What is 7/40 plus 2/4? (Answer: 27/40)

Exact Answer

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Problem: What is 7/40 plus 2/4?
Formula / Expression: 7/40 + 2/4
Final Answer: 27/40
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 40
Multiply the numerator and denominator of 7/40 by 1, and multiply the numerator and denominator of 2/4 by 10 so both fractions share the common base 40.
Working: 7 × 1/40 × 1 = 7/40 and 2 × 10/4 × 10 = 20/40

Step 3: Add the Numerators
Now add the numerators (7 + 20 = 27) and keep the common denominator 40 unchanged.
Working: 7 + 20/40 = 27/40

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 27 and 40 is 1, confirming that 27/40 cannot be reduced further—it is already in its simplest irreducible form.
Working: 27/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 27 by denominator 40 yields an exact terminating decimal of 0.675 (or 67.5%).
Working: 27 ÷ 40 = 0.675 (67.5%)

Key Values:
- Simplified Fraction: 27/40
- Mixed Number Form: 27/40
- Decimal Value: 0.675
- Percentage: 67.5%

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Solved with FractionsCalc:
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7/40 + 2/4 = 27/40

Simplified Fraction

27/40

Mixed Number

Proper (27/40)

Decimal Value

0.675

Percentage

67.5%

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Step-by-Step Solution: 7/40 + 2/4

Step 1

Find the Least Common Denominator (LCD)

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

LCD(40, 4) = 40

Step 2

Convert to Equivalent Fractions with Common Denominator 40

Multiply the numerator and denominator of 7/40 by 1, and multiply the numerator and denominator of 2/4 by 10 so both fractions share the common base 40.

7 × 1/40 × 1 = 7/40 and 2 × 10/4 × 10 = 20/40

Step 3

Add the Numerators

Now add the numerators (7 + 20 = 27) and keep the common denominator 40 unchanged.

7 + 20/40 = 27/40

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 27 and 40 is 1, confirming that 27/40 cannot be reduced further—it is already in its simplest irreducible form.

27/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 27 by denominator 40 yields an exact terminating decimal of 0.675 (or 67.5%).

27 ÷ 40 = 0.675 (67.5%)

Visual Representation

The diagram below illustrates 7/40 plus 2/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`27/40`
Mixed Number Form	`27/40`
Decimal Form	`0.675`
Percentage	`67.5%`

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Frequently Asked Questions

What is 7/40 plus 2/4 as a fraction?

7/40 + 2/4 in simplest fraction form is 27/40.

What is 7/40 plus 2/4 as a decimal?

7/40 + 2/4 converted to a decimal is 0.675.

What is 7/40 plus 2/4 as a percentage?

7/40 + 2/4 expressed as a percentage is 67.5%.

Does 7/40 plus 2/4 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.675) because the denominator in simplest terms contains only prime factors 2 and/or 5.