What is 21/60 plus 9/21? (Answer: 109/140)

Exact Answer

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Problem: What is 21/60 plus 9/21?
Formula / Expression: 21/60 + 9/21
Final Answer: 109/140
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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 21/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.
Working: 21 × 7/60 × 7 = 147/420 and 9 × 20/21 × 20 = 180/420

Step 3: Add the Numerators
Now add the numerators (147 + 180 = 327) and keep the common denominator 420 unchanged.
Working: 147 + 180/420 = 327/420

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 327 and 420, which is 3. Divide both the numerator and denominator by 3.
Working: 327 ÷ 3/420 ÷ 3 = 109/140

Step 5: Decimal & Percentage Representation
Dividing the numerator 109 by denominator 140 produces a repeating decimal (approximately 0.778571, or 77.8571%).
Working: 109 ÷ 140 = 0.778571 (77.8571%)

Key Values:
- Simplified Fraction: 109/140
- Mixed Number Form: 109/140
- Decimal Value: 0.778571
- Percentage: 77.8571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-21-60-plus-9-21/
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21/60 + 9/21 = 109/140

Simplified Fraction

109/140

Mixed Number

Proper (109/140)

Decimal Value

0.778571

Percentage

77.8571%

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Step-by-Step Solution: 21/60 + 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 21/60 by 7, and multiply the numerator and denominator of 9/21 by 20 so both fractions share the common base 420.

21 × 7/60 × 7 = 147/420 and 9 × 20/21 × 20 = 180/420

Step 3

Add the Numerators

Now add the numerators (147 + 180 = 327) and keep the common denominator 420 unchanged.

147 + 180/420 = 327/420

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 327 and 420, which is 3. Divide both the numerator and denominator by 3.

327 ÷ 3/420 ÷ 3 = 109/140

Step 5

Decimal & Percentage Representation

Dividing the numerator 109 by denominator 140 produces a repeating decimal (approximately 0.778571, or 77.8571%).

109 ÷ 140 = 0.778571 (77.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`109/140`
Mixed Number Form	`109/140`
Decimal Form	`0.778571`
Percentage	`77.8571%`

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Frequently Asked Questions

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

21/60 + 9/21 in simplest fraction form is 109/140.

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

21/60 + 9/21 converted to a decimal is 0.778571.

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

21/60 + 9/21 expressed as a percentage is 77.8571%.

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

It results in a repeating decimal (approximately 0.778571...) because the denominator contains prime factors other than 2 and 5.