What is 12/45 plus 8/21? (Answer: 68/105)

Exact Answer

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Problem: What is 12/45 plus 8/21?
Formula / Expression: 12/45 + 8/21
Final Answer: 68/105
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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 12/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.
Working: 12 × 7/45 × 7 = 84/315 and 8 × 15/21 × 15 = 120/315

Step 3: Add the Numerators
Now add the numerators (84 + 120 = 204) and keep the common denominator 315 unchanged.
Working: 84 + 120/315 = 204/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 204 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 204 ÷ 3/315 ÷ 3 = 68/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 68 by denominator 105 produces a repeating decimal (approximately 0.647619, or 64.7619%).
Working: 68 ÷ 105 = 0.647619 (64.7619%)

Key Values:
- Simplified Fraction: 68/105
- Mixed Number Form: 68/105
- Decimal Value: 0.647619
- Percentage: 64.7619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-12-45-plus-8-21/
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12/45 + 8/21 = 68/105

Simplified Fraction

68/105

Mixed Number

Proper (68/105)

Decimal Value

0.647619

Percentage

64.7619%

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Step-by-Step Solution: 12/45 + 8/21

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 12/45 by 7, and multiply the numerator and denominator of 8/21 by 15 so both fractions share the common base 315.

12 × 7/45 × 7 = 84/315 and 8 × 15/21 × 15 = 120/315

Step 3

Add the Numerators

Now add the numerators (84 + 120 = 204) and keep the common denominator 315 unchanged.

84 + 120/315 = 204/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 204 and 315, which is 3. Divide both the numerator and denominator by 3.

204 ÷ 3/315 ÷ 3 = 68/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 68 by denominator 105 produces a repeating decimal (approximately 0.647619, or 64.7619%).

68 ÷ 105 = 0.647619 (64.7619%)

Visual Representation

The diagram below illustrates 12/45 plus 8/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`68/105`
Mixed Number Form	`68/105`
Decimal Form	`0.647619`
Percentage	`64.7619%`

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Frequently Asked Questions

What is 12/45 plus 8/21 as a fraction?

12/45 + 8/21 in simplest fraction form is 68/105.

What is 12/45 plus 8/21 as a decimal?

12/45 + 8/21 converted to a decimal is 0.647619.

What is 12/45 plus 8/21 as a percentage?

12/45 + 8/21 expressed as a percentage is 64.7619%.

Does 12/45 plus 8/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.647619...) because the denominator contains prime factors other than 2 and 5.