What is 3/7 plus 7/10? (Answer: 79/70)

Exact Answer

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Problem: What is 3/7 plus 7/10?
Formula / Expression: 3/7 + 7/10
Final Answer: 1 9/70 (79/70)
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 70
Multiply the numerator and denominator of 3/7 by 10, and multiply the numerator and denominator of 7/10 by 7 so both fractions share the common base 70.
Working: 3 × 10/7 × 10 = 30/70 and 7 × 7/10 × 7 = 49/70

Step 3: Add the Numerators
Now add the numerators (30 + 49 = 79) and keep the common denominator 70 unchanged.
Working: 30 + 49/70 = 79/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 79 and 70 is 1, confirming that 79/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 79/70

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (79) is greater than the denominator (70), divide 79 by 70: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/70.
Working: 79/70 = 1 9/70

Step 6: Decimal & Percentage Representation
Dividing the numerator 79 by denominator 70 produces a repeating decimal (approximately 1.128571, or 112.8571%).
Working: 79 ÷ 70 = 1.128571 (112.8571%)

Key Values:
- Simplified Fraction: 79/70
- Mixed Number Form: 1 9/70
- Decimal Value: 1.128571
- Percentage: 112.8571%

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Solved with FractionsCalc:
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3/7 + 7/10 = 79/70

Simplified Fraction

79/70

Mixed Number

1 9/70

Decimal Value

1.128571

Percentage

112.8571%

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

Step 1

Find the Least Common Denominator (LCD)

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

LCD(7, 10) = 70

Step 2

Convert to Equivalent Fractions with Common Denominator 70

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

3 × 10/7 × 10 = 30/70 and 7 × 7/10 × 7 = 49/70

Step 3

Add the Numerators

Now add the numerators (30 + 49 = 79) and keep the common denominator 70 unchanged.

30 + 49/70 = 79/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 79 and 70 is 1, confirming that 79/70 cannot be reduced further—it is already in its simplest irreducible form.

79/70

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (79) is greater than the denominator (70), divide 79 by 70: it goes in 1 whole time(s) with a remainder of 9, giving the mixed number 1 9/70.

79/70 = 19/70

Step 6

Decimal & Percentage Representation

Dividing the numerator 79 by denominator 70 produces a repeating decimal (approximately 1.128571, or 112.8571%).

79 ÷ 70 = 1.128571 (112.8571%)

Visual Representation

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

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`79/70`
Mixed Number Form	`1 9/70`
Decimal Form	`1.128571`
Percentage	`112.8571%`

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Frequently Asked Questions

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

3/7 + 7/10 in simplest fraction form is 79/70 (or 1 9/70 as a mixed number).

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

3/7 + 7/10 converted to a decimal is 1.128571.

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

3/7 + 7/10 expressed as a percentage is 112.8571%.

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

Because the numerator is greater than the denominator, the improper fraction 79/70 can be written as the mixed number 1 9/70.

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

It results in a repeating decimal (approximately 1.128571...) because the denominator contains prime factors other than 2 and 5.