What is 4/7 plus 6/9? (Answer: 26/21)

Exact Answer

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Problem: What is 4/7 plus 6/9?
Formula / Expression: 4/7 + 6/9
Final Answer: 1 5/21 (26/21)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.
Working: LCD(7, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 4/7 by 9, and multiply the numerator and denominator of 6/9 by 7 so both fractions share the common base 63.
Working: 4 × 9/7 × 9 = 36/63 and 6 × 7/9 × 7 = 42/63

Step 3: Add the Numerators
Now add the numerators (36 + 42 = 78) and keep the common denominator 63 unchanged.
Working: 36 + 42/63 = 78/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 78 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 78 ÷ 3/63 ÷ 3 = 26/21

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (26) is greater than the denominator (21), divide 26 by 21: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/21.
Working: 26/21 = 1 5/21

Step 6: Decimal & Percentage Representation
Dividing the numerator 26 by denominator 21 produces a repeating decimal (approximately 1.238095, or 123.8095%).
Working: 26 ÷ 21 = 1.238095 (123.8095%)

Key Values:
- Simplified Fraction: 26/21
- Mixed Number Form: 1 5/21
- Decimal Value: 1.238095
- Percentage: 123.8095%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-7-plus-6-9/
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4/7 + 6/9 = 26/21

Simplified Fraction

26/21

Mixed Number

1 5/21

Decimal Value

1.238095

Percentage

123.8095%

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Step-by-Step Solution: 4/7 + 6/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 9 = 63.

LCD(7, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 4/7 by 9, and multiply the numerator and denominator of 6/9 by 7 so both fractions share the common base 63.

4 × 9/7 × 9 = 36/63 and 6 × 7/9 × 7 = 42/63

Step 3

Add the Numerators

Now add the numerators (36 + 42 = 78) and keep the common denominator 63 unchanged.

36 + 42/63 = 78/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 78 and 63, which is 3. Divide both the numerator and denominator by 3.

78 ÷ 3/63 ÷ 3 = 26/21

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (26) is greater than the denominator (21), divide 26 by 21: it goes in 1 whole time(s) with a remainder of 5, giving the mixed number 1 5/21.

26/21 = 15/21

Step 6

Decimal & Percentage Representation

Dividing the numerator 26 by denominator 21 produces a repeating decimal (approximately 1.238095, or 123.8095%).

26 ÷ 21 = 1.238095 (123.8095%)

Visual Representation

The diagram below illustrates 4/7 plus 6/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`26/21`
Mixed Number Form	`1 5/21`
Decimal Form	`1.238095`
Percentage	`123.8095%`

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Frequently Asked Questions

What is 4/7 plus 6/9 as a fraction?

4/7 + 6/9 in simplest fraction form is 26/21 (or 1 5/21 as a mixed number).

What is 4/7 plus 6/9 as a decimal?

4/7 + 6/9 converted to a decimal is 1.238095.

What is 4/7 plus 6/9 as a percentage?

4/7 + 6/9 expressed as a percentage is 123.8095%.

How do you write 4/7 plus 6/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 26/21 can be written as the mixed number 1 5/21.

Does 4/7 plus 6/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.238095...) because the denominator contains prime factors other than 2 and 5.