What is 1/48 plus 4/21? (Answer: 71/336)

Exact Answer

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Problem: What is 1/48 plus 4/21?
Formula / Expression: 1/48 + 4/21
Final Answer: 71/336
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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 4/21 by 16 so both fractions share the common base 336.
Working: 1 × 7/48 × 7 = 7/336 and 4 × 16/21 × 16 = 64/336

Step 3: Add the Numerators
Now add the numerators (7 + 64 = 71) and keep the common denominator 336 unchanged.
Working: 7 + 64/336 = 71/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 336 is 1, confirming that 71/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 336 produces a repeating decimal (approximately 0.21131, or 21.131%).
Working: 71 ÷ 336 = 0.21131 (21.131%)

Key Values:
- Simplified Fraction: 71/336
- Mixed Number Form: 71/336
- Decimal Value: 0.21131
- Percentage: 21.131%

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Solved with FractionsCalc:
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1/48 + 4/21 = 71/336

Simplified Fraction

71/336

Mixed Number

Proper (71/336)

Decimal Value

0.21131

Percentage

21.131%

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Step-by-Step Solution: 1/48 + 4/21

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 4/21 by 16 so both fractions share the common base 336.

1 × 7/48 × 7 = 7/336 and 4 × 16/21 × 16 = 64/336

Step 3

Add the Numerators

Now add the numerators (7 + 64 = 71) and keep the common denominator 336 unchanged.

7 + 64/336 = 71/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 336 is 1, confirming that 71/336 cannot be reduced further—it is already in its simplest irreducible form.

71/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 336 produces a repeating decimal (approximately 0.21131, or 21.131%).

71 ÷ 336 = 0.21131 (21.131%)

Visual Representation

The diagram below illustrates 1/48 plus 4/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/336`
Mixed Number Form	`71/336`
Decimal Form	`0.21131`
Percentage	`21.131%`

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Frequently Asked Questions

What is 1/48 plus 4/21 as a fraction?

1/48 + 4/21 in simplest fraction form is 71/336.

What is 1/48 plus 4/21 as a decimal?

1/48 + 4/21 converted to a decimal is 0.21131.

What is 1/48 plus 4/21 as a percentage?

1/48 + 4/21 expressed as a percentage is 21.131%.

Does 1/48 plus 4/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.21131...) because the denominator contains prime factors other than 2 and 5.