What is 2/21 plus 5/48? (Answer: 67/336)

Exact Answer

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Problem: What is 2/21 plus 5/48?
Formula / Expression: 2/21 + 5/48
Final Answer: 67/336
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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 2/21 by 16, and multiply the numerator and denominator of 5/48 by 7 so both fractions share the common base 336.
Working: 2 × 16/21 × 16 = 32/336 and 5 × 7/48 × 7 = 35/336

Step 3: Add the Numerators
Now add the numerators (32 + 35 = 67) and keep the common denominator 336 unchanged.
Working: 32 + 35/336 = 67/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 67 and 336 is 1, confirming that 67/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 67/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 336 produces a repeating decimal (approximately 0.199405, or 19.9405%).
Working: 67 ÷ 336 = 0.199405 (19.9405%)

Key Values:
- Simplified Fraction: 67/336
- Mixed Number Form: 67/336
- Decimal Value: 0.199405
- Percentage: 19.9405%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-21-plus-5-48/
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2/21 + 5/48 = 67/336

Simplified Fraction

67/336

Mixed Number

Proper (67/336)

Decimal Value

0.199405

Percentage

19.9405%

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Step-by-Step Solution: 2/21 + 5/48

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 2/21 by 16, and multiply the numerator and denominator of 5/48 by 7 so both fractions share the common base 336.

2 × 16/21 × 16 = 32/336 and 5 × 7/48 × 7 = 35/336

Step 3

Add the Numerators

Now add the numerators (32 + 35 = 67) and keep the common denominator 336 unchanged.

32 + 35/336 = 67/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 67 and 336 is 1, confirming that 67/336 cannot be reduced further—it is already in its simplest irreducible form.

67/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 336 produces a repeating decimal (approximately 0.199405, or 19.9405%).

67 ÷ 336 = 0.199405 (19.9405%)

Visual Representation

The diagram below illustrates 2/21 plus 5/48 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/336`
Mixed Number Form	`67/336`
Decimal Form	`0.199405`
Percentage	`19.9405%`

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Frequently Asked Questions

What is 2/21 plus 5/48 as a fraction?

2/21 + 5/48 in simplest fraction form is 67/336.

What is 2/21 plus 5/48 as a decimal?

2/21 + 5/48 converted to a decimal is 0.199405.

What is 2/21 plus 5/48 as a percentage?

2/21 + 5/48 expressed as a percentage is 19.9405%.

Does 2/21 plus 5/48 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.199405...) because the denominator contains prime factors other than 2 and 5.