What is 2/48 plus 3/21? (Answer: 31/168)

Exact Answer

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Problem: What is 2/48 plus 3/21?
Formula / Expression: 2/48 + 3/21
Final Answer: 31/168
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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 2/48 by 7, and multiply the numerator and denominator of 3/21 by 16 so both fractions share the common base 336.
Working: 2 × 7/48 × 7 = 14/336 and 3 × 16/21 × 16 = 48/336

Step 3: Add the Numerators
Now add the numerators (14 + 48 = 62) and keep the common denominator 336 unchanged.
Working: 14 + 48/336 = 62/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 62 and 336, which is 2. Divide both the numerator and denominator by 2.
Working: 62 ÷ 2/336 ÷ 2 = 31/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 168 produces a repeating decimal (approximately 0.184524, or 18.4524%).
Working: 31 ÷ 168 = 0.184524 (18.4524%)

Key Values:
- Simplified Fraction: 31/168
- Mixed Number Form: 31/168
- Decimal Value: 0.184524
- Percentage: 18.4524%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-48-plus-3-21/
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2/48 + 3/21 = 31/168

Simplified Fraction

31/168

Mixed Number

Proper (31/168)

Decimal Value

0.184524

Percentage

18.4524%

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Step-by-Step Solution: 2/48 + 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 2/48 by 7, and multiply the numerator and denominator of 3/21 by 16 so both fractions share the common base 336.

2 × 7/48 × 7 = 14/336 and 3 × 16/21 × 16 = 48/336

Step 3

Add the Numerators

Now add the numerators (14 + 48 = 62) and keep the common denominator 336 unchanged.

14 + 48/336 = 62/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 62 and 336, which is 2. Divide both the numerator and denominator by 2.

62 ÷ 2/336 ÷ 2 = 31/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 168 produces a repeating decimal (approximately 0.184524, or 18.4524%).

31 ÷ 168 = 0.184524 (18.4524%)

Visual Representation

The diagram below illustrates 2/48 plus 3/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/168`
Mixed Number Form	`31/168`
Decimal Form	`0.184524`
Percentage	`18.4524%`

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Frequently Asked Questions

What is 2/48 plus 3/21 as a fraction?

2/48 + 3/21 in simplest fraction form is 31/168.

What is 2/48 plus 3/21 as a decimal?

2/48 + 3/21 converted to a decimal is 0.184524.

What is 2/48 plus 3/21 as a percentage?

2/48 + 3/21 expressed as a percentage is 18.4524%.

Does 2/48 plus 3/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.184524...) because the denominator contains prime factors other than 2 and 5.