What is 2/35 plus 2/20? (Answer: 11/70)

Exact Answer

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Problem: What is 2/35 plus 2/20?
Formula / Expression: 2/35 + 2/20
Final Answer: 11/70
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 20 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 140 (which is smaller than their product 35 × 20 = 700, keeping the calculation simpler).
Working: LCD(35, 20) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 2/35 by 4, and multiply the numerator and denominator of 2/20 by 7 so both fractions share the common base 140.
Working: 2 × 4/35 × 4 = 8/140 and 2 × 7/20 × 7 = 14/140

Step 3: Add the Numerators
Now add the numerators (8 + 14 = 22) and keep the common denominator 140 unchanged.
Working: 8 + 14/140 = 22/140

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 22 and 140, which is 2. Divide both the numerator and denominator by 2.
Working: 22 ÷ 2/140 ÷ 2 = 11/70

Step 5: Decimal & Percentage Representation
Dividing the numerator 11 by denominator 70 produces a repeating decimal (approximately 0.157143, or 15.7143%).
Working: 11 ÷ 70 = 0.157143 (15.7143%)

Key Values:
- Simplified Fraction: 11/70
- Mixed Number Form: 11/70
- Decimal Value: 0.157143
- Percentage: 15.7143%

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2/35 + 2/20 = 11/70

Simplified Fraction

11/70

Mixed Number

Proper (11/70)

Decimal Value

0.157143

Percentage

15.7143%

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Step-by-Step Solution: 2/35 + 2/20

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 20 share a common factor (GCD = 5). Finding their Least Common Multiple gives an LCD of 140 (which is smaller than their product 35 × 20 = 700, keeping the calculation simpler).

LCD(35, 20) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 2/35 by 4, and multiply the numerator and denominator of 2/20 by 7 so both fractions share the common base 140.

2 × 4/35 × 4 = 8/140 and 2 × 7/20 × 7 = 14/140

Step 3

Add the Numerators

Now add the numerators (8 + 14 = 22) and keep the common denominator 140 unchanged.

8 + 14/140 = 22/140

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 22 and 140, which is 2. Divide both the numerator and denominator by 2.

22 ÷ 2/140 ÷ 2 = 11/70

Step 5

Decimal & Percentage Representation

Dividing the numerator 11 by denominator 70 produces a repeating decimal (approximately 0.157143, or 15.7143%).

11 ÷ 70 = 0.157143 (15.7143%)

Visual Representation

The diagram below illustrates 2/35 plus 2/20 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`11/70`
Mixed Number Form	`11/70`
Decimal Form	`0.157143`
Percentage	`15.7143%`

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Frequently Asked Questions

What is 2/35 plus 2/20 as a fraction?

2/35 + 2/20 in simplest fraction form is 11/70.

What is 2/35 plus 2/20 as a decimal?

2/35 + 2/20 converted to a decimal is 0.157143.

What is 2/35 plus 2/20 as a percentage?

2/35 + 2/20 expressed as a percentage is 15.7143%.

Does 2/35 plus 2/20 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.157143...) because the denominator contains prime factors other than 2 and 5.