What is 3/10 plus 5/7? (Answer: 71/70)

Exact Answer

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Problem: What is 3/10 plus 5/7?
Formula / Expression: 3/10 + 5/7
Final Answer: 1 1/70 (71/70)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.
Working: LCD(10, 7) = 70

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 3/10 by 7, and multiply the numerator and denominator of 5/7 by 10 so both fractions share the common base 70.
Working: 3 × 7/10 × 7 = 21/70 and 5 × 10/7 × 10 = 50/70

Step 3: Add the Numerators
Now add the numerators (21 + 50 = 71) and keep the common denominator 70 unchanged.
Working: 21 + 50/70 = 71/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 70 is 1, confirming that 71/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/70

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (71) is greater than the denominator (70), divide 71 by 70: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/70.
Working: 71/70 = 1 1/70

Step 6: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 70 produces a repeating decimal (approximately 1.014286, or 101.4286%).
Working: 71 ÷ 70 = 1.014286 (101.4286%)

Key Values:
- Simplified Fraction: 71/70
- Mixed Number Form: 1 1/70
- Decimal Value: 1.014286
- Percentage: 101.4286%

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Solved with FractionsCalc:
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3/10 + 5/7 = 71/70

Simplified Fraction

71/70

Mixed Number

1 1/70

Decimal Value

1.014286

Percentage

101.4286%

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Step-by-Step Solution: 3/10 + 5/7

Step 1

Find the Least Common Denominator (LCD)

The denominators 10 and 7 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 10 × 7 = 70.

LCD(10, 7) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

Multiply the numerator and denominator of 3/10 by 7, and multiply the numerator and denominator of 5/7 by 10 so both fractions share the common base 70.

3 × 7/10 × 7 = 21/70 and 5 × 10/7 × 10 = 50/70

Step 3

Add the Numerators

Now add the numerators (21 + 50 = 71) and keep the common denominator 70 unchanged.

21 + 50/70 = 71/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 70 is 1, confirming that 71/70 cannot be reduced further—it is already in its simplest irreducible form.

71/70

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (71) is greater than the denominator (70), divide 71 by 70: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/70.

71/70 = 11/70

Step 6

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 70 produces a repeating decimal (approximately 1.014286, or 101.4286%).

71 ÷ 70 = 1.014286 (101.4286%)

Visual Representation

The diagram below illustrates 3/10 plus 5/7 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/70`
Mixed Number Form	`1 1/70`
Decimal Form	`1.014286`
Percentage	`101.4286%`

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Frequently Asked Questions

What is 3/10 plus 5/7 as a fraction?

3/10 + 5/7 in simplest fraction form is 71/70 (or 1 1/70 as a mixed number).

What is 3/10 plus 5/7 as a decimal?

3/10 + 5/7 converted to a decimal is 1.014286.

What is 3/10 plus 5/7 as a percentage?

3/10 + 5/7 expressed as a percentage is 101.4286%.

How do you write 3/10 plus 5/7 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 71/70 can be written as the mixed number 1 1/70.

Does 3/10 plus 5/7 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.014286...) because the denominator contains prime factors other than 2 and 5.