What is 8/35 plus 12/21? (Answer: 4/5)

Exact Answer

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Problem: What is 8/35 plus 12/21?
Formula / Expression: 8/35 + 12/21
Final Answer: 4/5
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 105
Multiply the numerator and denominator of 8/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.
Working: 8 × 3/35 × 3 = 24/105 and 12 × 5/21 × 5 = 60/105

Step 3: Add the Numerators
Now add the numerators (24 + 60 = 84) and keep the common denominator 105 unchanged.
Working: 24 + 60/105 = 84/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 84 and 105, which is 21. Divide both the numerator and denominator by 21.
Working: 84 ÷ 21/105 ÷ 21 = 4/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).
Working: 4 ÷ 5 = 0.8 (80%)

Key Values:
- Simplified Fraction: 4/5
- Mixed Number Form: 4/5
- Decimal Value: 0.8
- Percentage: 80%

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Solved with FractionsCalc:
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8/35 + 12/21 = 4/5

Simplified Fraction

4/5

Mixed Number

Proper (4/5)

Decimal Value

0.8

Percentage

80%

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Step-by-Step Solution: 8/35 + 12/21

Step 1

Find the Least Common Denominator (LCD)

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

LCD(35, 21) = 105

Step 2

Convert to Equivalent Fractions with Common Denominator 105

Multiply the numerator and denominator of 8/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.

8 × 3/35 × 3 = 24/105 and 12 × 5/21 × 5 = 60/105

Step 3

Add the Numerators

Now add the numerators (24 + 60 = 84) and keep the common denominator 105 unchanged.

24 + 60/105 = 84/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 84 and 105, which is 21. Divide both the numerator and denominator by 21.

84 ÷ 21/105 ÷ 21 = 4/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 4 by denominator 5 yields an exact terminating decimal of 0.8 (or 80%).

4 ÷ 5 = 0.8 (80%)

Visual Representation

The diagram below illustrates 8/35 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`4/5`
Mixed Number Form	`4/5`
Decimal Form	`0.8`
Percentage	`80%`

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Frequently Asked Questions

What is 8/35 plus 12/21 as a fraction?

8/35 + 12/21 in simplest fraction form is 4/5.

What is 8/35 plus 12/21 as a decimal?

8/35 + 12/21 converted to a decimal is 0.8.

What is 8/35 plus 12/21 as a percentage?

8/35 + 12/21 expressed as a percentage is 80%.

Does 8/35 plus 12/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.8) because the denominator in simplest terms contains only prime factors 2 and/or 5.