What is 2/10 plus 9/28? (Answer: 73/140)

Exact Answer

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Problem: What is 2/10 plus 9/28?
Formula / Expression: 2/10 + 9/28
Final Answer: 73/140
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 28 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 140 (which is smaller than their product 10 × 28 = 280, keeping the calculation simpler).
Working: LCD(10, 28) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 2/10 by 14, and multiply the numerator and denominator of 9/28 by 5 so both fractions share the common base 140.
Working: 2 × 14/10 × 14 = 28/140 and 9 × 5/28 × 5 = 45/140

Step 3: Add the Numerators
Now add the numerators (28 + 45 = 73) and keep the common denominator 140 unchanged.
Working: 28 + 45/140 = 73/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 73 and 140 is 1, confirming that 73/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 73/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 73 by denominator 140 produces a repeating decimal (approximately 0.521429, or 52.1429%).
Working: 73 ÷ 140 = 0.521429 (52.1429%)

Key Values:
- Simplified Fraction: 73/140
- Mixed Number Form: 73/140
- Decimal Value: 0.521429
- Percentage: 52.1429%

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Solved with FractionsCalc:
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2/10 + 9/28 = 73/140

Simplified Fraction

73/140

Mixed Number

Proper (73/140)

Decimal Value

0.521429

Percentage

52.1429%

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Step-by-Step Solution: 2/10 + 9/28

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 28 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 140 (which is smaller than their product 10 × 28 = 280, keeping the calculation simpler).

LCD(10, 28) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 2/10 by 14, and multiply the numerator and denominator of 9/28 by 5 so both fractions share the common base 140.

2 × 14/10 × 14 = 28/140 and 9 × 5/28 × 5 = 45/140

Step 3

Add the Numerators

Now add the numerators (28 + 45 = 73) and keep the common denominator 140 unchanged.

28 + 45/140 = 73/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 73 and 140 is 1, confirming that 73/140 cannot be reduced further—it is already in its simplest irreducible form.

73/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 73 by denominator 140 produces a repeating decimal (approximately 0.521429, or 52.1429%).

73 ÷ 140 = 0.521429 (52.1429%)

Visual Representation

The diagram below illustrates 2/10 plus 9/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`73/140`
Mixed Number Form	`73/140`
Decimal Form	`0.521429`
Percentage	`52.1429%`

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Frequently Asked Questions

What is 2/10 plus 9/28 as a fraction?

2/10 + 9/28 in simplest fraction form is 73/140.

What is 2/10 plus 9/28 as a decimal?

2/10 + 9/28 converted to a decimal is 0.521429.

What is 2/10 plus 9/28 as a percentage?

2/10 + 9/28 expressed as a percentage is 52.1429%.

Does 2/10 plus 9/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.521429...) because the denominator contains prime factors other than 2 and 5.