What is 4/9 plus 10/22? (Answer: 89/99)

Exact Answer

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Problem: What is 4/9 plus 10/22?
Formula / Expression: 4/9 + 10/22
Final Answer: 89/99
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.
Working: LCD(9, 22) = 198

Step 2: Convert to Equivalent Fractions with Common Denominator 198
Multiply the numerator and denominator of 4/9 by 22, and multiply the numerator and denominator of 10/22 by 9 so both fractions share the common base 198.
Working: 4 × 22/9 × 22 = 88/198 and 10 × 9/22 × 9 = 90/198

Step 3: Add the Numerators
Now add the numerators (88 + 90 = 178) and keep the common denominator 198 unchanged.
Working: 88 + 90/198 = 178/198

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 178 and 198, which is 2. Divide both the numerator and denominator by 2.
Working: 178 ÷ 2/198 ÷ 2 = 89/99

Step 5: Decimal & Percentage Representation
Dividing the numerator 89 by denominator 99 produces a repeating decimal (approximately 0.89899, or 89.899%).
Working: 89 ÷ 99 = 0.89899 (89.899%)

Key Values:
- Simplified Fraction: 89/99
- Mixed Number Form: 89/99
- Decimal Value: 0.89899
- Percentage: 89.899%

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Solved with FractionsCalc:
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4/9 + 10/22 = 89/99

Simplified Fraction

89/99

Mixed Number

Proper (89/99)

Decimal Value

0.89899

Percentage

89.899%

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Step-by-Step Solution: 4/9 + 10/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 9 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 9 × 22 = 198.

LCD(9, 22) = 198

Step 2

Convert to Equivalent Fractions with Common Denominator 198

Multiply the numerator and denominator of 4/9 by 22, and multiply the numerator and denominator of 10/22 by 9 so both fractions share the common base 198.

4 × 22/9 × 22 = 88/198 and 10 × 9/22 × 9 = 90/198

Step 3

Add the Numerators

Now add the numerators (88 + 90 = 178) and keep the common denominator 198 unchanged.

88 + 90/198 = 178/198

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 178 and 198, which is 2. Divide both the numerator and denominator by 2.

178 ÷ 2/198 ÷ 2 = 89/99

Step 5

Decimal & Percentage Representation

Dividing the numerator 89 by denominator 99 produces a repeating decimal (approximately 0.89899, or 89.899%).

89 ÷ 99 = 0.89899 (89.899%)

Visual Representation

The diagram below illustrates 4/9 plus 10/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`89/99`
Mixed Number Form	`89/99`
Decimal Form	`0.89899`
Percentage	`89.899%`

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Frequently Asked Questions

What is 4/9 plus 10/22 as a fraction?

4/9 + 10/22 in simplest fraction form is 89/99.

What is 4/9 plus 10/22 as a decimal?

4/9 + 10/22 converted to a decimal is 0.89899.

What is 4/9 plus 10/22 as a percentage?

4/9 + 10/22 expressed as a percentage is 89.899%.

Does 4/9 plus 10/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.89899...) because the denominator contains prime factors other than 2 and 5.