What is 1/4 plus 4/7? (Answer: 23/28)

Exact Answer

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Problem: What is 1/4 plus 4/7?
Formula / Expression: 1/4 + 4/7
Final Answer: 23/28
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 28
Multiply the numerator and denominator of 1/4 by 7, and multiply the numerator and denominator of 4/7 by 4 so both fractions share the common base 28.
Working: 1 × 7/4 × 7 = 7/28 and 4 × 4/7 × 4 = 16/28

Step 3: Add the Numerators
Now add the numerators (7 + 16 = 23) and keep the common denominator 28 unchanged.
Working: 7 + 16/28 = 23/28

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 23 and 28 is 1, confirming that 23/28 cannot be reduced further—it is already in its simplest irreducible form.
Working: 23/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 23 by denominator 28 produces a repeating decimal (approximately 0.821429, or 82.1429%).
Working: 23 ÷ 28 = 0.821429 (82.1429%)

Key Values:
- Simplified Fraction: 23/28
- Mixed Number Form: 23/28
- Decimal Value: 0.821429
- Percentage: 82.1429%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-1-4-plus-4-7/
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1/4 + 4/7 = 23/28

Simplified Fraction

23/28

Mixed Number

Proper (23/28)

Decimal Value

0.821429

Percentage

82.1429%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(4, 7) = 28

Step 2

Convert to Equivalent Fractions with Common Denominator 28

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

1 × 7/4 × 7 = 7/28 and 4 × 4/7 × 4 = 16/28

Step 3

Add the Numerators

Now add the numerators (7 + 16 = 23) and keep the common denominator 28 unchanged.

7 + 16/28 = 23/28

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 23 and 28 is 1, confirming that 23/28 cannot be reduced further—it is already in its simplest irreducible form.

23/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 23 by denominator 28 produces a repeating decimal (approximately 0.821429, or 82.1429%).

23 ÷ 28 = 0.821429 (82.1429%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`23/28`
Mixed Number Form	`23/28`
Decimal Form	`0.821429`
Percentage	`82.1429%`

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Frequently Asked Questions

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

1/4 + 4/7 in simplest fraction form is 23/28.

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

1/4 + 4/7 converted to a decimal is 0.821429.

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

1/4 + 4/7 expressed as a percentage is 82.1429%.

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

It results in a repeating decimal (approximately 0.821429...) because the denominator contains prime factors other than 2 and 5.