What is 12/48 plus 9/21? (Answer: 19/28)

Exact Answer

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Problem: What is 12/48 plus 9/21?
Formula / Expression: 12/48 + 9/21
Final Answer: 19/28
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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 12/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.
Working: 12 × 7/48 × 7 = 84/336 and 9 × 16/21 × 16 = 144/336

Step 3: Add the Numerators
Now add the numerators (84 + 144 = 228) and keep the common denominator 336 unchanged.
Working: 84 + 144/336 = 228/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 228 and 336, which is 12. Divide both the numerator and denominator by 12.
Working: 228 ÷ 12/336 ÷ 12 = 19/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 28 produces a repeating decimal (approximately 0.678571, or 67.8571%).
Working: 19 ÷ 28 = 0.678571 (67.8571%)

Key Values:
- Simplified Fraction: 19/28
- Mixed Number Form: 19/28
- Decimal Value: 0.678571
- Percentage: 67.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-48-plus-9-21/
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12/48 + 9/21 = 19/28

Simplified Fraction

19/28

Mixed Number

Proper (19/28)

Decimal Value

0.678571

Percentage

67.8571%

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Step-by-Step Solution: 12/48 + 9/21

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 12/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.

12 × 7/48 × 7 = 84/336 and 9 × 16/21 × 16 = 144/336

Step 3

Add the Numerators

Now add the numerators (84 + 144 = 228) and keep the common denominator 336 unchanged.

84 + 144/336 = 228/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 228 and 336, which is 12. Divide both the numerator and denominator by 12.

228 ÷ 12/336 ÷ 12 = 19/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 28 produces a repeating decimal (approximately 0.678571, or 67.8571%).

19 ÷ 28 = 0.678571 (67.8571%)

Visual Representation

The diagram below illustrates 12/48 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/28`
Mixed Number Form	`19/28`
Decimal Form	`0.678571`
Percentage	`67.8571%`

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Frequently Asked Questions

What is 12/48 plus 9/21 as a fraction?

12/48 + 9/21 in simplest fraction form is 19/28.

What is 12/48 plus 9/21 as a decimal?

12/48 + 9/21 converted to a decimal is 0.678571.

What is 12/48 plus 9/21 as a percentage?

12/48 + 9/21 expressed as a percentage is 67.8571%.

Does 12/48 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.678571...) because the denominator contains prime factors other than 2 and 5.