What is 7/40 plus 2/3? (Answer: 101/120)

Exact Answer

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Problem: What is 7/40 plus 2/3?
Formula / Expression: 7/40 + 2/3
Final Answer: 101/120
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 3 = 120.
Working: LCD(40, 3) = 120

Step 2: Convert to Equivalent Fractions with Common Denominator 120
Multiply the numerator and denominator of 7/40 by 3, and multiply the numerator and denominator of 2/3 by 40 so both fractions share the common base 120.
Working: 7 × 3/40 × 3 = 21/120 and 2 × 40/3 × 40 = 80/120

Step 3: Add the Numerators
Now add the numerators (21 + 80 = 101) and keep the common denominator 120 unchanged.
Working: 21 + 80/120 = 101/120

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 120 is 1, confirming that 101/120 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/120

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 120 produces a repeating decimal (approximately 0.841667, or 84.1667%).
Working: 101 ÷ 120 = 0.841667 (84.1667%)

Key Values:
- Simplified Fraction: 101/120
- Mixed Number Form: 101/120
- Decimal Value: 0.841667
- Percentage: 84.1667%

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7/40 + 2/3 = 101/120

Simplified Fraction

101/120

Mixed Number

Proper (101/120)

Decimal Value

0.841667

Percentage

84.1667%

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

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 3 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 3 = 120.

LCD(40, 3) = 120

Step 2

Convert to Equivalent Fractions with Common Denominator 120

Multiply the numerator and denominator of 7/40 by 3, and multiply the numerator and denominator of 2/3 by 40 so both fractions share the common base 120.

7 × 3/40 × 3 = 21/120 and 2 × 40/3 × 40 = 80/120

Step 3

Add the Numerators

Now add the numerators (21 + 80 = 101) and keep the common denominator 120 unchanged.

21 + 80/120 = 101/120

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 120 is 1, confirming that 101/120 cannot be reduced further—it is already in its simplest irreducible form.

101/120

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 120 produces a repeating decimal (approximately 0.841667, or 84.1667%).

101 ÷ 120 = 0.841667 (84.1667%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/120`
Mixed Number Form	`101/120`
Decimal Form	`0.841667`
Percentage	`84.1667%`

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Frequently Asked Questions

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

7/40 + 2/3 in simplest fraction form is 101/120.

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

7/40 + 2/3 converted to a decimal is 0.841667.

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

7/40 + 2/3 expressed as a percentage is 84.1667%.

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

It results in a repeating decimal (approximately 0.841667...) because the denominator contains prime factors other than 2 and 5.