What is 2/40 plus 3/7? (Answer: 67/140)

Exact Answer

==================================================
Problem: What is 2/40 plus 3/7?
Formula / Expression: 2/40 + 3/7
Final Answer: 67/140
==================================================

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 2/40 by 7, and multiply the numerator and denominator of 3/7 by 40 so both fractions share the common base 280.
Working: 2 × 7/40 × 7 = 14/280 and 3 × 40/7 × 40 = 120/280

Step 3: Add the Numerators
Now add the numerators (14 + 120 = 134) and keep the common denominator 280 unchanged.
Working: 14 + 120/280 = 134/280

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 134 and 280, which is 2. Divide both the numerator and denominator by 2.
Working: 134 ÷ 2/280 ÷ 2 = 67/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 67 by denominator 140 produces a repeating decimal (approximately 0.478571, or 47.8571%).
Working: 67 ÷ 140 = 0.478571 (47.8571%)

Key Values:
- Simplified Fraction: 67/140
- Mixed Number Form: 67/140
- Decimal Value: 0.478571
- Percentage: 47.8571%

--------------------------------------------------
Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-40-plus-3-7/
==================================================

2/40 + 3/7 = 67/140

Simplified Fraction

67/140

Mixed Number

Proper (67/140)

Decimal Value

0.478571

Percentage

47.8571%

Reduce / Convert Fraction:

Convert Fraction:

Enter Decimal Number:

Enter Percentage: %

What is % of

From Value: To Value:

Simplify Ratio: :

Switch to Proportion / Missing X Solver (A/B = C/D) →

Enter 3 known numbers and leave 1 empty (or type x) to solve:

← Switch to Ratio Simplifier (A:B)

Provide any 2 values below to calculate the remaining:

Price before discount

Discount

Price after discount

You saved

+ Add Sales Tax & Extra Coupon (Optional)

Sales Tax: % Extra Off: %

Provide any 2 values below to calculate the remaining:

Cost

Markup

REVENUE

Gross Profit

Profit Margin

Bill Subtotal

Tip Percentage

Split (People)

👥

Quick Tip:

Total Bill

Split Between

👥

Tip % (Optional)

Include Tip:

Total Price

Quantity

Unit of Measure

← Discount & Sales Tax • Ratio Simplifier (A:B) →

First Number: Second Number:

Find All Factors of:

Dividend: ÷ Divisor:

Number to Round: To Nearest:

Method: Standard (5+ ↑) Always Up (Ceil) Always Down (Floor)

Presets:

√ Square Root of: OR Power (x^y): ^{^}

x² + x + = 0

Number (n! & log):

Circle Radius (r):

Side a: Side b:

Angle (Degrees): °

Numbers (comma separated):

Total Items (n): Choose (r):

Decimal Number:

Number (1–3999):

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

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

2 × 7/40 × 7 = 14/280 and 3 × 40/7 × 40 = 120/280

Step 3

Add the Numerators

Now add the numerators (14 + 120 = 134) and keep the common denominator 280 unchanged.

14 + 120/280 = 134/280

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 134 and 280, which is 2. Divide both the numerator and denominator by 2.

134 ÷ 2/280 ÷ 2 = 67/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 67 by denominator 140 produces a repeating decimal (approximately 0.478571, or 47.8571%).

67 ÷ 140 = 0.478571 (47.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`67/140`
Mixed Number Form	`67/140`
Decimal Form	`0.478571`
Percentage	`47.8571%`

Was this solution helpful?

Help us improve our free step-by-step tools

Frequently Asked Questions

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

2/40 + 3/7 in simplest fraction form is 67/140.

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

2/40 + 3/7 converted to a decimal is 0.478571.

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

2/40 + 3/7 expressed as a percentage is 47.8571%.

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

It results in a repeating decimal (approximately 0.478571...) because the denominator contains prime factors other than 2 and 5.