What is 9/22 plus 4/8? (Answer: 10/11)

Exact Answer

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Problem: What is 9/22 plus 4/8?
Formula / Expression: 9/22 + 4/8
Final Answer: 10/11
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 22 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 88 (which is smaller than their product 22 × 8 = 176, keeping the calculation simpler).
Working: LCD(22, 8) = 88

Step 2: Convert to Equivalent Fractions with Common Denominator 88
Multiply the numerator and denominator of 9/22 by 4, and multiply the numerator and denominator of 4/8 by 11 so both fractions share the common base 88.
Working: 9 × 4/22 × 4 = 36/88 and 4 × 11/8 × 11 = 44/88

Step 3: Add the Numerators
Now add the numerators (36 + 44 = 80) and keep the common denominator 88 unchanged.
Working: 36 + 44/88 = 80/88

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 80 and 88, which is 8. Divide both the numerator and denominator by 8.
Working: 80 ÷ 8/88 ÷ 8 = 10/11

Step 5: Decimal & Percentage Representation
Dividing the numerator 10 by denominator 11 produces a repeating decimal (approximately 0.909091, or 90.9091%).
Working: 10 ÷ 11 = 0.909091 (90.9091%)

Key Values:
- Simplified Fraction: 10/11
- Mixed Number Form: 10/11
- Decimal Value: 0.909091
- Percentage: 90.9091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-22-plus-4-8/
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9/22 + 4/8 = 10/11

Simplified Fraction

10/11

Mixed Number

Proper (10/11)

Decimal Value

0.909091

Percentage

90.9091%

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Step-by-Step Solution: 9/22 + 4/8

Step 1

Find the Least Common Denominator (LCD)

The denominators 22 and 8 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 88 (which is smaller than their product 22 × 8 = 176, keeping the calculation simpler).

LCD(22, 8) = 88

Step 2

Convert to Equivalent Fractions with Common Denominator 88

Multiply the numerator and denominator of 9/22 by 4, and multiply the numerator and denominator of 4/8 by 11 so both fractions share the common base 88.

9 × 4/22 × 4 = 36/88 and 4 × 11/8 × 11 = 44/88

Step 3

Add the Numerators

Now add the numerators (36 + 44 = 80) and keep the common denominator 88 unchanged.

36 + 44/88 = 80/88

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 80 and 88, which is 8. Divide both the numerator and denominator by 8.

80 ÷ 8/88 ÷ 8 = 10/11

Step 5

Decimal & Percentage Representation

Dividing the numerator 10 by denominator 11 produces a repeating decimal (approximately 0.909091, or 90.9091%).

10 ÷ 11 = 0.909091 (90.9091%)

Visual Representation

The diagram below illustrates 9/22 plus 4/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`10/11`
Mixed Number Form	`10/11`
Decimal Form	`0.909091`
Percentage	`90.9091%`

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Frequently Asked Questions

What is 9/22 plus 4/8 as a fraction?

9/22 + 4/8 in simplest fraction form is 10/11.

What is 9/22 plus 4/8 as a decimal?

9/22 + 4/8 converted to a decimal is 0.909091.

What is 9/22 plus 4/8 as a percentage?

9/22 + 4/8 expressed as a percentage is 90.9091%.

Does 9/22 plus 4/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.909091...) because the denominator contains prime factors other than 2 and 5.