Number

Proper (9/14)

Decimal Value

0.642857

Percentage

64.2857%

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Step-by-Step Solution: 3/21 + 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 3/21 by 4, and multiply the numerator and denominator of 2/4 by 21 so both fractions share the common base 84.

3 × 4/21 × 4 = 12/84 and 2 × 21/4 × 21 = 42/84

Step 3

Add the Numerators

Now add the numerators (12 + 42 = 54) and keep the common denominator 84 unchanged.

12 + 42/84 = 54/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 54 and 84, which is 6. Divide both the numerator and denominator by 6.

54 ÷ 6/84 ÷ 6 = 9/14

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 14 produces a repeating decimal (approximately 0.642857, or 64.2857%).

9 ÷ 14 = 0.642857 (64.2857%)

Visual Representation

The diagram below illustrates 3/21 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/14`
Mixed Number Form	`9/14`
Decimal Form	`0.642857`
Percentage	`64.2857%`

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Frequently Asked Questions

What is 3/21 plus 2/4 as a fraction?

3/21 + 2/4 in simplest fraction form is 9/14.

What is 3/21 plus 2/4 as a decimal?

3/21 + 2/4 converted to a decimal is 0.642857.

What is 3/21 plus 2/4 as a percentage?

3/21 + 2/4 expressed as a percentage is 64.2857%.

Does 3/21 plus 2/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.642857...) because the denominator contains prime factors other than 2 and 5.