What is 9/45 plus 9/21? (Answer: 22/35)

Exact Answer

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Problem: What is 9/45 plus 9/21?
Formula / Expression: 9/45 + 9/21
Final Answer: 22/35
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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 9/21 by 15 so both fractions share the common base 315.
Working: 9 × 7/45 × 7 = 63/315 and 9 × 15/21 × 15 = 135/315

Step 3: Add the Numerators
Now add the numerators (63 + 135 = 198) and keep the common denominator 315 unchanged.
Working: 63 + 135/315 = 198/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 198 and 315, which is 9. Divide both the numerator and denominator by 9.
Working: 198 ÷ 9/315 ÷ 9 = 22/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 22 by denominator 35 produces a repeating decimal (approximately 0.628571, or 62.8571%).
Working: 22 ÷ 35 = 0.628571 (62.8571%)

Key Values:
- Simplified Fraction: 22/35
- Mixed Number Form: 22/35
- Decimal Value: 0.628571
- Percentage: 62.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-45-plus-9-21/
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9/45 + 9/21 = 22/35

Simplified Fraction

22/35

Mixed Number

Proper (22/35)

Decimal Value

0.628571

Percentage

62.8571%

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Step-by-Step Solution: 9/45 + 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 9/45 by 7, and multiply the numerator and denominator of 9/21 by 15 so both fractions share the common base 315.

9 × 7/45 × 7 = 63/315 and 9 × 15/21 × 15 = 135/315

Step 3

Add the Numerators

Now add the numerators (63 + 135 = 198) and keep the common denominator 315 unchanged.

63 + 135/315 = 198/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 198 and 315, which is 9. Divide both the numerator and denominator by 9.

198 ÷ 9/315 ÷ 9 = 22/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 22 by denominator 35 produces a repeating decimal (approximately 0.628571, or 62.8571%).

22 ÷ 35 = 0.628571 (62.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`22/35`
Mixed Number Form	`22/35`
Decimal Form	`0.628571`
Percentage	`62.8571%`

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Frequently Asked Questions

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

9/45 + 9/21 in simplest fraction form is 22/35.

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

9/45 + 9/21 converted to a decimal is 0.628571.

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

9/45 + 9/21 expressed as a percentage is 62.8571%.

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

It results in a repeating decimal (approximately 0.628571...) because the denominator contains prime factors other than 2 and 5.