What is 1/7 plus 9/22? (Answer: 85/154)

Exact Answer

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Problem: What is 1/7 plus 9/22?
Formula / Expression: 1/7 + 9/22
Final Answer: 85/154
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.
Working: LCD(7, 22) = 154

Step 2: Convert to Equivalent Fractions with Common Denominator 154
Multiply the numerator and denominator of 1/7 by 22, and multiply the numerator and denominator of 9/22 by 7 so both fractions share the common base 154.
Working: 1 × 22/7 × 22 = 22/154 and 9 × 7/22 × 7 = 63/154

Step 3: Add the Numerators
Now add the numerators (22 + 63 = 85) and keep the common denominator 154 unchanged.
Working: 22 + 63/154 = 85/154

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 85 and 154 is 1, confirming that 85/154 cannot be reduced further—it is already in its simplest irreducible form.
Working: 85/154

Step 5: Decimal & Percentage Representation
Dividing the numerator 85 by denominator 154 produces a repeating decimal (approximately 0.551948, or 55.1948%).
Working: 85 ÷ 154 = 0.551948 (55.1948%)

Key Values:
- Simplified Fraction: 85/154
- Mixed Number Form: 85/154
- Decimal Value: 0.551948
- Percentage: 55.1948%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-7-plus-9-22/
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1/7 + 9/22 = 85/154

Simplified Fraction

85/154

Mixed Number

Proper (85/154)

Decimal Value

0.551948

Percentage

55.1948%

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Step-by-Step Solution: 1/7 + 9/22

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 22 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 22 = 154.

LCD(7, 22) = 154

Step 2

Convert to Equivalent Fractions with Common Denominator 154

Multiply the numerator and denominator of 1/7 by 22, and multiply the numerator and denominator of 9/22 by 7 so both fractions share the common base 154.

1 × 22/7 × 22 = 22/154 and 9 × 7/22 × 7 = 63/154

Step 3

Add the Numerators

Now add the numerators (22 + 63 = 85) and keep the common denominator 154 unchanged.

22 + 63/154 = 85/154

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 85 and 154 is 1, confirming that 85/154 cannot be reduced further—it is already in its simplest irreducible form.

85/154

Step 5

Decimal & Percentage Representation

Dividing the numerator 85 by denominator 154 produces a repeating decimal (approximately 0.551948, or 55.1948%).

85 ÷ 154 = 0.551948 (55.1948%)

Visual Representation

The diagram below illustrates 1/7 plus 9/22 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`85/154`
Mixed Number Form	`85/154`
Decimal Form	`0.551948`
Percentage	`55.1948%`

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Frequently Asked Questions

What is 1/7 plus 9/22 as a fraction?

1/7 + 9/22 in simplest fraction form is 85/154.

What is 1/7 plus 9/22 as a decimal?

1/7 + 9/22 converted to a decimal is 0.551948.

What is 1/7 plus 9/22 as a percentage?

1/7 + 9/22 expressed as a percentage is 55.1948%.

Does 1/7 plus 9/22 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.551948...) because the denominator contains prime factors other than 2 and 5.