What is 1/48 plus 3/21? (Answer: 55/336)

Exact Answer

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Problem: What is 1/48 plus 3/21?
Formula / Expression: 1/48 + 3/21
Final Answer: 55/336
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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 1/48 by 7, and multiply the numerator and denominator of 3/21 by 16 so both fractions share the common base 336.
Working: 1 × 7/48 × 7 = 7/336 and 3 × 16/21 × 16 = 48/336

Step 3: Add the Numerators
Now add the numerators (7 + 48 = 55) and keep the common denominator 336 unchanged.
Working: 7 + 48/336 = 55/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 55 and 336 is 1, confirming that 55/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 55/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 55 by denominator 336 produces a repeating decimal (approximately 0.16369, or 16.369%).
Working: 55 ÷ 336 = 0.16369 (16.369%)

Key Values:
- Simplified Fraction: 55/336
- Mixed Number Form: 55/336
- Decimal Value: 0.16369
- Percentage: 16.369%

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Solved with FractionsCalc:
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1/48 + 3/21 = 55/336

Simplified Fraction

55/336

Mixed Number

Proper (55/336)

Decimal Value

0.16369

Percentage

16.369%

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Step-by-Step Solution: 1/48 + 3/21

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 1/48 by 7, and multiply the numerator and denominator of 3/21 by 16 so both fractions share the common base 336.

1 × 7/48 × 7 = 7/336 and 3 × 16/21 × 16 = 48/336

Step 3

Add the Numerators

Now add the numerators (7 + 48 = 55) and keep the common denominator 336 unchanged.

7 + 48/336 = 55/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 55 and 336 is 1, confirming that 55/336 cannot be reduced further—it is already in its simplest irreducible form.

55/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 55 by denominator 336 produces a repeating decimal (approximately 0.16369, or 16.369%).

55 ÷ 336 = 0.16369 (16.369%)

Visual Representation

The diagram below illustrates 1/48 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`55/336`
Mixed Number Form	`55/336`
Decimal Form	`0.16369`
Percentage	`16.369%`

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Frequently Asked Questions

What is 1/48 plus 3/21 as a fraction?

1/48 + 3/21 in simplest fraction form is 55/336.

What is 1/48 plus 3/21 as a decimal?

1/48 + 3/21 converted to a decimal is 0.16369.

What is 1/48 plus 3/21 as a percentage?

1/48 + 3/21 expressed as a percentage is 16.369%.

Does 1/48 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.16369...) because the denominator contains prime factors other than 2 and 5.