What is 3/48 plus 11/21? (Answer: 197/336)

Exact Answer

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Problem: What is 3/48 plus 11/21?
Formula / Expression: 3/48 + 11/21
Final Answer: 197/336
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 3/48 by 7, and multiply the numerator and denominator of 11/21 by 16 so both fractions share the common base 336.
Working: 3 × 7/48 × 7 = 21/336 and 11 × 16/21 × 16 = 176/336

Step 3: Add the Numerators
Now add the numerators (21 + 176 = 197) and keep the common denominator 336 unchanged.
Working: 21 + 176/336 = 197/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 197 and 336 is 1, confirming that 197/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 197/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 197 by denominator 336 produces a repeating decimal (approximately 0.58631, or 58.631%).
Working: 197 ÷ 336 = 0.58631 (58.631%)

Key Values:
- Simplified Fraction: 197/336
- Mixed Number Form: 197/336
- Decimal Value: 0.58631
- Percentage: 58.631%

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Solved with FractionsCalc:
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3/48 + 11/21 = 197/336

Simplified Fraction

197/336

Mixed Number

Proper (197/336)

Decimal Value

0.58631

Percentage

58.631%

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Step-by-Step Solution: 3/48 + 11/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(48, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 3/48 by 7, and multiply the numerator and denominator of 11/21 by 16 so both fractions share the common base 336.

3 × 7/48 × 7 = 21/336 and 11 × 16/21 × 16 = 176/336

Step 3

Add the Numerators

Now add the numerators (21 + 176 = 197) and keep the common denominator 336 unchanged.

21 + 176/336 = 197/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 197 and 336 is 1, confirming that 197/336 cannot be reduced further—it is already in its simplest irreducible form.

197/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 197 by denominator 336 produces a repeating decimal (approximately 0.58631, or 58.631%).

197 ÷ 336 = 0.58631 (58.631%)

Visual Representation

The diagram below illustrates 3/48 plus 11/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`197/336`
Mixed Number Form	`197/336`
Decimal Form	`0.58631`
Percentage	`58.631%`

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Frequently Asked Questions

What is 3/48 plus 11/21 as a fraction?

3/48 + 11/21 in simplest fraction form is 197/336.

What is 3/48 plus 11/21 as a decimal?

3/48 + 11/21 converted to a decimal is 0.58631.

What is 3/48 plus 11/21 as a percentage?

3/48 + 11/21 expressed as a percentage is 58.631%.

Does 3/48 plus 11/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.58631...) because the denominator contains prime factors other than 2 and 5.