What is 3/4 plus 6/7? (Answer: 45/28)

Exact Answer

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Problem: What is 3/4 plus 6/7?
Formula / Expression: 3/4 + 6/7
Final Answer: 1 17/28 (45/28)
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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 3/4 by 7, and multiply the numerator and denominator of 6/7 by 4 so both fractions share the common base 28.
Working: 3 × 7/4 × 7 = 21/28 and 6 × 4/7 × 4 = 24/28

Step 3: Add the Numerators
Now add the numerators (21 + 24 = 45) and keep the common denominator 28 unchanged.
Working: 21 + 24/28 = 45/28

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 45 and 28 is 1, confirming that 45/28 cannot be reduced further—it is already in its simplest irreducible form.
Working: 45/28

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (45) is greater than the denominator (28), divide 45 by 28: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/28.
Working: 45/28 = 1 17/28

Step 6: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 28 produces a repeating decimal (approximately 1.607143, or 160.7143%).
Working: 45 ÷ 28 = 1.607143 (160.7143%)

Key Values:
- Simplified Fraction: 45/28
- Mixed Number Form: 1 17/28
- Decimal Value: 1.607143
- Percentage: 160.7143%

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Solved with FractionsCalc:
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3/4 + 6/7 = 45/28

Simplified Fraction

45/28

Mixed Number

1 17/28

Decimal Value

1.607143

Percentage

160.7143%

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Step-by-Step Solution: 3/4 + 6/7

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 3/4 by 7, and multiply the numerator and denominator of 6/7 by 4 so both fractions share the common base 28.

3 × 7/4 × 7 = 21/28 and 6 × 4/7 × 4 = 24/28

Step 3

Add the Numerators

Now add the numerators (21 + 24 = 45) and keep the common denominator 28 unchanged.

21 + 24/28 = 45/28

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 45 and 28 is 1, confirming that 45/28 cannot be reduced further—it is already in its simplest irreducible form.

45/28

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (45) is greater than the denominator (28), divide 45 by 28: it goes in 1 whole time(s) with a remainder of 17, giving the mixed number 1 17/28.

45/28 = 117/28

Step 6

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 28 produces a repeating decimal (approximately 1.607143, or 160.7143%).

45 ÷ 28 = 1.607143 (160.7143%)

Visual Representation

The diagram below illustrates 3/4 plus 6/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/28`
Mixed Number Form	`1 17/28`
Decimal Form	`1.607143`
Percentage	`160.7143%`

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Frequently Asked Questions

What is 3/4 plus 6/7 as a fraction?

3/4 + 6/7 in simplest fraction form is 45/28 (or 1 17/28 as a mixed number).

What is 3/4 plus 6/7 as a decimal?

3/4 + 6/7 converted to a decimal is 1.607143.

What is 3/4 plus 6/7 as a percentage?

3/4 + 6/7 expressed as a percentage is 160.7143%.

How do you write 3/4 plus 6/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 45/28 can be written as the mixed number 1 17/28.

Does 3/4 plus 6/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.607143...) because the denominator contains prime factors other than 2 and 5.