What is 2/10 plus 4/16? (Answer: 9/20)

Exact Answer

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Problem: What is 2/10 plus 4/16?
Formula / Expression: 2/10 + 4/16
Final Answer: 9/20
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 80
Multiply the numerator and denominator of 2/10 by 8, and multiply the numerator and denominator of 4/16 by 5 so both fractions share the common base 80.
Working: 2 × 8/10 × 8 = 16/80 and 4 × 5/16 × 5 = 20/80

Step 3: Add the Numerators
Now add the numerators (16 + 20 = 36) and keep the common denominator 80 unchanged.
Working: 16 + 20/80 = 36/80

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 36 and 80, which is 4. Divide both the numerator and denominator by 4.
Working: 36 ÷ 4/80 ÷ 4 = 9/20

Step 5: Decimal & Percentage Representation
Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).
Working: 9 ÷ 20 = 0.45 (45%)

Key Values:
- Simplified Fraction: 9/20
- Mixed Number Form: 9/20
- Decimal Value: 0.45
- Percentage: 45%

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Solved with FractionsCalc:
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2/10 + 4/16 = 9/20

Simplified Fraction

9/20

Mixed Number

Proper (9/20)

Decimal Value

0.45

Percentage

45%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(10, 16) = 80

Step 2

Convert to Equivalent Fractions with Common Denominator 80

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

2 × 8/10 × 8 = 16/80 and 4 × 5/16 × 5 = 20/80

Step 3

Add the Numerators

Now add the numerators (16 + 20 = 36) and keep the common denominator 80 unchanged.

16 + 20/80 = 36/80

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 36 and 80, which is 4. Divide both the numerator and denominator by 4.

36 ÷ 4/80 ÷ 4 = 9/20

Step 5

Decimal & Percentage Representation

Dividing the numerator 9 by denominator 20 yields an exact terminating decimal of 0.45 (or 45%).

9 ÷ 20 = 0.45 (45%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`9/20`
Mixed Number Form	`9/20`
Decimal Form	`0.45`
Percentage	`45%`

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Frequently Asked Questions

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

2/10 + 4/16 in simplest fraction form is 9/20.

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

2/10 + 4/16 converted to a decimal is 0.45.

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

2/10 + 4/16 expressed as a percentage is 45%.

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

It results in an exact terminating decimal (0.45) because the denominator in simplest terms contains only prime factors 2 and/or 5.