What is 2/40 plus 2/23? (Answer: 63/460)

Exact Answer

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Problem: What is 2/40 plus 2/23?
Formula / Expression: 2/40 + 2/23
Final Answer: 63/460
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 23 = 920.
Working: LCD(40, 23) = 920

Step 2: Convert to Equivalent Fractions with Common Denominator 920
Multiply the numerator and denominator of 2/40 by 23, and multiply the numerator and denominator of 2/23 by 40 so both fractions share the common base 920.
Working: 2 × 23/40 × 23 = 46/920 and 2 × 40/23 × 40 = 80/920

Step 3: Add the Numerators
Now add the numerators (46 + 80 = 126) and keep the common denominator 920 unchanged.
Working: 46 + 80/920 = 126/920

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 126 and 920, which is 2. Divide both the numerator and denominator by 2.
Working: 126 ÷ 2/920 ÷ 2 = 63/460

Step 5: Decimal & Percentage Representation
Dividing the numerator 63 by denominator 460 produces a repeating decimal (approximately 0.136957, or 13.6957%).
Working: 63 ÷ 460 = 0.136957 (13.6957%)

Key Values:
- Simplified Fraction: 63/460
- Mixed Number Form: 63/460
- Decimal Value: 0.136957
- Percentage: 13.6957%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-40-plus-2-23/
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2/40 + 2/23 = 63/460

Simplified Fraction

63/460

Mixed Number

Proper (63/460)

Decimal Value

0.136957

Percentage

13.6957%

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Step-by-Step Solution: 2/40 + 2/23

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 23 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 23 = 920.

LCD(40, 23) = 920

Step 2

Convert to Equivalent Fractions with Common Denominator 920

Multiply the numerator and denominator of 2/40 by 23, and multiply the numerator and denominator of 2/23 by 40 so both fractions share the common base 920.

2 × 23/40 × 23 = 46/920 and 2 × 40/23 × 40 = 80/920

Step 3

Add the Numerators

Now add the numerators (46 + 80 = 126) and keep the common denominator 920 unchanged.

46 + 80/920 = 126/920

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 126 and 920, which is 2. Divide both the numerator and denominator by 2.

126 ÷ 2/920 ÷ 2 = 63/460

Step 5

Decimal & Percentage Representation

Dividing the numerator 63 by denominator 460 produces a repeating decimal (approximately 0.136957, or 13.6957%).

63 ÷ 460 = 0.136957 (13.6957%)

Visual Representation

The diagram below illustrates 2/40 plus 2/23 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`63/460`
Mixed Number Form	`63/460`
Decimal Form	`0.136957`
Percentage	`13.6957%`

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Frequently Asked Questions

What is 2/40 plus 2/23 as a fraction?

2/40 + 2/23 in simplest fraction form is 63/460.

What is 2/40 plus 2/23 as a decimal?

2/40 + 2/23 converted to a decimal is 0.136957.

What is 2/40 plus 2/23 as a percentage?

2/40 + 2/23 expressed as a percentage is 13.6957%.

Does 2/40 plus 2/23 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.136957...) because the denominator contains prime factors other than 2 and 5.