What is 3/9 plus 4/7? (Answer: 19/21)

Exact Answer

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Problem: What is 3/9 plus 4/7?
Formula / Expression: 3/9 + 4/7
Final Answer: 19/21
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 3/9 by 7, and multiply the numerator and denominator of 4/7 by 9 so both fractions share the common base 63.
Working: 3 × 7/9 × 7 = 21/63 and 4 × 9/7 × 9 = 36/63

Step 3: Add the Numerators
Now add the numerators (21 + 36 = 57) and keep the common denominator 63 unchanged.
Working: 21 + 36/63 = 57/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 57 and 63, which is 3. Divide both the numerator and denominator by 3.
Working: 57 ÷ 3/63 ÷ 3 = 19/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 19 by denominator 21 produces a repeating decimal (approximately 0.904762, or 90.4762%).
Working: 19 ÷ 21 = 0.904762 (90.4762%)

Key Values:
- Simplified Fraction: 19/21
- Mixed Number Form: 19/21
- Decimal Value: 0.904762
- Percentage: 90.4762%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-9-plus-4-7/
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3/9 + 4/7 = 19/21

Simplified Fraction

19/21

Mixed Number

Proper (19/21)

Decimal Value

0.904762

Percentage

90.4762%

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Step-by-Step Solution: 3/9 + 4/7

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 7) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 3/9 by 7, and multiply the numerator and denominator of 4/7 by 9 so both fractions share the common base 63.

3 × 7/9 × 7 = 21/63 and 4 × 9/7 × 9 = 36/63

Step 3

Add the Numerators

Now add the numerators (21 + 36 = 57) and keep the common denominator 63 unchanged.

21 + 36/63 = 57/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 57 and 63, which is 3. Divide both the numerator and denominator by 3.

57 ÷ 3/63 ÷ 3 = 19/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 19 by denominator 21 produces a repeating decimal (approximately 0.904762, or 90.4762%).

19 ÷ 21 = 0.904762 (90.4762%)

Visual Representation

The diagram below illustrates 3/9 plus 4/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`19/21`
Mixed Number Form	`19/21`
Decimal Form	`0.904762`
Percentage	`90.4762%`

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Frequently Asked Questions

What is 3/9 plus 4/7 as a fraction?

3/9 + 4/7 in simplest fraction form is 19/21.

What is 3/9 plus 4/7 as a decimal?

3/9 + 4/7 converted to a decimal is 0.904762.

What is 3/9 plus 4/7 as a percentage?

3/9 + 4/7 expressed as a percentage is 90.4762%.

Does 3/9 plus 4/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.904762...) because the denominator contains prime factors other than 2 and 5.