What is 2/7 plus 9/28? (Answer: 17/28)

Exact Answer

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Problem: What is 2/7 plus 9/28?
Formula / Expression: 2/7 + 9/28
Final Answer: 17/28
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
Notice that 28 is an exact multiple of 7 (7 × 4 = 28). The Least Common Denominator (LCD) is simply 28, meaning we only need to scale one fraction.
Working: LCD(7, 28) = 28

Step 2: Convert to Equivalent Fractions with Common Denominator 28
Multiply the numerator and denominator of 2/7 by 4, and multiply the numerator and denominator of 9/28 by 1 so both fractions share the common base 28.
Working: 2 × 4/7 × 4 = 8/28 and 9 × 1/28 × 1 = 9/28

Step 3: Add the Numerators
Now add the numerators (8 + 9 = 17) and keep the common denominator 28 unchanged.
Working: 8 + 9/28 = 17/28

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 17 and 28 is 1, confirming that 17/28 cannot be reduced further—it is already in its simplest irreducible form.
Working: 17/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 28 produces a repeating decimal (approximately 0.607143, or 60.7143%).
Working: 17 ÷ 28 = 0.607143 (60.7143%)

Key Values:
- Simplified Fraction: 17/28
- Mixed Number Form: 17/28
- Decimal Value: 0.607143
- Percentage: 60.7143%

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Solved with FractionsCalc:
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2/7 + 9/28 = 17/28

Simplified Fraction

17/28

Mixed Number

Proper (17/28)

Decimal Value

0.607143

Percentage

60.7143%

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Step-by-Step Solution: 2/7 + 9/28

Step 1

Find the Least Common Denominator (LCD)

Notice that 28 is an exact multiple of 7 (7 × 4 = 28). The Least Common Denominator (LCD) is simply 28, meaning we only need to scale one fraction.

LCD(7, 28) = 28

Step 2

Convert to Equivalent Fractions with Common Denominator 28

Multiply the numerator and denominator of 2/7 by 4, and multiply the numerator and denominator of 9/28 by 1 so both fractions share the common base 28.

2 × 4/7 × 4 = 8/28 and 9 × 1/28 × 1 = 9/28

Step 3

Add the Numerators

Now add the numerators (8 + 9 = 17) and keep the common denominator 28 unchanged.

8 + 9/28 = 17/28

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 17 and 28 is 1, confirming that 17/28 cannot be reduced further—it is already in its simplest irreducible form.

17/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 28 produces a repeating decimal (approximately 0.607143, or 60.7143%).

17 ÷ 28 = 0.607143 (60.7143%)

Visual Representation

The diagram below illustrates 2/7 plus 9/28 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/28`
Mixed Number Form	`17/28`
Decimal Form	`0.607143`
Percentage	`60.7143%`

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Frequently Asked Questions

What is 2/7 plus 9/28 as a fraction?

2/7 + 9/28 in simplest fraction form is 17/28.

What is 2/7 plus 9/28 as a decimal?

2/7 + 9/28 converted to a decimal is 0.607143.

What is 2/7 plus 9/28 as a percentage?

2/7 + 9/28 expressed as a percentage is 60.7143%.

Does 2/7 plus 9/28 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.607143...) because the denominator contains prime factors other than 2 and 5.