What is 6/48 plus 12/21? (Answer: 39/56)

Exact Answer

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Problem: What is 6/48 plus 12/21?
Formula / Expression: 6/48 + 12/21
Final Answer: 39/56
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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 6/48 by 7, and multiply the numerator and denominator of 12/21 by 16 so both fractions share the common base 336.
Working: 6 × 7/48 × 7 = 42/336 and 12 × 16/21 × 16 = 192/336

Step 3: Add the Numerators
Now add the numerators (42 + 192 = 234) and keep the common denominator 336 unchanged.
Working: 42 + 192/336 = 234/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 234 and 336, which is 6. Divide both the numerator and denominator by 6.
Working: 234 ÷ 6/336 ÷ 6 = 39/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 39 by denominator 56 produces a repeating decimal (approximately 0.696429, or 69.6429%).
Working: 39 ÷ 56 = 0.696429 (69.6429%)

Key Values:
- Simplified Fraction: 39/56
- Mixed Number Form: 39/56
- Decimal Value: 0.696429
- Percentage: 69.6429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-48-plus-12-21/
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6/48 + 12/21 = 39/56

Simplified Fraction

39/56

Mixed Number

Proper (39/56)

Decimal Value

0.696429

Percentage

69.6429%

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Step-by-Step Solution: 6/48 + 12/21

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 6/48 by 7, and multiply the numerator and denominator of 12/21 by 16 so both fractions share the common base 336.

6 × 7/48 × 7 = 42/336 and 12 × 16/21 × 16 = 192/336

Step 3

Add the Numerators

Now add the numerators (42 + 192 = 234) and keep the common denominator 336 unchanged.

42 + 192/336 = 234/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 234 and 336, which is 6. Divide both the numerator and denominator by 6.

234 ÷ 6/336 ÷ 6 = 39/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 39 by denominator 56 produces a repeating decimal (approximately 0.696429, or 69.6429%).

39 ÷ 56 = 0.696429 (69.6429%)

Visual Representation

The diagram below illustrates 6/48 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`39/56`
Mixed Number Form	`39/56`
Decimal Form	`0.696429`
Percentage	`69.6429%`

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Frequently Asked Questions

What is 6/48 plus 12/21 as a fraction?

6/48 + 12/21 in simplest fraction form is 39/56.

What is 6/48 plus 12/21 as a decimal?

6/48 + 12/21 converted to a decimal is 0.696429.

What is 6/48 plus 12/21 as a percentage?

6/48 + 12/21 expressed as a percentage is 69.6429%.

Does 6/48 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.696429...) because the denominator contains prime factors other than 2 and 5.