What is 4/23 plus 2/7? (Answer: 74/161)

Exact Answer

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Problem: What is 4/23 plus 2/7?
Formula / Expression: 4/23 + 2/7
Final Answer: 74/161
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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 4/23 by 7, and multiply the numerator and denominator of 2/7 by 23 so both fractions share the common base 161.
Working: 4 × 7/23 × 7 = 28/161 and 2 × 23/7 × 23 = 46/161

Step 3: Add the Numerators
Now add the numerators (28 + 46 = 74) and keep the common denominator 161 unchanged.
Working: 28 + 46/161 = 74/161

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 74 and 161 is 1, confirming that 74/161 cannot be reduced further—it is already in its simplest irreducible form.
Working: 74/161

Step 5: Decimal & Percentage Representation
Dividing the numerator 74 by denominator 161 produces a repeating decimal (approximately 0.459627, or 45.9627%).
Working: 74 ÷ 161 = 0.459627 (45.9627%)

Key Values:
- Simplified Fraction: 74/161
- Mixed Number Form: 74/161
- Decimal Value: 0.459627
- Percentage: 45.9627%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-23-plus-2-7/
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4/23 + 2/7 = 74/161

Simplified Fraction

74/161

Mixed Number

Proper (74/161)

Decimal Value

0.459627

Percentage

45.9627%

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Step-by-Step Solution: 4/23 + 2/7

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 4/23 by 7, and multiply the numerator and denominator of 2/7 by 23 so both fractions share the common base 161.

4 × 7/23 × 7 = 28/161 and 2 × 23/7 × 23 = 46/161

Step 3

Add the Numerators

Now add the numerators (28 + 46 = 74) and keep the common denominator 161 unchanged.

28 + 46/161 = 74/161

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 74 and 161 is 1, confirming that 74/161 cannot be reduced further—it is already in its simplest irreducible form.

74/161

Step 5

Decimal & Percentage Representation

Dividing the numerator 74 by denominator 161 produces a repeating decimal (approximately 0.459627, or 45.9627%).

74 ÷ 161 = 0.459627 (45.9627%)

Visual Representation

The diagram below illustrates 4/23 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`74/161`
Mixed Number Form	`74/161`
Decimal Form	`0.459627`
Percentage	`45.9627%`

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Frequently Asked Questions

What is 4/23 plus 2/7 as a fraction?

4/23 + 2/7 in simplest fraction form is 74/161.

What is 4/23 plus 2/7 as a decimal?

4/23 + 2/7 converted to a decimal is 0.459627.

What is 4/23 plus 2/7 as a percentage?

4/23 + 2/7 expressed as a percentage is 45.9627%.

Does 4/23 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.459627...) because the denominator contains prime factors other than 2 and 5.