What is 5/28 plus 2/7? (Answer: 13/28)

Exact Answer

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Problem: What is 5/28 plus 2/7?
Formula / Expression: 5/28 + 2/7
Final Answer: 13/28
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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(28, 7) = 28

Step 2: Convert to Equivalent Fractions with Common Denominator 28
Multiply the numerator and denominator of 5/28 by 1, and multiply the numerator and denominator of 2/7 by 4 so both fractions share the common base 28.
Working: 5 × 1/28 × 1 = 5/28 and 2 × 4/7 × 4 = 8/28

Step 3: Add the Numerators
Now add the numerators (5 + 8 = 13) and keep the common denominator 28 unchanged.
Working: 5 + 8/28 = 13/28

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 13 and 28 is 1, confirming that 13/28 cannot be reduced further—it is already in its simplest irreducible form.
Working: 13/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).
Working: 13 ÷ 28 = 0.464286 (46.4286%)

Key Values:
- Simplified Fraction: 13/28
- Mixed Number Form: 13/28
- Decimal Value: 0.464286
- Percentage: 46.4286%

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Solved with FractionsCalc:
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5/28 + 2/7 = 13/28

Simplified Fraction

13/28

Mixed Number

Proper (13/28)

Decimal Value

0.464286

Percentage

46.4286%

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Step-by-Step Solution: 5/28 + 2/7

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(28, 7) = 28

Step 2

Convert to Equivalent Fractions with Common Denominator 28

Multiply the numerator and denominator of 5/28 by 1, and multiply the numerator and denominator of 2/7 by 4 so both fractions share the common base 28.

5 × 1/28 × 1 = 5/28 and 2 × 4/7 × 4 = 8/28

Step 3

Add the Numerators

Now add the numerators (5 + 8 = 13) and keep the common denominator 28 unchanged.

5 + 8/28 = 13/28

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 13 and 28 is 1, confirming that 13/28 cannot be reduced further—it is already in its simplest irreducible form.

13/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 28 produces a repeating decimal (approximately 0.464286, or 46.4286%).

13 ÷ 28 = 0.464286 (46.4286%)

Visual Representation

The diagram below illustrates 5/28 plus 2/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/28`
Mixed Number Form	`13/28`
Decimal Form	`0.464286`
Percentage	`46.4286%`

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Frequently Asked Questions

What is 5/28 plus 2/7 as a fraction?

5/28 + 2/7 in simplest fraction form is 13/28.

What is 5/28 plus 2/7 as a decimal?

5/28 + 2/7 converted to a decimal is 0.464286.

What is 5/28 plus 2/7 as a percentage?

5/28 + 2/7 expressed as a percentage is 46.4286%.

Does 5/28 plus 2/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.464286...) because the denominator contains prime factors other than 2 and 5.