What is 1/35 plus 12/21? (Answer: 3/5)

Exact Answer

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Problem: What is 1/35 plus 12/21?
Formula / Expression: 1/35 + 12/21
Final Answer: 3/5
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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 1/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.
Working: 1 × 3/35 × 3 = 3/105 and 12 × 5/21 × 5 = 60/105

Step 3: Add the Numerators
Now add the numerators (3 + 60 = 63) and keep the common denominator 105 unchanged.
Working: 3 + 60/105 = 63/105

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 63 and 105, which is 21. Divide both the numerator and denominator by 21.
Working: 63 ÷ 21/105 ÷ 21 = 3/5

Step 5: Decimal & Percentage Representation
Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).
Working: 3 ÷ 5 = 0.6 (60%)

Key Values:
- Simplified Fraction: 3/5
- Mixed Number Form: 3/5
- Decimal Value: 0.6
- Percentage: 60%

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Solved with FractionsCalc:
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1/35 + 12/21 = 3/5

Simplified Fraction

3/5

Mixed Number

Proper (3/5)

Decimal Value

0.6

Percentage

60%

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Step-by-Step Solution: 1/35 + 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 1/35 by 3, and multiply the numerator and denominator of 12/21 by 5 so both fractions share the common base 105.

1 × 3/35 × 3 = 3/105 and 12 × 5/21 × 5 = 60/105

Step 3

Add the Numerators

Now add the numerators (3 + 60 = 63) and keep the common denominator 105 unchanged.

3 + 60/105 = 63/105

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 63 and 105, which is 21. Divide both the numerator and denominator by 21.

63 ÷ 21/105 ÷ 21 = 3/5

Step 5

Decimal & Percentage Representation

Dividing the numerator 3 by denominator 5 yields an exact terminating decimal of 0.6 (or 60%).

3 ÷ 5 = 0.6 (60%)

Visual Representation

The diagram below illustrates 1/35 plus 12/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`3/5`
Mixed Number Form	`3/5`
Decimal Form	`0.6`
Percentage	`60%`

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Frequently Asked Questions

What is 1/35 plus 12/21 as a fraction?

1/35 + 12/21 in simplest fraction form is 3/5.

What is 1/35 plus 12/21 as a decimal?

1/35 + 12/21 converted to a decimal is 0.6.

What is 1/35 plus 12/21 as a percentage?

1/35 + 12/21 expressed as a percentage is 60%.

Does 1/35 plus 12/21 result in a terminating or repeating decimal?

It results in an exact terminating decimal (0.6) because the denominator in simplest terms contains only prime factors 2 and/or 5.