What is 21/64 plus 9/21? (Answer: 339/448)

Exact Answer

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Problem: What is 21/64 plus 9/21?
Formula / Expression: 21/64 + 9/21
Final Answer: 339/448
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 64 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 64 × 21 = 1344.
Working: LCD(64, 21) = 1344

Step 2: Convert to Equivalent Fractions with Common Denominator 1344
Multiply the numerator and denominator of 21/64 by 21, and multiply the numerator and denominator of 9/21 by 64 so both fractions share the common base 1344.
Working: 21 × 21/64 × 21 = 441/1344 and 9 × 64/21 × 64 = 576/1344

Step 3: Add the Numerators
Now add the numerators (441 + 576 = 1017) and keep the common denominator 1344 unchanged.
Working: 441 + 576/1344 = 1017/1344

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 1017 and 1344, which is 3. Divide both the numerator and denominator by 3.
Working: 1017 ÷ 3/1344 ÷ 3 = 339/448

Step 5: Decimal & Percentage Representation
Dividing the numerator 339 by denominator 448 produces a repeating decimal (approximately 0.756696, or 75.6696%).
Working: 339 ÷ 448 = 0.756696 (75.6696%)

Key Values:
- Simplified Fraction: 339/448
- Mixed Number Form: 339/448
- Decimal Value: 0.756696
- Percentage: 75.6696%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-21-64-plus-9-21/
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21/64 + 9/21 = 339/448

Simplified Fraction

339/448

Mixed Number

Proper (339/448)

Decimal Value

0.756696

Percentage

75.6696%

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Step-by-Step Solution: 21/64 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 64 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 64 × 21 = 1344.

LCD(64, 21) = 1344

Step 2

Convert to Equivalent Fractions with Common Denominator 1344

Multiply the numerator and denominator of 21/64 by 21, and multiply the numerator and denominator of 9/21 by 64 so both fractions share the common base 1344.

21 × 21/64 × 21 = 441/1344 and 9 × 64/21 × 64 = 576/1344

Step 3

Add the Numerators

Now add the numerators (441 + 576 = 1017) and keep the common denominator 1344 unchanged.

441 + 576/1344 = 1017/1344

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 1017 and 1344, which is 3. Divide both the numerator and denominator by 3.

1017 ÷ 3/1344 ÷ 3 = 339/448

Step 5

Decimal & Percentage Representation

Dividing the numerator 339 by denominator 448 produces a repeating decimal (approximately 0.756696, or 75.6696%).

339 ÷ 448 = 0.756696 (75.6696%)

Visual Representation

The diagram below illustrates 21/64 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`339/448`
Mixed Number Form	`339/448`
Decimal Form	`0.756696`
Percentage	`75.6696%`

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Frequently Asked Questions

What is 21/64 plus 9/21 as a fraction?

21/64 + 9/21 in simplest fraction form is 339/448.

What is 21/64 plus 9/21 as a decimal?

21/64 + 9/21 converted to a decimal is 0.756696.

What is 21/64 plus 9/21 as a percentage?

21/64 + 9/21 expressed as a percentage is 75.6696%.

Does 21/64 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.756696...) because the denominator contains prime factors other than 2 and 5.