What is 6/45 plus 9/21? (Answer: 59/105)

Exact Answer

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Problem: What is 6/45 plus 9/21?
Formula / Expression: 6/45 + 9/21
Final Answer: 59/105
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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 6/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.
Working: 6 × 7/45 × 7 = 42/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (42 + 135 = 177) and keep the common denominator 315 unchanged.
Working: 42 + 135/315 = 177/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 177 and 315, which is 3. Divide both the numerator and denominator by 3.
Working: 177 ÷ 3/315 ÷ 3 = 59/105

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 105 produces a repeating decimal (approximately 0.561905, or 56.1905%).
Working: 59 ÷ 105 = 0.561905 (56.1905%)

Key Values:
- Simplified Fraction: 59/105
- Mixed Number Form: 59/105
- Decimal Value: 0.561905
- Percentage: 56.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-45-plus-9-21/
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6/45 + 9/21 = 59/105

Simplified Fraction

59/105

Mixed Number

Proper (59/105)

Decimal Value

0.561905

Percentage

56.1905%

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Step-by-Step Solution: 6/45 + 9/21

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 6/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.

6 × 7/45 × 7 = 42/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (42 + 135 = 177) and keep the common denominator 315 unchanged.

42 + 135/315 = 177/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 177 and 315, which is 3. Divide both the numerator and denominator by 3.

177 ÷ 3/315 ÷ 3 = 59/105

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 105 produces a repeating decimal (approximately 0.561905, or 56.1905%).

59 ÷ 105 = 0.561905 (56.1905%)

Visual Representation

The diagram below illustrates 6/45 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/105`
Mixed Number Form	`59/105`
Decimal Form	`0.561905`
Percentage	`56.1905%`

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Frequently Asked Questions

What is 6/45 plus 9/21 as a fraction?

6/45 + 9/21 in simplest fraction form is 59/105.

What is 6/45 plus 9/21 as a decimal?

6/45 + 9/21 converted to a decimal is 0.561905.

What is 6/45 plus 9/21 as a percentage?

6/45 + 9/21 expressed as a percentage is 56.1905%.

Does 6/45 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.561905...) because the denominator contains prime factors other than 2 and 5.