What is 20/64 plus 9/21? (Answer: 83/112)

Exact Answer

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Problem: What is 20/64 plus 9/21?
Formula / Expression: 20/64 + 9/21
Final Answer: 83/112
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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 20/64 by 21, and multiply the numerator and denominator of 9/21 by 64 so both fractions share the common base 1344.
Working: 20 × 21/64 × 21 = 420/1344 and 9 × 64/21 × 64 = 576/1344

Step 3: Add the Numerators
Now add the numerators (420 + 576 = 996) and keep the common denominator 1344 unchanged.
Working: 420 + 576/1344 = 996/1344

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 996 and 1344, which is 12. Divide both the numerator and denominator by 12.
Working: 996 ÷ 12/1344 ÷ 12 = 83/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 83 by denominator 112 produces a repeating decimal (approximately 0.741071, or 74.1071%).
Working: 83 ÷ 112 = 0.741071 (74.1071%)

Key Values:
- Simplified Fraction: 83/112
- Mixed Number Form: 83/112
- Decimal Value: 0.741071
- Percentage: 74.1071%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-20-64-plus-9-21/
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20/64 + 9/21 = 83/112

Simplified Fraction

83/112

Mixed Number

Proper (83/112)

Decimal Value

0.741071

Percentage

74.1071%

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Step-by-Step Solution: 20/64 + 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 20/64 by 21, and multiply the numerator and denominator of 9/21 by 64 so both fractions share the common base 1344.

20 × 21/64 × 21 = 420/1344 and 9 × 64/21 × 64 = 576/1344

Step 3

Add the Numerators

Now add the numerators (420 + 576 = 996) and keep the common denominator 1344 unchanged.

420 + 576/1344 = 996/1344

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 996 and 1344, which is 12. Divide both the numerator and denominator by 12.

996 ÷ 12/1344 ÷ 12 = 83/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 83 by denominator 112 produces a repeating decimal (approximately 0.741071, or 74.1071%).

83 ÷ 112 = 0.741071 (74.1071%)

Visual Representation

The diagram below illustrates 20/64 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`83/112`
Mixed Number Form	`83/112`
Decimal Form	`0.741071`
Percentage	`74.1071%`

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Frequently Asked Questions

What is 20/64 plus 9/21 as a fraction?

20/64 + 9/21 in simplest fraction form is 83/112.

What is 20/64 plus 9/21 as a decimal?

20/64 + 9/21 converted to a decimal is 0.741071.

What is 20/64 plus 9/21 as a percentage?

20/64 + 9/21 expressed as a percentage is 74.1071%.

Does 20/64 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.741071...) because the denominator contains prime factors other than 2 and 5.