What is 5/21 plus 3/12? (Answer: 41/84)

Exact Answer

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Problem: What is 5/21 plus 3/12?
Formula / Expression: 5/21 + 3/12
Final Answer: 41/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 12 = 252, keeping the calculation simpler).
Working: LCD(21, 12) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 5/21 by 4, and multiply the numerator and denominator of 3/12 by 7 so both fractions share the common base 84.
Working: 5 × 4/21 × 4 = 20/84 and 3 × 7/12 × 7 = 21/84

Step 3: Add the Numerators
Now add the numerators (20 + 21 = 41) and keep the common denominator 84 unchanged.
Working: 20 + 21/84 = 41/84

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 41 and 84 is 1, confirming that 41/84 cannot be reduced further—it is already in its simplest irreducible form.
Working: 41/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 84 produces a repeating decimal (approximately 0.488095, or 48.8095%).
Working: 41 ÷ 84 = 0.488095 (48.8095%)

Key Values:
- Simplified Fraction: 41/84
- Mixed Number Form: 41/84
- Decimal Value: 0.488095
- Percentage: 48.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-21-plus-3-12/
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5/21 + 3/12 = 41/84

Simplified Fraction

41/84

Mixed Number

Proper (41/84)

Decimal Value

0.488095

Percentage

48.8095%

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Step-by-Step Solution: 5/21 + 3/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 12 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 21 × 12 = 252, keeping the calculation simpler).

LCD(21, 12) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 5/21 by 4, and multiply the numerator and denominator of 3/12 by 7 so both fractions share the common base 84.

5 × 4/21 × 4 = 20/84 and 3 × 7/12 × 7 = 21/84

Step 3

Add the Numerators

Now add the numerators (20 + 21 = 41) and keep the common denominator 84 unchanged.

20 + 21/84 = 41/84

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 41 and 84 is 1, confirming that 41/84 cannot be reduced further—it is already in its simplest irreducible form.

41/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 84 produces a repeating decimal (approximately 0.488095, or 48.8095%).

41 ÷ 84 = 0.488095 (48.8095%)

Visual Representation

The diagram below illustrates 5/21 plus 3/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/84`
Mixed Number Form	`41/84`
Decimal Form	`0.488095`
Percentage	`48.8095%`

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Frequently Asked Questions

What is 5/21 plus 3/12 as a fraction?

5/21 + 3/12 in simplest fraction form is 41/84.

What is 5/21 plus 3/12 as a decimal?

5/21 + 3/12 converted to a decimal is 0.488095.

What is 5/21 plus 3/12 as a percentage?

5/21 + 3/12 expressed as a percentage is 48.8095%.

Does 5/21 plus 3/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.488095...) because the denominator contains prime factors other than 2 and 5.