What is 11/48 plus 5/21? (Answer: 157/336)

Exact Answer

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Problem: What is 11/48 plus 5/21?
Formula / Expression: 11/48 + 5/21
Final Answer: 157/336
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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 11/48 by 7, and multiply the numerator and denominator of 5/21 by 16 so both fractions share the common base 336.
Working: 11 × 7/48 × 7 = 77/336 and 5 × 16/21 × 16 = 80/336

Step 3: Add the Numerators
Now add the numerators (77 + 80 = 157) and keep the common denominator 336 unchanged.
Working: 77 + 80/336 = 157/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 157 and 336 is 1, confirming that 157/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 157/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 157 by denominator 336 produces a repeating decimal (approximately 0.467262, or 46.7262%).
Working: 157 ÷ 336 = 0.467262 (46.7262%)

Key Values:
- Simplified Fraction: 157/336
- Mixed Number Form: 157/336
- Decimal Value: 0.467262
- Percentage: 46.7262%

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Solved with FractionsCalc:
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11/48 + 5/21 = 157/336

Simplified Fraction

157/336

Mixed Number

Proper (157/336)

Decimal Value

0.467262

Percentage

46.7262%

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Step-by-Step Solution: 11/48 + 5/21

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 11/48 by 7, and multiply the numerator and denominator of 5/21 by 16 so both fractions share the common base 336.

11 × 7/48 × 7 = 77/336 and 5 × 16/21 × 16 = 80/336

Step 3

Add the Numerators

Now add the numerators (77 + 80 = 157) and keep the common denominator 336 unchanged.

77 + 80/336 = 157/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 157 and 336 is 1, confirming that 157/336 cannot be reduced further—it is already in its simplest irreducible form.

157/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 157 by denominator 336 produces a repeating decimal (approximately 0.467262, or 46.7262%).

157 ÷ 336 = 0.467262 (46.7262%)

Visual Representation

The diagram below illustrates 11/48 plus 5/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`157/336`
Mixed Number Form	`157/336`
Decimal Form	`0.467262`
Percentage	`46.7262%`

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Frequently Asked Questions

What is 11/48 plus 5/21 as a fraction?

11/48 + 5/21 in simplest fraction form is 157/336.

What is 11/48 plus 5/21 as a decimal?

11/48 + 5/21 converted to a decimal is 0.467262.

What is 11/48 plus 5/21 as a percentage?

11/48 + 5/21 expressed as a percentage is 46.7262%.

Does 11/48 plus 5/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.467262...) because the denominator contains prime factors other than 2 and 5.