What is 21/40 plus 12/21? (Answer: 307/280)

Exact Answer

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Problem: What is 21/40 plus 12/21?
Formula / Expression: 21/40 + 12/21
Final Answer: 1 27/280 (307/280)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.
Working: LCD(40, 21) = 840

Step 2: Convert to Equivalent Fractions with Common Denominator 840
Multiply the numerator and denominator of 21/40 by 21, and multiply the numerator and denominator of 12/21 by 40 so both fractions share the common base 840.
Working: 21 × 21/40 × 21 = 441/840 and 12 × 40/21 × 40 = 480/840

Step 3: Add the Numerators
Now add the numerators (441 + 480 = 921) and keep the common denominator 840 unchanged.
Working: 441 + 480/840 = 921/840

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 921 and 840, which is 3. Divide both the numerator and denominator by 3.
Working: 921 ÷ 3/840 ÷ 3 = 307/280

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (307) is greater than the denominator (280), divide 307 by 280: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/280.
Working: 307/280 = 1 27/280

Step 6: Decimal & Percentage Representation
Dividing the numerator 307 by denominator 280 produces a repeating decimal (approximately 1.096429, or 109.6429%).
Working: 307 ÷ 280 = 1.096429 (109.6429%)

Key Values:
- Simplified Fraction: 307/280
- Mixed Number Form: 1 27/280
- Decimal Value: 1.096429
- Percentage: 109.6429%

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21/40 + 12/21 = 307/280

Simplified Fraction

307/280

Mixed Number

1 27/280

Decimal Value

1.096429

Percentage

109.6429%

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Step-by-Step Solution: 21/40 + 12/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 40 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 40 × 21 = 840.

LCD(40, 21) = 840

Step 2

Convert to Equivalent Fractions with Common Denominator 840

Multiply the numerator and denominator of 21/40 by 21, and multiply the numerator and denominator of 12/21 by 40 so both fractions share the common base 840.

21 × 21/40 × 21 = 441/840 and 12 × 40/21 × 40 = 480/840

Step 3

Add the Numerators

Now add the numerators (441 + 480 = 921) and keep the common denominator 840 unchanged.

441 + 480/840 = 921/840

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 921 and 840, which is 3. Divide both the numerator and denominator by 3.

921 ÷ 3/840 ÷ 3 = 307/280

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (307) is greater than the denominator (280), divide 307 by 280: it goes in 1 whole time(s) with a remainder of 27, giving the mixed number 1 27/280.

307/280 = 127/280

Step 6

Decimal & Percentage Representation

Dividing the numerator 307 by denominator 280 produces a repeating decimal (approximately 1.096429, or 109.6429%).

307 ÷ 280 = 1.096429 (109.6429%)

Visual Representation

The diagram below illustrates 21/40 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`307/280`
Mixed Number Form	`1 27/280`
Decimal Form	`1.096429`
Percentage	`109.6429%`

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Frequently Asked Questions

What is 21/40 plus 12/21 as a fraction?

21/40 + 12/21 in simplest fraction form is 307/280 (or 1 27/280 as a mixed number).

What is 21/40 plus 12/21 as a decimal?

21/40 + 12/21 converted to a decimal is 1.096429.

What is 21/40 plus 12/21 as a percentage?

21/40 + 12/21 expressed as a percentage is 109.6429%.

How do you write 21/40 plus 12/21 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 307/280 can be written as the mixed number 1 27/280.

Does 21/40 plus 12/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.096429...) because the denominator contains prime factors other than 2 and 5.