What is 8/22 plus 3/8? (Answer: 65/88)

Exact Answer

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Problem: What is 8/22 plus 3/8?
Formula / Expression: 8/22 + 3/8
Final Answer: 65/88
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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 8/22 by 4, and multiply the numerator and denominator of 3/8 by 11 so both fractions share the common base 88.
Working: 8 × 4/22 × 4 = 32/88 and 3 × 11/8 × 11 = 33/88

Step 3: Add the Numerators
Now add the numerators (32 + 33 = 65) and keep the common denominator 88 unchanged.
Working: 32 + 33/88 = 65/88

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 65 and 88 is 1, confirming that 65/88 cannot be reduced further—it is already in its simplest irreducible form.
Working: 65/88

Step 5: Decimal & Percentage Representation
Dividing the numerator 65 by denominator 88 produces a repeating decimal (approximately 0.738636, or 73.8636%).
Working: 65 ÷ 88 = 0.738636 (73.8636%)

Key Values:
- Simplified Fraction: 65/88
- Mixed Number Form: 65/88
- Decimal Value: 0.738636
- Percentage: 73.8636%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-8-22-plus-3-8/
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8/22 + 3/8 = 65/88

Simplified Fraction

65/88

Mixed Number

Proper (65/88)

Decimal Value

0.738636

Percentage

73.8636%

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Step-by-Step Solution: 8/22 + 3/8

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 8/22 by 4, and multiply the numerator and denominator of 3/8 by 11 so both fractions share the common base 88.

8 × 4/22 × 4 = 32/88 and 3 × 11/8 × 11 = 33/88

Step 3

Add the Numerators

Now add the numerators (32 + 33 = 65) and keep the common denominator 88 unchanged.

32 + 33/88 = 65/88

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 65 and 88 is 1, confirming that 65/88 cannot be reduced further—it is already in its simplest irreducible form.

65/88

Step 5

Decimal & Percentage Representation

Dividing the numerator 65 by denominator 88 produces a repeating decimal (approximately 0.738636, or 73.8636%).

65 ÷ 88 = 0.738636 (73.8636%)

Visual Representation

The diagram below illustrates 8/22 plus 3/8 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`65/88`
Mixed Number Form	`65/88`
Decimal Form	`0.738636`
Percentage	`73.8636%`

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Frequently Asked Questions

What is 8/22 plus 3/8 as a fraction?

8/22 + 3/8 in simplest fraction form is 65/88.

What is 8/22 plus 3/8 as a decimal?

8/22 + 3/8 converted to a decimal is 0.738636.

What is 8/22 plus 3/8 as a percentage?

8/22 + 3/8 expressed as a percentage is 73.8636%.

Does 8/22 plus 3/8 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.738636...) because the denominator contains prime factors other than 2 and 5.