What is 3/7 plus 3/4? (Answer: 33/28)

Exact Answer

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Problem: What is 3/7 plus 3/4?
Formula / Expression: 3/7 + 3/4
Final Answer: 1 5/28 (33/28)
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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 3/7 by 4, and multiply the numerator and denominator of 3/4 by 7 so both fractions share the common base 28.
Working: 3 × 4/7 × 4 = 12/28 and 3 × 7/4 × 7 = 21/28

Step 3: Add the Numerators
Now add the numerators (12 + 21 = 33) and keep the common denominator 28 unchanged.
Working: 12 + 21/28 = 33/28

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 33 and 28 is 1, confirming that 33/28 cannot be reduced further—it is already in its simplest irreducible form.
Working: 33/28

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (33) is greater than the denominator (28), divide 33 by 28: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/28.
Working: 33/28 = 1 5/28

Step 6: Decimal & Percentage Representation
Dividing the numerator 33 by denominator 28 produces a repeating decimal (approximately 1.178571, or 117.8571%).
Working: 33 ÷ 28 = 1.178571 (117.8571%)

Key Values:
- Simplified Fraction: 33/28
- Mixed Number Form: 1 5/28
- Decimal Value: 1.178571
- Percentage: 117.8571%

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Solved with FractionsCalc:
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3/7 + 3/4 = 33/28

Simplified Fraction

33/28

Mixed Number

1 5/28

Decimal Value

1.178571

Percentage

117.8571%

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Step-by-Step Solution: 3/7 + 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 3/7 by 4, and multiply the numerator and denominator of 3/4 by 7 so both fractions share the common base 28.

3 × 4/7 × 4 = 12/28 and 3 × 7/4 × 7 = 21/28

Step 3

Add the Numerators

Now add the numerators (12 + 21 = 33) and keep the common denominator 28 unchanged.

12 + 21/28 = 33/28

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 33 and 28 is 1, confirming that 33/28 cannot be reduced further—it is already in its simplest irreducible form.

33/28

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (33) is greater than the denominator (28), divide 33 by 28: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/28.

33/28 = 15/28

Step 6

Decimal & Percentage Representation

Dividing the numerator 33 by denominator 28 produces a repeating decimal (approximately 1.178571, or 117.8571%).

33 ÷ 28 = 1.178571 (117.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`33/28`
Mixed Number Form	`1 5/28`
Decimal Form	`1.178571`
Percentage	`117.8571%`

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Frequently Asked Questions

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

3/7 + 3/4 in simplest fraction form is 33/28 (or 1 5/28 as a mixed number).

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

3/7 + 3/4 converted to a decimal is 1.178571.

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

3/7 + 3/4 expressed as a percentage is 117.8571%.

How do you write 3/7 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 33/28 can be written as the mixed number 1 5/28.

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

It results in a repeating decimal (approximately 1.178571...) because the denominator contains prime factors other than 2 and 5.