What is 3/48 plus 3/21? (Answer: 23/112)

Exact Answer

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Problem: What is 3/48 plus 3/21?
Formula / Expression: 3/48 + 3/21
Final Answer: 23/112
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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 3/48 by 7, and multiply the numerator and denominator of 3/21 by 16 so both fractions share the common base 336.
Working: 3 × 7/48 × 7 = 21/336 and 3 × 16/21 × 16 = 48/336

Step 3: Add the Numerators
Now add the numerators (21 + 48 = 69) and keep the common denominator 336 unchanged.
Working: 21 + 48/336 = 69/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 69 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 69 ÷ 3/336 ÷ 3 = 23/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 112 produces a repeating decimal (approximately 0.205357, or 20.5357%).
Working: 23 ÷ 112 = 0.205357 (20.5357%)

Key Values:
- Simplified Fraction: 23/112
- Mixed Number Form: 23/112
- Decimal Value: 0.205357
- Percentage: 20.5357%

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Solved with FractionsCalc:
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3/48 + 3/21 = 23/112

Simplified Fraction

23/112

Mixed Number

Proper (23/112)

Decimal Value

0.205357

Percentage

20.5357%

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

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

Step 3

Add the Numerators

Now add the numerators (21 + 48 = 69) and keep the common denominator 336 unchanged.

21 + 48/336 = 69/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 69 and 336, which is 3. Divide both the numerator and denominator by 3.

69 ÷ 3/336 ÷ 3 = 23/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 112 produces a repeating decimal (approximately 0.205357, or 20.5357%).

23 ÷ 112 = 0.205357 (20.5357%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/112`
Mixed Number Form	`23/112`
Decimal Form	`0.205357`
Percentage	`20.5357%`

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Frequently Asked Questions

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

3/48 + 3/21 in simplest fraction form is 23/112.

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

3/48 + 3/21 converted to a decimal is 0.205357.

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

3/48 + 3/21 expressed as a percentage is 20.5357%.

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

It results in a repeating decimal (approximately 0.205357...) because the denominator contains prime factors other than 2 and 5.