What is 20/60 plus 9/21? (Answer: 16/21)

Exact Answer

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Problem: What is 20/60 plus 9/21?
Formula / Expression: 20/60 + 9/21
Final Answer: 16/21
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 60 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 60 × 21 = 1260, keeping the calculation simpler).
Working: LCD(60, 21) = 420

Step 2: Convert to Equivalent Fractions with Common Denominator 420
Multiply the numerator and denominator of 20/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.
Working: 20 × 7/60 × 7 = 140/420 and 9 × 20/21 × 20 = 180/420

Step 3: Add the Numerators
Now add the numerators (140 + 180 = 320) and keep the common denominator 420 unchanged.
Working: 140 + 180/420 = 320/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 320 and 420, which is 20. Divide both the numerator and denominator by 20.
Working: 320 ÷ 20/420 ÷ 20 = 16/21

Step 5: Decimal & Percentage Representation
Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).
Working: 16 ÷ 21 = 0.761905 (76.1905%)

Key Values:
- Simplified Fraction: 16/21
- Mixed Number Form: 16/21
- Decimal Value: 0.761905
- Percentage: 76.1905%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-20-60-plus-9-21/
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20/60 + 9/21 = 16/21

Simplified Fraction

16/21

Mixed Number

Proper (16/21)

Decimal Value

0.761905

Percentage

76.1905%

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Step-by-Step Solution: 20/60 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 60 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 420 (which is smaller than their product 60 × 21 = 1260, keeping the calculation simpler).

LCD(60, 21) = 420

Step 2

Convert to Equivalent Fractions with Common Denominator 420

Multiply the numerator and denominator of 20/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.

20 × 7/60 × 7 = 140/420 and 9 × 20/21 × 20 = 180/420

Step 3

Add the Numerators

Now add the numerators (140 + 180 = 320) and keep the common denominator 420 unchanged.

140 + 180/420 = 320/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 320 and 420, which is 20. Divide both the numerator and denominator by 20.

320 ÷ 20/420 ÷ 20 = 16/21

Step 5

Decimal & Percentage Representation

Dividing the numerator 16 by denominator 21 produces a repeating decimal (approximately 0.761905, or 76.1905%).

16 ÷ 21 = 0.761905 (76.1905%)

Visual Representation

The diagram below illustrates 20/60 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`16/21`
Mixed Number Form	`16/21`
Decimal Form	`0.761905`
Percentage	`76.1905%`

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Frequently Asked Questions

What is 20/60 plus 9/21 as a fraction?

20/60 + 9/21 in simplest fraction form is 16/21.

What is 20/60 plus 9/21 as a decimal?

20/60 + 9/21 converted to a decimal is 0.761905.

What is 20/60 plus 9/21 as a percentage?

20/60 + 9/21 expressed as a percentage is 76.1905%.

Does 20/60 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.761905...) because the denominator contains prime factors other than 2 and 5.