What is 3/45 plus 12/21? (Answer: 67/105)

Exact Answer

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Problem: What is 3/45 plus 12/21?
Formula / Expression: 3/45 + 12/21
Final Answer: 67/105
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 3/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 3 × 7/45 × 7 = 21/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (21 + 180 = 201) and keep the common denominator 315 unchanged.
Working: 21 + 180/315 = 201/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 201 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 201 ÷ 3/315 ÷ 3 = 67/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 105 produces a repeating decimal (approximately 0.638095, or 63.8095%).
Working: 67 ÷ 105 = 0.638095 (63.8095%)

Key Values:
- Simplified Fraction: 67/105
- Mixed Number Form: 67/105
- Decimal Value: 0.638095
- Percentage: 63.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-45-plus-12-21/
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3/45 + 12/21 = 67/105

Simplified Fraction

67/105

Mixed Number

Proper (67/105)

Decimal Value

0.638095

Percentage

63.8095%

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Step-by-Step Solution: 3/45 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 3/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.

3 × 7/45 × 7 = 21/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (21 + 180 = 201) and keep the common denominator 315 unchanged.

21 + 180/315 = 201/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 201 and 315, which is 3. Divide both the numerator and denominator by 3.

201 ÷ 3/315 ÷ 3 = 67/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 105 produces a repeating decimal (approximately 0.638095, or 63.8095%).

67 ÷ 105 = 0.638095 (63.8095%)

Visual Representation

The diagram below illustrates 3/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/105`
Mixed Number Form	`67/105`
Decimal Form	`0.638095`
Percentage	`63.8095%`

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Frequently Asked Questions

What is 3/45 plus 12/21 as a fraction?

3/45 + 12/21 in simplest fraction form is 67/105.

What is 3/45 plus 12/21 as a decimal?

3/45 + 12/21 converted to a decimal is 0.638095.

What is 3/45 plus 12/21 as a percentage?

3/45 + 12/21 expressed as a percentage is 63.8095%.

Does 3/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.638095...) because the denominator contains prime factors other than 2 and 5.