What is 1/7 plus 3/4? (Answer: 25/28)

Exact Answer

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Problem: What is 1/7 plus 3/4?
Formula / Expression: 1/7 + 3/4
Final Answer: 25/28
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 4 = 28.
Working: LCD(7, 4) = 28

Step 2: Convert to Equivalent Fractions with Common Denominator 28
Multiply the numerator and denominator of 1/7 by 4, and multiply the numerator and denominator of 3/4 by 7 so both fractions share the common base 28.
Working: 1 × 4/7 × 4 = 4/28 and 3 × 7/4 × 7 = 21/28

Step 3: Add the Numerators
Now add the numerators (4 + 21 = 25) and keep the common denominator 28 unchanged.
Working: 4 + 21/28 = 25/28

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 25 and 28 is 1, confirming that 25/28 cannot be reduced further—it is already in its simplest irreducible form.
Working: 25/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 25 by denominator 28 produces a repeating decimal (approximately 0.892857, or 89.2857%).
Working: 25 ÷ 28 = 0.892857 (89.2857%)

Key Values:
- Simplified Fraction: 25/28
- Mixed Number Form: 25/28
- Decimal Value: 0.892857
- Percentage: 89.2857%

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Solved with FractionsCalc:
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1/7 + 3/4 = 25/28

Simplified Fraction

25/28

Mixed Number

Proper (25/28)

Decimal Value

0.892857

Percentage

89.2857%

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Step-by-Step Solution: 1/7 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 4 = 28.

LCD(7, 4) = 28

Step 2

Convert to Equivalent Fractions with Common Denominator 28

Multiply the numerator and denominator of 1/7 by 4, and multiply the numerator and denominator of 3/4 by 7 so both fractions share the common base 28.

1 × 4/7 × 4 = 4/28 and 3 × 7/4 × 7 = 21/28

Step 3

Add the Numerators

Now add the numerators (4 + 21 = 25) and keep the common denominator 28 unchanged.

4 + 21/28 = 25/28

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 25 and 28 is 1, confirming that 25/28 cannot be reduced further—it is already in its simplest irreducible form.

25/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 25 by denominator 28 produces a repeating decimal (approximately 0.892857, or 89.2857%).

25 ÷ 28 = 0.892857 (89.2857%)

Visual Representation

The diagram below illustrates 1/7 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`25/28`
Mixed Number Form	`25/28`
Decimal Form	`0.892857`
Percentage	`89.2857%`

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Frequently Asked Questions

What is 1/7 plus 3/4 as a fraction?

1/7 + 3/4 in simplest fraction form is 25/28.

What is 1/7 plus 3/4 as a decimal?

1/7 + 3/4 converted to a decimal is 0.892857.

What is 1/7 plus 3/4 as a percentage?

1/7 + 3/4 expressed as a percentage is 89.2857%.

Does 1/7 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.892857...) because the denominator contains prime factors other than 2 and 5.