What is 3/24 plus 12/21? (Answer: 39/56)

Exact Answer

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Problem: What is 3/24 plus 12/21?
Formula / Expression: 3/24 + 12/21
Final Answer: 39/56
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).
Working: LCD(24, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 3/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.
Working: 3 × 7/24 × 7 = 21/168 and 12 × 8/21 × 8 = 96/168

Step 3: Add the Numerators
Now add the numerators (21 + 96 = 117) and keep the common denominator 168 unchanged.
Working: 21 + 96/168 = 117/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 117 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 117 ÷ 3/168 ÷ 3 = 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-3-24-plus-12-21/
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3/24 + 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: 3/24 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 24 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 24 × 21 = 504, keeping the calculation simpler).

LCD(24, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 3/24 by 7, and multiply the numerator and denominator of 12/21 by 8 so both fractions share the common base 168.

3 × 7/24 × 7 = 21/168 and 12 × 8/21 × 8 = 96/168

Step 3

Add the Numerators

Now add the numerators (21 + 96 = 117) and keep the common denominator 168 unchanged.

21 + 96/168 = 117/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 117 and 168, which is 3. Divide both the numerator and denominator by 3.

117 ÷ 3/168 ÷ 3 = 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 3/24 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 3/24 plus 12/21 as a fraction?

3/24 + 12/21 in simplest fraction form is 39/56.

What is 3/24 plus 12/21 as a decimal?

3/24 + 12/21 converted to a decimal is 0.696429.

What is 3/24 plus 12/21 as a percentage?

3/24 + 12/21 expressed as a percentage is 69.6429%.

Does 3/24 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.