What is 2/40 plus 2/17? (Answer: 57/340)

Exact Answer

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Problem: What is 2/40 plus 2/17?
Formula / Expression: 2/40 + 2/17
Final Answer: 57/340
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 17 = 680.
Working: LCD(40, 17) = 680

Step 2: Convert to Equivalent Fractions with Common Denominator 680
Multiply the numerator and denominator of 2/40 by 17, and multiply the numerator and denominator of 2/17 by 40 so both fractions share the common base 680.
Working: 2 × 17/40 × 17 = 34/680 and 2 × 40/17 × 40 = 80/680

Step 3: Add the Numerators
Now add the numerators (34 + 80 = 114) and keep the common denominator 680 unchanged.
Working: 34 + 80/680 = 114/680

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 114 and 680, which is 2. Divide both the numerator and denominator by 2.
Working: 114 ÷ 2/680 ÷ 2 = 57/340

Step 5: Decimal & Percentage Representation
Dividing the numerator 57 by denominator 340 produces a repeating decimal (approximately 0.167647, or 16.7647%).
Working: 57 ÷ 340 = 0.167647 (16.7647%)

Key Values:
- Simplified Fraction: 57/340
- Mixed Number Form: 57/340
- Decimal Value: 0.167647
- Percentage: 16.7647%

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Solved with FractionsCalc:
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2/40 + 2/17 = 57/340

Simplified Fraction

57/340

Mixed Number

Proper (57/340)

Decimal Value

0.167647

Percentage

16.7647%

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Step-by-Step Solution: 2/40 + 2/17

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 17 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 17 = 680.

LCD(40, 17) = 680

Step 2

Convert to Equivalent Fractions with Common Denominator 680

Multiply the numerator and denominator of 2/40 by 17, and multiply the numerator and denominator of 2/17 by 40 so both fractions share the common base 680.

2 × 17/40 × 17 = 34/680 and 2 × 40/17 × 40 = 80/680

Step 3

Add the Numerators

Now add the numerators (34 + 80 = 114) and keep the common denominator 680 unchanged.

34 + 80/680 = 114/680

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 114 and 680, which is 2. Divide both the numerator and denominator by 2.

114 ÷ 2/680 ÷ 2 = 57/340

Step 5

Decimal & Percentage Representation

Dividing the numerator 57 by denominator 340 produces a repeating decimal (approximately 0.167647, or 16.7647%).

57 ÷ 340 = 0.167647 (16.7647%)

Visual Representation

The diagram below illustrates 2/40 plus 2/17 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`57/340`
Mixed Number Form	`57/340`
Decimal Form	`0.167647`
Percentage	`16.7647%`

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Frequently Asked Questions

What is 2/40 plus 2/17 as a fraction?

2/40 + 2/17 in simplest fraction form is 57/340.

What is 2/40 plus 2/17 as a decimal?

2/40 + 2/17 converted to a decimal is 0.167647.

What is 2/40 plus 2/17 as a percentage?

2/40 + 2/17 expressed as a percentage is 16.7647%.

Does 2/40 plus 2/17 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.167647...) because the denominator contains prime factors other than 2 and 5.