What is 5/45 plus 12/21? (Answer: 43/63)

Exact Answer

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Problem: What is 5/45 plus 12/21?
Formula / Expression: 5/45 + 12/21
Final Answer: 43/63
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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 5/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.
Working: 5 × 7/45 × 7 = 35/315 and 12 × 15/21 × 15 = 180/315

Step 3: Add the Numerators
Now add the numerators (35 + 180 = 215) and keep the common denominator 315 unchanged.
Working: 35 + 180/315 = 215/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 215 and 315, which is 5. Divide both the numerator and denominator by 5.
Working: 215 ÷ 5/315 ÷ 5 = 43/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 43 by denominator 63 produces a repeating decimal (approximately 0.68254, or 68.254%).
Working: 43 ÷ 63 = 0.68254 (68.254%)

Key Values:
- Simplified Fraction: 43/63
- Mixed Number Form: 43/63
- Decimal Value: 0.68254
- Percentage: 68.254%

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Solved with FractionsCalc:
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5/45 + 12/21 = 43/63

Simplified Fraction

43/63

Mixed Number

Proper (43/63)

Decimal Value

0.68254

Percentage

68.254%

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Step-by-Step Solution: 5/45 + 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 5/45 by 7, and multiply the numerator and denominator of 12/21 by 15 so both fractions share the common base 315.

5 × 7/45 × 7 = 35/315 and 12 × 15/21 × 15 = 180/315

Step 3

Add the Numerators

Now add the numerators (35 + 180 = 215) and keep the common denominator 315 unchanged.

35 + 180/315 = 215/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 215 and 315, which is 5. Divide both the numerator and denominator by 5.

215 ÷ 5/315 ÷ 5 = 43/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 43 by denominator 63 produces a repeating decimal (approximately 0.68254, or 68.254%).

43 ÷ 63 = 0.68254 (68.254%)

Visual Representation

The diagram below illustrates 5/45 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`43/63`
Mixed Number Form	`43/63`
Decimal Form	`0.68254`
Percentage	`68.254%`

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Frequently Asked Questions

What is 5/45 plus 12/21 as a fraction?

5/45 + 12/21 in simplest fraction form is 43/63.

What is 5/45 plus 12/21 as a decimal?

5/45 + 12/21 converted to a decimal is 0.68254.

What is 5/45 plus 12/21 as a percentage?

5/45 + 12/21 expressed as a percentage is 68.254%.

Does 5/45 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.68254...) because the denominator contains prime factors other than 2 and 5.