What is 12/21 plus 20/35? (Answer: 8/7)

Exact Answer

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Problem: What is 12/21 plus 20/35?
Formula / Expression: 12/21 + 20/35
Final Answer: 1 1/7 (8/7)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).
Working: LCD(21, 35) = 105

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 12/21 by 5, and multiply the numerator and denominator of 20/35 by 3 so both fractions share the common base 105.
Working: 12 × 5/21 × 5 = 60/105 and 20 × 3/35 × 3 = 60/105

Step 3: Add the Numerators
Now add the numerators (60 + 60 = 120) and keep the common denominator 105 unchanged.
Working: 60 + 60/105 = 120/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 120 and 105, which is 15. Divide both the numerator and denominator by 15.
Working: 120 ÷ 15/105 ÷ 15 = 8/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.
Working: 8/7 = 1 1/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).
Working: 8 ÷ 7 = 1.142857 (114.2857%)

Key Values:
- Simplified Fraction: 8/7
- Mixed Number Form: 1 1/7
- Decimal Value: 1.142857
- Percentage: 114.2857%

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12/21 + 20/35 = 8/7

Simplified Fraction

8/7

Mixed Number

1 1/7

Decimal Value

1.142857

Percentage

114.2857%

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Step-by-Step Solution: 12/21 + 20/35

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 35 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 105 (which is smaller than their product 21 × 35 = 735, keeping the calculation simpler).

LCD(21, 35) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 12/21 by 5, and multiply the numerator and denominator of 20/35 by 3 so both fractions share the common base 105.

12 × 5/21 × 5 = 60/105 and 20 × 3/35 × 3 = 60/105

Step 3

Add the Numerators

Now add the numerators (60 + 60 = 120) and keep the common denominator 105 unchanged.

60 + 60/105 = 120/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 120 and 105, which is 15. Divide both the numerator and denominator by 15.

120 ÷ 15/105 ÷ 15 = 8/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.

8/7 = 11/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).

8 ÷ 7 = 1.142857 (114.2857%)

Visual Representation

The diagram below illustrates 12/21 plus 20/35 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/7`
Mixed Number Form	`1 1/7`
Decimal Form	`1.142857`
Percentage	`114.2857%`

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Frequently Asked Questions

What is 12/21 plus 20/35 as a fraction?

12/21 + 20/35 in simplest fraction form is 8/7 (or 1 1/7 as a mixed number).

What is 12/21 plus 20/35 as a decimal?

12/21 + 20/35 converted to a decimal is 1.142857.

What is 12/21 plus 20/35 as a percentage?

12/21 + 20/35 expressed as a percentage is 114.2857%.

How do you write 12/21 plus 20/35 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 8/7 can be written as the mixed number 1 1/7.

Does 12/21 plus 20/35 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.142857...) because the denominator contains prime factors other than 2 and 5.