What is 3/22 plus 3/8? (Answer: 45/88)

Exact Answer

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Problem: What is 3/22 plus 3/8?
Formula / Expression: 3/22 + 3/8
Final Answer: 45/88
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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 3/22 by 4, and multiply the numerator and denominator of 3/8 by 11 so both fractions share the common base 88.
Working: 3 × 4/22 × 4 = 12/88 and 3 × 11/8 × 11 = 33/88

Step 3: Add the Numerators
Now add the numerators (12 + 33 = 45) and keep the common denominator 88 unchanged.
Working: 12 + 33/88 = 45/88

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 45 and 88 is 1, confirming that 45/88 cannot be reduced further—it is already in its simplest irreducible form.
Working: 45/88

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 88 produces a repeating decimal (approximately 0.511364, or 51.1364%).
Working: 45 ÷ 88 = 0.511364 (51.1364%)

Key Values:
- Simplified Fraction: 45/88
- Mixed Number Form: 45/88
- Decimal Value: 0.511364
- Percentage: 51.1364%

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Solved with FractionsCalc:
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3/22 + 3/8 = 45/88

Simplified Fraction

45/88

Mixed Number

Proper (45/88)

Decimal Value

0.511364

Percentage

51.1364%

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

3 × 4/22 × 4 = 12/88 and 3 × 11/8 × 11 = 33/88

Step 3

Add the Numerators

Now add the numerators (12 + 33 = 45) and keep the common denominator 88 unchanged.

12 + 33/88 = 45/88

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 45 and 88 is 1, confirming that 45/88 cannot be reduced further—it is already in its simplest irreducible form.

45/88

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 88 produces a repeating decimal (approximately 0.511364, or 51.1364%).

45 ÷ 88 = 0.511364 (51.1364%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/88`
Mixed Number Form	`45/88`
Decimal Form	`0.511364`
Percentage	`51.1364%`

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Frequently Asked Questions

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

3/22 + 3/8 in simplest fraction form is 45/88.

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

3/22 + 3/8 converted to a decimal is 0.511364.

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

3/22 + 3/8 expressed as a percentage is 51.1364%.

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

It results in a repeating decimal (approximately 0.511364...) because the denominator contains prime factors other than 2 and 5.