What is 5/48 plus 8/21? (Answer: 163/336)

Exact Answer

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Problem: What is 5/48 plus 8/21?
Formula / Expression: 5/48 + 8/21
Final Answer: 163/336
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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 5/48 by 7, and multiply the numerator and denominator of 8/21 by 16 so both fractions share the common base 336.
Working: 5 × 7/48 × 7 = 35/336 and 8 × 16/21 × 16 = 128/336

Step 3: Add the Numerators
Now add the numerators (35 + 128 = 163) and keep the common denominator 336 unchanged.
Working: 35 + 128/336 = 163/336

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 163 and 336 is 1, confirming that 163/336 cannot be reduced further—it is already in its simplest irreducible form.
Working: 163/336

Step 5: Decimal & Percentage Representation
Dividing the numerator 163 by denominator 336 produces a repeating decimal (approximately 0.485119, or 48.5119%).
Working: 163 ÷ 336 = 0.485119 (48.5119%)

Key Values:
- Simplified Fraction: 163/336
- Mixed Number Form: 163/336
- Decimal Value: 0.485119
- Percentage: 48.5119%

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Solved with FractionsCalc:
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5/48 + 8/21 = 163/336

Simplified Fraction

163/336

Mixed Number

Proper (163/336)

Decimal Value

0.485119

Percentage

48.5119%

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Step-by-Step Solution: 5/48 + 8/21

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 5/48 by 7, and multiply the numerator and denominator of 8/21 by 16 so both fractions share the common base 336.

5 × 7/48 × 7 = 35/336 and 8 × 16/21 × 16 = 128/336

Step 3

Add the Numerators

Now add the numerators (35 + 128 = 163) and keep the common denominator 336 unchanged.

35 + 128/336 = 163/336

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 163 and 336 is 1, confirming that 163/336 cannot be reduced further—it is already in its simplest irreducible form.

163/336

Step 5

Decimal & Percentage Representation

Dividing the numerator 163 by denominator 336 produces a repeating decimal (approximately 0.485119, or 48.5119%).

163 ÷ 336 = 0.485119 (48.5119%)

Visual Representation

The diagram below illustrates 5/48 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`163/336`
Mixed Number Form	`163/336`
Decimal Form	`0.485119`
Percentage	`48.5119%`

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Frequently Asked Questions

What is 5/48 plus 8/21 as a fraction?

5/48 + 8/21 in simplest fraction form is 163/336.

What is 5/48 plus 8/21 as a decimal?

5/48 + 8/21 converted to a decimal is 0.485119.

What is 5/48 plus 8/21 as a percentage?

5/48 + 8/21 expressed as a percentage is 48.5119%.

Does 5/48 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.485119...) because the denominator contains prime factors other than 2 and 5.