What is 4/21 plus 9/45? (Answer: 41/105)

Exact Answer

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Problem: What is 4/21 plus 9/45?
Formula / Expression: 4/21 + 9/45
Final Answer: 41/105
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 4/21 by 15, and multiply the numerator and denominator of 9/45 by 7 so both fractions share the common base 315.
Working: 4 × 15/21 × 15 = 60/315 and 9 × 7/45 × 7 = 63/315

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 315 unchanged.
Working: 60 + 63/315 = 123/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/315 ÷ 3 = 41/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 105 produces a repeating decimal (approximately 0.390476, or 39.0476%).
Working: 41 ÷ 105 = 0.390476 (39.0476%)

Key Values:
- Simplified Fraction: 41/105
- Mixed Number Form: 41/105
- Decimal Value: 0.390476
- Percentage: 39.0476%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-21-plus-9-45/
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4/21 + 9/45 = 41/105

Simplified Fraction

41/105

Mixed Number

Proper (41/105)

Decimal Value

0.390476

Percentage

39.0476%

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Step-by-Step Solution: 4/21 + 9/45

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 45) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 4/21 by 15, and multiply the numerator and denominator of 9/45 by 7 so both fractions share the common base 315.

4 × 15/21 × 15 = 60/315 and 9 × 7/45 × 7 = 63/315

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 315 unchanged.

60 + 63/315 = 123/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 315, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/315 ÷ 3 = 41/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 105 produces a repeating decimal (approximately 0.390476, or 39.0476%).

41 ÷ 105 = 0.390476 (39.0476%)

Visual Representation

The diagram below illustrates 4/21 plus 9/45 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/105`
Mixed Number Form	`41/105`
Decimal Form	`0.390476`
Percentage	`39.0476%`

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Frequently Asked Questions

What is 4/21 plus 9/45 as a fraction?

4/21 + 9/45 in simplest fraction form is 41/105.

What is 4/21 plus 9/45 as a decimal?

4/21 + 9/45 converted to a decimal is 0.390476.

What is 4/21 plus 9/45 as a percentage?

4/21 + 9/45 expressed as a percentage is 39.0476%.

Does 4/21 plus 9/45 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.390476...) because the denominator contains prime factors other than 2 and 5.