What is 3/40 plus 2/7? (Answer: 101/280)

Exact Answer

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Problem: What is 3/40 plus 2/7?
Formula / Expression: 3/40 + 2/7
Final Answer: 101/280
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 7 = 280.
Working: LCD(40, 7) = 280

Step 2: Convert to Equivalent Fractions with Common Denominator 280
Multiply the numerator and denominator of 3/40 by 7, and multiply the numerator and denominator of 2/7 by 40 so both fractions share the common base 280.
Working: 3 × 7/40 × 7 = 21/280 and 2 × 40/7 × 40 = 80/280

Step 3: Add the Numerators
Now add the numerators (21 + 80 = 101) and keep the common denominator 280 unchanged.
Working: 21 + 80/280 = 101/280

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 280 is 1, confirming that 101/280 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/280

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 280 produces a repeating decimal (approximately 0.360714, or 36.0714%).
Working: 101 ÷ 280 = 0.360714 (36.0714%)

Key Values:
- Simplified Fraction: 101/280
- Mixed Number Form: 101/280
- Decimal Value: 0.360714
- Percentage: 36.0714%

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3/40 + 2/7 = 101/280

Simplified Fraction

101/280

Mixed Number

Proper (101/280)

Decimal Value

0.360714

Percentage

36.0714%

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Step-by-Step Solution: 3/40 + 2/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 7 = 280.

LCD(40, 7) = 280

Step 2

Convert to Equivalent Fractions with Common Denominator 280

Multiply the numerator and denominator of 3/40 by 7, and multiply the numerator and denominator of 2/7 by 40 so both fractions share the common base 280.

3 × 7/40 × 7 = 21/280 and 2 × 40/7 × 40 = 80/280

Step 3

Add the Numerators

Now add the numerators (21 + 80 = 101) and keep the common denominator 280 unchanged.

21 + 80/280 = 101/280

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 280 is 1, confirming that 101/280 cannot be reduced further—it is already in its simplest irreducible form.

101/280

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 280 produces a repeating decimal (approximately 0.360714, or 36.0714%).

101 ÷ 280 = 0.360714 (36.0714%)

Visual Representation

The diagram below illustrates 3/40 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/280`
Mixed Number Form	`101/280`
Decimal Form	`0.360714`
Percentage	`36.0714%`

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Frequently Asked Questions

What is 3/40 plus 2/7 as a fraction?

3/40 + 2/7 in simplest fraction form is 101/280.

What is 3/40 plus 2/7 as a decimal?

3/40 + 2/7 converted to a decimal is 0.360714.

What is 3/40 plus 2/7 as a percentage?

3/40 + 2/7 expressed as a percentage is 36.0714%.

Does 3/40 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.360714...) because the denominator contains prime factors other than 2 and 5.