What is 9/45 plus 6/21? (Answer: 17/35)

Exact Answer

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Problem: What is 9/45 plus 6/21?
Formula / Expression: 9/45 + 6/21
Final Answer: 17/35
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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 9/45 by 7, and multiply the numerator and denominator of 6/21 by 15 so both fractions share the common base 315.
Working: 9 × 7/45 × 7 = 63/315 and 6 × 15/21 × 15 = 90/315

Step 3: Add the Numerators
Now add the numerators (63 + 90 = 153) and keep the common denominator 315 unchanged.
Working: 63 + 90/315 = 153/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 153 and 315, which is 9. Divide both the numerator and denominator by 9.
Working: 153 ÷ 9/315 ÷ 9 = 17/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 35 produces a repeating decimal (approximately 0.485714, or 48.5714%).
Working: 17 ÷ 35 = 0.485714 (48.5714%)

Key Values:
- Simplified Fraction: 17/35
- Mixed Number Form: 17/35
- Decimal Value: 0.485714
- Percentage: 48.5714%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-45-plus-6-21/
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9/45 + 6/21 = 17/35

Simplified Fraction

17/35

Mixed Number

Proper (17/35)

Decimal Value

0.485714

Percentage

48.5714%

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

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

9 × 7/45 × 7 = 63/315 and 6 × 15/21 × 15 = 90/315

Step 3

Add the Numerators

Now add the numerators (63 + 90 = 153) and keep the common denominator 315 unchanged.

63 + 90/315 = 153/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 153 and 315, which is 9. Divide both the numerator and denominator by 9.

153 ÷ 9/315 ÷ 9 = 17/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 35 produces a repeating decimal (approximately 0.485714, or 48.5714%).

17 ÷ 35 = 0.485714 (48.5714%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/35`
Mixed Number Form	`17/35`
Decimal Form	`0.485714`
Percentage	`48.5714%`

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Frequently Asked Questions

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

9/45 + 6/21 in simplest fraction form is 17/35.

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

9/45 + 6/21 converted to a decimal is 0.485714.

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

9/45 + 6/21 expressed as a percentage is 48.5714%.

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

It results in a repeating decimal (approximately 0.485714...) because the denominator contains prime factors other than 2 and 5.