What is 3/8 plus 9/22? (Answer: 69/88)

Exact Answer

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Problem: What is 3/8 plus 9/22?
Formula / Expression: 3/8 + 9/22
Final Answer: 69/88
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 88
Multiply the numerator and denominator of 3/8 by 11, and multiply the numerator and denominator of 9/22 by 4 so both fractions share the common base 88.
Working: 3 × 11/8 × 11 = 33/88 and 9 × 4/22 × 4 = 36/88

Step 3: Add the Numerators
Now add the numerators (33 + 36 = 69) and keep the common denominator 88 unchanged.
Working: 33 + 36/88 = 69/88

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 69 and 88 is 1, confirming that 69/88 cannot be reduced further—it is already in its simplest irreducible form.
Working: 69/88

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 88 produces a repeating decimal (approximately 0.784091, or 78.4091%).
Working: 69 ÷ 88 = 0.784091 (78.4091%)

Key Values:
- Simplified Fraction: 69/88
- Mixed Number Form: 69/88
- Decimal Value: 0.784091
- Percentage: 78.4091%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-8-plus-9-22/
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3/8 + 9/22 = 69/88

Simplified Fraction

69/88

Mixed Number

Proper (69/88)

Decimal Value

0.784091

Percentage

78.4091%

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Step-by-Step Solution: 3/8 + 9/22

Step 1

Find the Least Common Denominator (LCD)

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

LCD(8, 22) = 88

Step 2

Convert to Equivalent Fractions with Common Denominator 88

Multiply the numerator and denominator of 3/8 by 11, and multiply the numerator and denominator of 9/22 by 4 so both fractions share the common base 88.

3 × 11/8 × 11 = 33/88 and 9 × 4/22 × 4 = 36/88

Step 3

Add the Numerators

Now add the numerators (33 + 36 = 69) and keep the common denominator 88 unchanged.

33 + 36/88 = 69/88

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 69 and 88 is 1, confirming that 69/88 cannot be reduced further—it is already in its simplest irreducible form.

69/88

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 88 produces a repeating decimal (approximately 0.784091, or 78.4091%).

69 ÷ 88 = 0.784091 (78.4091%)

Visual Representation

The diagram below illustrates 3/8 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/88`
Mixed Number Form	`69/88`
Decimal Form	`0.784091`
Percentage	`78.4091%`

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Frequently Asked Questions

What is 3/8 plus 9/22 as a fraction?

3/8 + 9/22 in simplest fraction form is 69/88.

What is 3/8 plus 9/22 as a decimal?

3/8 + 9/22 converted to a decimal is 0.784091.

What is 3/8 plus 9/22 as a percentage?

3/8 + 9/22 expressed as a percentage is 78.4091%.

Does 3/8 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.784091...) because the denominator contains prime factors other than 2 and 5.