What is 2/40 plus 2/19? (Answer: 59/380)

Exact Answer

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Problem: What is 2/40 plus 2/19?
Formula / Expression: 2/40 + 2/19
Final Answer: 59/380
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 19 = 760.
Working: LCD(40, 19) = 760

Step 2: Convert to Equivalent Fractions with Common Denominator 760
Multiply the numerator and denominator of 2/40 by 19, and multiply the numerator and denominator of 2/19 by 40 so both fractions share the common base 760.
Working: 2 × 19/40 × 19 = 38/760 and 2 × 40/19 × 40 = 80/760

Step 3: Add the Numerators
Now add the numerators (38 + 80 = 118) and keep the common denominator 760 unchanged.
Working: 38 + 80/760 = 118/760

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 118 and 760, which is 2. Divide both the numerator and denominator by 2.
Working: 118 ÷ 2/760 ÷ 2 = 59/380

Step 5: Decimal & Percentage Representation
Dividing the numerator 59 by denominator 380 produces a repeating decimal (approximately 0.155263, or 15.5263%).
Working: 59 ÷ 380 = 0.155263 (15.5263%)

Key Values:
- Simplified Fraction: 59/380
- Mixed Number Form: 59/380
- Decimal Value: 0.155263
- Percentage: 15.5263%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-40-plus-2-19/
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2/40 + 2/19 = 59/380

Simplified Fraction

59/380

Mixed Number

Proper (59/380)

Decimal Value

0.155263

Percentage

15.5263%

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Step-by-Step Solution: 2/40 + 2/19

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 19 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 19 = 760.

LCD(40, 19) = 760

Step 2

Convert to Equivalent Fractions with Common Denominator 760

Multiply the numerator and denominator of 2/40 by 19, and multiply the numerator and denominator of 2/19 by 40 so both fractions share the common base 760.

2 × 19/40 × 19 = 38/760 and 2 × 40/19 × 40 = 80/760

Step 3

Add the Numerators

Now add the numerators (38 + 80 = 118) and keep the common denominator 760 unchanged.

38 + 80/760 = 118/760

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 118 and 760, which is 2. Divide both the numerator and denominator by 2.

118 ÷ 2/760 ÷ 2 = 59/380

Step 5

Decimal & Percentage Representation

Dividing the numerator 59 by denominator 380 produces a repeating decimal (approximately 0.155263, or 15.5263%).

59 ÷ 380 = 0.155263 (15.5263%)

Visual Representation

The diagram below illustrates 2/40 plus 2/19 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`59/380`
Mixed Number Form	`59/380`
Decimal Form	`0.155263`
Percentage	`15.5263%`

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Frequently Asked Questions

What is 2/40 plus 2/19 as a fraction?

2/40 + 2/19 in simplest fraction form is 59/380.

What is 2/40 plus 2/19 as a decimal?

2/40 + 2/19 converted to a decimal is 0.155263.

What is 2/40 plus 2/19 as a percentage?

2/40 + 2/19 expressed as a percentage is 15.5263%.

Does 2/40 plus 2/19 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.155263...) because the denominator contains prime factors other than 2 and 5.