What is 22/55 plus 9/21? (Answer: 29/35)

Exact Answer

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Problem: What is 22/55 plus 9/21?
Formula / Expression: 22/55 + 9/21
Final Answer: 29/35
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 55 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 21 = 1155.
Working: LCD(55, 21) = 1155

Step 2: Convert to Equivalent Fractions with Common Denominator 1155
Multiply the numerator and denominator of 22/55 by 21, and multiply the numerator and denominator of 9/21 by 55 so both fractions share the common base 1155.
Working: 22 × 21/55 × 21 = 462/1155 and 9 × 55/21 × 55 = 495/1155

Step 3: Add the Numerators
Now add the numerators (462 + 495 = 957) and keep the common denominator 1155 unchanged.
Working: 462 + 495/1155 = 957/1155

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 957 and 1155, which is 33. Divide both the numerator and denominator by 33.
Working: 957 ÷ 33/1155 ÷ 33 = 29/35

Step 5: Decimal & Percentage Representation
Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).
Working: 29 ÷ 35 = 0.828571 (82.8571%)

Key Values:
- Simplified Fraction: 29/35
- Mixed Number Form: 29/35
- Decimal Value: 0.828571
- Percentage: 82.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-22-55-plus-9-21/
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22/55 + 9/21 = 29/35

Simplified Fraction

29/35

Mixed Number

Proper (29/35)

Decimal Value

0.828571

Percentage

82.8571%

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Step-by-Step Solution: 22/55 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 55 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 55 × 21 = 1155.

LCD(55, 21) = 1155

Step 2

Convert to Equivalent Fractions with Common Denominator 1155

Multiply the numerator and denominator of 22/55 by 21, and multiply the numerator and denominator of 9/21 by 55 so both fractions share the common base 1155.

22 × 21/55 × 21 = 462/1155 and 9 × 55/21 × 55 = 495/1155

Step 3

Add the Numerators

Now add the numerators (462 + 495 = 957) and keep the common denominator 1155 unchanged.

462 + 495/1155 = 957/1155

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 957 and 1155, which is 33. Divide both the numerator and denominator by 33.

957 ÷ 33/1155 ÷ 33 = 29/35

Step 5

Decimal & Percentage Representation

Dividing the numerator 29 by denominator 35 produces a repeating decimal (approximately 0.828571, or 82.8571%).

29 ÷ 35 = 0.828571 (82.8571%)

Visual Representation

The diagram below illustrates 22/55 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`29/35`
Mixed Number Form	`29/35`
Decimal Form	`0.828571`
Percentage	`82.8571%`

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Frequently Asked Questions

What is 22/55 plus 9/21 as a fraction?

22/55 + 9/21 in simplest fraction form is 29/35.

What is 22/55 plus 9/21 as a decimal?

22/55 + 9/21 converted to a decimal is 0.828571.

What is 22/55 plus 9/21 as a percentage?

22/55 + 9/21 expressed as a percentage is 82.8571%.

Does 22/55 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.828571...) because the denominator contains prime factors other than 2 and 5.