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

Exact Answer

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

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).
Working: LCD(21, 9) = 63

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 7/21 by 3, and multiply the numerator and denominator of 4/9 by 7 so both fractions share the common base 63.
Working: 7 × 3/21 × 3 = 21/63 and 4 × 7/9 × 7 = 28/63

Step 3: Add the Numerators
Now add the numerators (21 + 28 = 49) and keep the common denominator 63 unchanged.
Working: 21 + 28/63 = 49/63

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 49 and 63, which is 7. Divide both the numerator and denominator by 7.
Working: 49 ÷ 7/63 ÷ 7 = 7/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).
Working: 7 ÷ 9 = 0.777778 (77.7778%)

Key Values:
- Simplified Fraction: 7/9
- Mixed Number Form: 7/9
- Decimal Value: 0.777778
- Percentage: 77.7778%

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

Simplified Fraction

7/9

Mixed Number

Proper (7/9)

Decimal Value

0.777778

Percentage

77.7778%

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Step-by-Step Solution: 7/21 + 4/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 9 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 63 (which is smaller than their product 21 × 9 = 189, keeping the calculation simpler).

LCD(21, 9) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 7/21 by 3, and multiply the numerator and denominator of 4/9 by 7 so both fractions share the common base 63.

7 × 3/21 × 3 = 21/63 and 4 × 7/9 × 7 = 28/63

Step 3

Add the Numerators

Now add the numerators (21 + 28 = 49) and keep the common denominator 63 unchanged.

21 + 28/63 = 49/63

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 49 and 63, which is 7. Divide both the numerator and denominator by 7.

49 ÷ 7/63 ÷ 7 = 7/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 9 produces a repeating decimal (approximately 0.777778, or 77.7778%).

7 ÷ 9 = 0.777778 (77.7778%)

Visual Representation

The diagram below illustrates 7/21 plus 4/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/9`
Mixed Number Form	`7/9`
Decimal Form	`0.777778`
Percentage	`77.7778%`

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Frequently Asked Questions

What is 7/21 plus 4/9 as a fraction?

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

What is 7/21 plus 4/9 as a decimal?

7/21 + 4/9 converted to a decimal is 0.777778.

What is 7/21 plus 4/9 as a percentage?

7/21 + 4/9 expressed as a percentage is 77.7778%.

Does 7/21 plus 4/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.777778...) because the denominator contains prime factors other than 2 and 5.