What is 9/23 plus 3/7? (Answer: 132/161)

Exact Answer

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Problem: What is 9/23 plus 3/7?
Formula / Expression: 9/23 + 3/7
Final Answer: 132/161
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 23 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 7 = 161.
Working: LCD(23, 7) = 161

Step 2: Convert to Equivalent Fractions with Common Denominator 161
Multiply the numerator and denominator of 9/23 by 7, and multiply the numerator and denominator of 3/7 by 23 so both fractions share the common base 161.
Working: 9 × 7/23 × 7 = 63/161 and 3 × 23/7 × 23 = 69/161

Step 3: Add the Numerators
Now add the numerators (63 + 69 = 132) and keep the common denominator 161 unchanged.
Working: 63 + 69/161 = 132/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 132 and 161 is 1, confirming that 132/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 132/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 132 by denominator 161 produces a repeating decimal (approximately 0.819876, or 81.9876%).
Working: 132 ÷ 161 = 0.819876 (81.9876%)

Key Values:
- Simplified Fraction: 132/161
- Mixed Number Form: 132/161
- Decimal Value: 0.819876
- Percentage: 81.9876%

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Solved with FractionsCalc:
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9/23 + 3/7 = 132/161

Simplified Fraction

132/161

Mixed Number

Proper (132/161)

Decimal Value

0.819876

Percentage

81.9876%

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Step-by-Step Solution: 9/23 + 3/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 23 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 23 × 7 = 161.

LCD(23, 7) = 161

Step 2

Convert to Equivalent Fractions with Common Denominator 161

Multiply the numerator and denominator of 9/23 by 7, and multiply the numerator and denominator of 3/7 by 23 so both fractions share the common base 161.

9 × 7/23 × 7 = 63/161 and 3 × 23/7 × 23 = 69/161

Step 3

Add the Numerators

Now add the numerators (63 + 69 = 132) and keep the common denominator 161 unchanged.

63 + 69/161 = 132/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 132 and 161 is 1, confirming that 132/161 cannot be reduced further—it is already in its simplest irreducible form.

132/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 132 by denominator 161 produces a repeating decimal (approximately 0.819876, or 81.9876%).

132 ÷ 161 = 0.819876 (81.9876%)

Visual Representation

The diagram below illustrates 9/23 plus 3/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`132/161`
Mixed Number Form	`132/161`
Decimal Form	`0.819876`
Percentage	`81.9876%`

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Frequently Asked Questions

What is 9/23 plus 3/7 as a fraction?

9/23 + 3/7 in simplest fraction form is 132/161.

What is 9/23 plus 3/7 as a decimal?

9/23 + 3/7 converted to a decimal is 0.819876.

What is 9/23 plus 3/7 as a percentage?

9/23 + 3/7 expressed as a percentage is 81.9876%.

Does 9/23 plus 3/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.819876...) because the denominator contains prime factors other than 2 and 5.