What is 2/40 plus 2/10? (Answer: 1/4)

Exact Answer

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Problem: What is 2/40 plus 2/10?
Formula / Expression: 2/40 + 2/10
Final Answer: 1/4
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 40 is an exact multiple of 10 (10 × 4 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.
Working: LCD(40, 10) = 40

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 2/40 by 1, and multiply the numerator and denominator of 2/10 by 4 so both fractions share the common base 40.
Working: 2 × 1/40 × 1 = 2/40 and 2 × 4/10 × 4 = 8/40

Step 3: Add the Numerators
Now add the numerators (2 + 8 = 10) and keep the common denominator 40 unchanged.
Working: 2 + 8/40 = 10/40

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 10 and 40, which is 10. Divide both the numerator and denominator by 10.
Working: 10 ÷ 10/40 ÷ 10 = 1/4

Step 5: Decimal & Percentage Representation
Dividing the numerator 1 by denominator 4 yields an exact terminating decimal of 0.25 (or 25%).
Working: 1 ÷ 4 = 0.25 (25%)

Key Values:
- Simplified Fraction: 1/4
- Mixed Number Form: 1/4
- Decimal Value: 0.25
- Percentage: 25%

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2/40 + 2/10 = 1/4

Simplified Fraction

1/4

Mixed Number

Proper (1/4)

Decimal Value

0.25

Percentage

25%

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Step-by-Step Solution: 2/40 + 2/10

Step 1

Find the Least Common Denominator (LCD)

Notice that 40 is an exact multiple of 10 (10 × 4 = 40). The Least Common Denominator (LCD) is simply 40, meaning we only need to scale one fraction.

LCD(40, 10) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 2/40 by 1, and multiply the numerator and denominator of 2/10 by 4 so both fractions share the common base 40.

2 × 1/40 × 1 = 2/40 and 2 × 4/10 × 4 = 8/40

Step 3

Add the Numerators

Now add the numerators (2 + 8 = 10) and keep the common denominator 40 unchanged.

2 + 8/40 = 10/40

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 10 and 40, which is 10. Divide both the numerator and denominator by 10.

10 ÷ 10/40 ÷ 10 = 1/4

Step 5

Decimal & Percentage Representation

Dividing the numerator 1 by denominator 4 yields an exact terminating decimal of 0.25 (or 25%).

1 ÷ 4 = 0.25 (25%)

Visual Representation

The diagram below illustrates 2/40 plus 2/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`1/4`
Mixed Number Form	`1/4`
Decimal Form	`0.25`
Percentage	`25%`

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Frequently Asked Questions

What is 2/40 plus 2/10 as a fraction?

2/40 + 2/10 in simplest fraction form is 1/4.

What is 2/40 plus 2/10 as a decimal?

2/40 + 2/10 converted to a decimal is 0.25.

What is 2/40 plus 2/10 as a percentage?

2/40 + 2/10 expressed as a percentage is 25%.

Does 2/40 plus 2/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.25) because the denominator in simplest terms contains only prime factors 2 and/or 5.