What is 4/9 plus 10/21? (Answer: 58/63)

Exact Answer

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Problem: What is 4/9 plus 10/21?
Formula / Expression: 4/9 + 10/21
Final Answer: 58/63
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 63
Multiply the numerator and denominator of 4/9 by 7, and multiply the numerator and denominator of 10/21 by 3 so both fractions share the common base 63.
Working: 4 × 7/9 × 7 = 28/63 and 10 × 3/21 × 3 = 30/63

Step 3: Add the Numerators
Now add the numerators (28 + 30 = 58) and keep the common denominator 63 unchanged.
Working: 28 + 30/63 = 58/63

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 58 and 63 is 1, confirming that 58/63 cannot be reduced further—it is already in its simplest irreducible form.
Working: 58/63

Step 5: Decimal & Percentage Representation
Dividing the numerator 58 by denominator 63 produces a repeating decimal (approximately 0.920635, or 92.0635%).
Working: 58 ÷ 63 = 0.920635 (92.0635%)

Key Values:
- Simplified Fraction: 58/63
- Mixed Number Form: 58/63
- Decimal Value: 0.920635
- Percentage: 92.0635%

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Solved with FractionsCalc:
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4/9 + 10/21 = 58/63

Simplified Fraction

58/63

Mixed Number

Proper (58/63)

Decimal Value

0.920635

Percentage

92.0635%

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Step-by-Step Solution: 4/9 + 10/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(9, 21) = 63

Step 2

Convert to Equivalent Fractions with Common Denominator 63

Multiply the numerator and denominator of 4/9 by 7, and multiply the numerator and denominator of 10/21 by 3 so both fractions share the common base 63.

4 × 7/9 × 7 = 28/63 and 10 × 3/21 × 3 = 30/63

Step 3

Add the Numerators

Now add the numerators (28 + 30 = 58) and keep the common denominator 63 unchanged.

28 + 30/63 = 58/63

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 58 and 63 is 1, confirming that 58/63 cannot be reduced further—it is already in its simplest irreducible form.

58/63

Step 5

Decimal & Percentage Representation

Dividing the numerator 58 by denominator 63 produces a repeating decimal (approximately 0.920635, or 92.0635%).

58 ÷ 63 = 0.920635 (92.0635%)

Visual Representation

The diagram below illustrates 4/9 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`58/63`
Mixed Number Form	`58/63`
Decimal Form	`0.920635`
Percentage	`92.0635%`

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Frequently Asked Questions

What is 4/9 plus 10/21 as a fraction?

4/9 + 10/21 in simplest fraction form is 58/63.

What is 4/9 plus 10/21 as a decimal?

4/9 + 10/21 converted to a decimal is 0.920635.

What is 4/9 plus 10/21 as a percentage?

4/9 + 10/21 expressed as a percentage is 92.0635%.

Does 4/9 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.920635...) because the denominator contains prime factors other than 2 and 5.