What is 3/70 plus 2/13? (Answer: 179/910)

Exact Answer

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Problem: What is 3/70 plus 2/13?
Formula / Expression: 3/70 + 2/13
Final Answer: 179/910
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 70 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 70 × 13 = 910.
Working: LCD(70, 13) = 910

Step 2: Convert to Equivalent Fractions with Common Denominator 910
Multiply the numerator and denominator of 3/70 by 13, and multiply the numerator and denominator of 2/13 by 70 so both fractions share the common base 910.
Working: 3 × 13/70 × 13 = 39/910 and 2 × 70/13 × 70 = 140/910

Step 3: Add the Numerators
Now add the numerators (39 + 140 = 179) and keep the common denominator 910 unchanged.
Working: 39 + 140/910 = 179/910

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 179 and 910 is 1, confirming that 179/910 cannot be reduced further—it is already in its simplest irreducible form.
Working: 179/910

Step 5: Decimal & Percentage Representation
Dividing the numerator 179 by denominator 910 produces a repeating decimal (approximately 0.196703, or 19.6703%).
Working: 179 ÷ 910 = 0.196703 (19.6703%)

Key Values:
- Simplified Fraction: 179/910
- Mixed Number Form: 179/910
- Decimal Value: 0.196703
- Percentage: 19.6703%

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Solved with FractionsCalc:
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3/70 + 2/13 = 179/910

Simplified Fraction

179/910

Mixed Number

Proper (179/910)

Decimal Value

0.196703

Percentage

19.6703%

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Step-by-Step Solution: 3/70 + 2/13

Step 1

Find the Least Common Denominator (LCD)

The denominators 70 and 13 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 70 × 13 = 910.

LCD(70, 13) = 910

Step 2

Convert to Equivalent Fractions with Common Denominator 910

Multiply the numerator and denominator of 3/70 by 13, and multiply the numerator and denominator of 2/13 by 70 so both fractions share the common base 910.

3 × 13/70 × 13 = 39/910 and 2 × 70/13 × 70 = 140/910

Step 3

Add the Numerators

Now add the numerators (39 + 140 = 179) and keep the common denominator 910 unchanged.

39 + 140/910 = 179/910

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 179 and 910 is 1, confirming that 179/910 cannot be reduced further—it is already in its simplest irreducible form.

179/910

Step 5

Decimal & Percentage Representation

Dividing the numerator 179 by denominator 910 produces a repeating decimal (approximately 0.196703, or 19.6703%).

179 ÷ 910 = 0.196703 (19.6703%)

Visual Representation

The diagram below illustrates 3/70 plus 2/13 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`179/910`
Mixed Number Form	`179/910`
Decimal Form	`0.196703`
Percentage	`19.6703%`

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Frequently Asked Questions

What is 3/70 plus 2/13 as a fraction?

3/70 + 2/13 in simplest fraction form is 179/910.

What is 3/70 plus 2/13 as a decimal?

3/70 + 2/13 converted to a decimal is 0.196703.

What is 3/70 plus 2/13 as a percentage?

3/70 + 2/13 expressed as a percentage is 19.6703%.

Does 3/70 plus 2/13 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.196703...) because the denominator contains prime factors other than 2 and 5.