What is 3/12 plus 7/21? (Answer: 7/12)

Exact Answer

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Problem: What is 3/12 plus 7/21?
Formula / Expression: 3/12 + 7/21
Final Answer: 7/12
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).
Working: LCD(12, 21) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 3/12 by 7, and multiply the numerator and denominator of 7/21 by 4 so both fractions share the common base 84.
Working: 3 × 7/12 × 7 = 21/84 and 7 × 4/21 × 4 = 28/84

Step 3: Add the Numerators
Now add the numerators (21 + 28 = 49) and keep the common denominator 84 unchanged.
Working: 21 + 28/84 = 49/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 49 and 84, which is 7. Divide both the numerator and denominator by 7.
Working: 49 ÷ 7/84 ÷ 7 = 7/12

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).
Working: 7 ÷ 12 = 0.583333 (58.3333%)

Key Values:
- Simplified Fraction: 7/12
- Mixed Number Form: 7/12
- Decimal Value: 0.583333
- Percentage: 58.3333%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-12-plus-7-21/
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3/12 + 7/21 = 7/12

Simplified Fraction

7/12

Mixed Number

Proper (7/12)

Decimal Value

0.583333

Percentage

58.3333%

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Step-by-Step Solution: 3/12 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 12 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 84 (which is smaller than their product 12 × 21 = 252, keeping the calculation simpler).

LCD(12, 21) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 3/12 by 7, and multiply the numerator and denominator of 7/21 by 4 so both fractions share the common base 84.

3 × 7/12 × 7 = 21/84 and 7 × 4/21 × 4 = 28/84

Step 3

Add the Numerators

Now add the numerators (21 + 28 = 49) and keep the common denominator 84 unchanged.

21 + 28/84 = 49/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 49 and 84, which is 7. Divide both the numerator and denominator by 7.

49 ÷ 7/84 ÷ 7 = 7/12

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 12 produces a repeating decimal (approximately 0.583333, or 58.3333%).

7 ÷ 12 = 0.583333 (58.3333%)

Visual Representation

The diagram below illustrates 3/12 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/12`
Mixed Number Form	`7/12`
Decimal Form	`0.583333`
Percentage	`58.3333%`

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Frequently Asked Questions

What is 3/12 plus 7/21 as a fraction?

3/12 + 7/21 in simplest fraction form is 7/12.

What is 3/12 plus 7/21 as a decimal?

3/12 + 7/21 converted to a decimal is 0.583333.

What is 3/12 plus 7/21 as a percentage?

3/12 + 7/21 expressed as a percentage is 58.3333%.

Does 3/12 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.583333...) because the denominator contains prime factors other than 2 and 5.