What is 2/40 plus 2/16? (Answer: 7/40)

Exact Answer

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Problem: What is 2/40 plus 2/16?
Formula / Expression: 2/40 + 2/16
Final Answer: 7/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 16 share a common factor (GCD = 8). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 40 × 16 = 640, keeping the calculation simpler).
Working: LCD(40, 16) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/40 by 2, and multiply the numerator and denominator of 2/16 by 5 so both fractions share the common base 80.
Working: 2 × 2/40 × 2 = 4/80 and 2 × 5/16 × 5 = 10/80

Step 3: Add the Numerators
Now add the numerators (4 + 10 = 14) and keep the common denominator 80 unchanged.
Working: 4 + 10/80 = 14/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 14 and 80, which is 2. Divide both the numerator and denominator by 2.
Working: 14 ÷ 2/80 ÷ 2 = 7/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 40 yields an exact terminating decimal of 0.175 (or 17.5%).
Working: 7 ÷ 40 = 0.175 (17.5%)

Key Values:
- Simplified Fraction: 7/40
- Mixed Number Form: 7/40
- Decimal Value: 0.175
- Percentage: 17.5%

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Solved with FractionsCalc:
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2/40 + 2/16 = 7/40

Simplified Fraction

7/40

Mixed Number

Proper (7/40)

Decimal Value

0.175

Percentage

17.5%

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Step-by-Step Solution: 2/40 + 2/16

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 16 share a common factor (GCD = 8). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 40 × 16 = 640, keeping the calculation simpler).

LCD(40, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 2/40 by 2, and multiply the numerator and denominator of 2/16 by 5 so both fractions share the common base 80.

2 × 2/40 × 2 = 4/80 and 2 × 5/16 × 5 = 10/80

Step 3

Add the Numerators

Now add the numerators (4 + 10 = 14) and keep the common denominator 80 unchanged.

4 + 10/80 = 14/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 14 and 80, which is 2. Divide both the numerator and denominator by 2.

14 ÷ 2/80 ÷ 2 = 7/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 40 yields an exact terminating decimal of 0.175 (or 17.5%).

7 ÷ 40 = 0.175 (17.5%)

Visual Representation

The diagram below illustrates 2/40 plus 2/16 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/40`
Mixed Number Form	`7/40`
Decimal Form	`0.175`
Percentage	`17.5%`

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Frequently Asked Questions

What is 2/40 plus 2/16 as a fraction?

2/40 + 2/16 in simplest fraction form is 7/40.

What is 2/40 plus 2/16 as a decimal?

2/40 + 2/16 converted to a decimal is 0.175.

What is 2/40 plus 2/16 as a percentage?

2/40 + 2/16 expressed as a percentage is 17.5%.

Does 2/40 plus 2/16 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.175) because the denominator in simplest terms contains only prime factors 2 and/or 5.