What is 9/28 plus 2/5? (Answer: 101/140)

Exact Answer

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Problem: What is 9/28 plus 2/5?
Formula / Expression: 9/28 + 2/5
Final Answer: 101/140
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 28 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 5 = 140.
Working: LCD(28, 5) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 9/28 by 5, and multiply the numerator and denominator of 2/5 by 28 so both fractions share the common base 140.
Working: 9 × 5/28 × 5 = 45/140 and 2 × 28/5 × 28 = 56/140

Step 3: Add the Numerators
Now add the numerators (45 + 56 = 101) and keep the common denominator 140 unchanged.
Working: 45 + 56/140 = 101/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 101 and 140 is 1, confirming that 101/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 101/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 101 by denominator 140 produces a repeating decimal (approximately 0.721429, or 72.1429%).
Working: 101 ÷ 140 = 0.721429 (72.1429%)

Key Values:
- Simplified Fraction: 101/140
- Mixed Number Form: 101/140
- Decimal Value: 0.721429
- Percentage: 72.1429%

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9/28 + 2/5 = 101/140

Simplified Fraction

101/140

Mixed Number

Proper (101/140)

Decimal Value

0.721429

Percentage

72.1429%

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Step-by-Step Solution: 9/28 + 2/5

Step 1

Find the Least Common Denominator (LCD)

The denominators 28 and 5 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 28 × 5 = 140.

LCD(28, 5) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

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

9 × 5/28 × 5 = 45/140 and 2 × 28/5 × 28 = 56/140

Step 3

Add the Numerators

Now add the numerators (45 + 56 = 101) and keep the common denominator 140 unchanged.

45 + 56/140 = 101/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 101 and 140 is 1, confirming that 101/140 cannot be reduced further—it is already in its simplest irreducible form.

101/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 101 by denominator 140 produces a repeating decimal (approximately 0.721429, or 72.1429%).

101 ÷ 140 = 0.721429 (72.1429%)

Visual Representation

The diagram below illustrates 9/28 plus 2/5 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`101/140`
Mixed Number Form	`101/140`
Decimal Form	`0.721429`
Percentage	`72.1429%`

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Frequently Asked Questions

What is 9/28 plus 2/5 as a fraction?

9/28 + 2/5 in simplest fraction form is 101/140.

What is 9/28 plus 2/5 as a decimal?

9/28 + 2/5 converted to a decimal is 0.721429.

What is 9/28 plus 2/5 as a percentage?

9/28 + 2/5 expressed as a percentage is 72.1429%.

Does 9/28 plus 2/5 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.721429...) because the denominator contains prime factors other than 2 and 5.