What is 2/16 plus 4/10? (Answer: 21/40)

Exact Answer

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Problem: What is 2/16 plus 4/10?
Formula / Expression: 2/16 + 4/10
Final Answer: 21/40
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 16 × 10 = 160, keeping the calculation simpler).
Working: LCD(16, 10) = 80

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/16 by 5, and multiply the numerator and denominator of 4/10 by 8 so both fractions share the common base 80.
Working: 2 × 5/16 × 5 = 10/80 and 4 × 8/10 × 8 = 32/80

Step 3: Add the Numerators
Now add the numerators (10 + 32 = 42) and keep the common denominator 80 unchanged.
Working: 10 + 32/80 = 42/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 42 and 80, which is 2. Divide both the numerator and denominator by 2.
Working: 42 ÷ 2/80 ÷ 2 = 21/40

Step 5: Decimal & Percentage Representation
Dividing the numerator 21 by denominator 40 yields an exact terminating decimal of 0.525 (or 52.5%).
Working: 21 ÷ 40 = 0.525 (52.5%)

Key Values:
- Simplified Fraction: 21/40
- Mixed Number Form: 21/40
- Decimal Value: 0.525
- Percentage: 52.5%

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Solved with FractionsCalc:
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2/16 + 4/10 = 21/40

Simplified Fraction

21/40

Mixed Number

Proper (21/40)

Decimal Value

0.525

Percentage

52.5%

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Step-by-Step Solution: 2/16 + 4/10

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 10 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 80 (which is smaller than their product 16 × 10 = 160, keeping the calculation simpler).

LCD(16, 10) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

Multiply the numerator and denominator of 2/16 by 5, and multiply the numerator and denominator of 4/10 by 8 so both fractions share the common base 80.

2 × 5/16 × 5 = 10/80 and 4 × 8/10 × 8 = 32/80

Step 3

Add the Numerators

Now add the numerators (10 + 32 = 42) and keep the common denominator 80 unchanged.

10 + 32/80 = 42/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 42 and 80, which is 2. Divide both the numerator and denominator by 2.

42 ÷ 2/80 ÷ 2 = 21/40

Step 5

Decimal & Percentage Representation

Dividing the numerator 21 by denominator 40 yields an exact terminating decimal of 0.525 (or 52.5%).

21 ÷ 40 = 0.525 (52.5%)

Visual Representation

The diagram below illustrates 2/16 plus 4/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`21/40`
Mixed Number Form	`21/40`
Decimal Form	`0.525`
Percentage	`52.5%`

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Frequently Asked Questions

What is 2/16 plus 4/10 as a fraction?

2/16 + 4/10 in simplest fraction form is 21/40.

What is 2/16 plus 4/10 as a decimal?

2/16 + 4/10 converted to a decimal is 0.525.

What is 2/16 plus 4/10 as a percentage?

2/16 + 4/10 expressed as a percentage is 52.5%.

Does 2/16 plus 4/10 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.525) because the denominator in simplest terms contains only prime factors 2 and/or 5.