What is 5/21 plus 12/48? (Answer: 41/84)

Exact Answer

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Problem: What is 5/21 plus 12/48?
Formula / Expression: 5/21 + 12/48
Final Answer: 41/84
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 48 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 21 × 48 = 1008, keeping the calculation simpler).
Working: LCD(21, 48) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 5/21 by 16, and multiply the numerator and denominator of 12/48 by 7 so both fractions share the common base 336.
Working: 5 × 16/21 × 16 = 80/336 and 12 × 7/48 × 7 = 84/336

Step 3: Add the Numerators
Now add the numerators (80 + 84 = 164) and keep the common denominator 336 unchanged.
Working: 80 + 84/336 = 164/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 164 and 336, which is 4. Divide both the numerator and denominator by 4.
Working: 164 ÷ 4/336 ÷ 4 = 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-12-48/
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5/21 + 12/48 = 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 + 12/48

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 48 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 21 × 48 = 1008, keeping the calculation simpler).

LCD(21, 48) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 5/21 by 16, and multiply the numerator and denominator of 12/48 by 7 so both fractions share the common base 336.

5 × 16/21 × 16 = 80/336 and 12 × 7/48 × 7 = 84/336

Step 3

Add the Numerators

Now add the numerators (80 + 84 = 164) and keep the common denominator 336 unchanged.

80 + 84/336 = 164/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 164 and 336, which is 4. Divide both the numerator and denominator by 4.

164 ÷ 4/336 ÷ 4 = 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 12/48 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 12/48 as a fraction?

5/21 + 12/48 in simplest fraction form is 41/84.

What is 5/21 plus 12/48 as a decimal?

5/21 + 12/48 converted to a decimal is 0.488095.

What is 5/21 plus 12/48 as a percentage?

5/21 + 12/48 expressed as a percentage is 48.8095%.

Does 5/21 plus 12/48 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.