What is 3/7 plus 9/10? (Answer: 93/70)

Exact Answer

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Problem: What is 3/7 plus 9/10?
Formula / Expression: 3/7 + 9/10
Final Answer: 1 23/70 (93/70)
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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 9/10 by 7 so both fractions share the common base 70.
Working: 3 × 10/7 × 10 = 30/70 and 9 × 7/10 × 7 = 63/70

Step 3: Add the Numerators
Now add the numerators (30 + 63 = 93) and keep the common denominator 70 unchanged.
Working: 30 + 63/70 = 93/70

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 93 and 70 is 1, confirming that 93/70 cannot be reduced further—it is already in its simplest irreducible form.
Working: 93/70

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (93) is greater than the denominator (70), divide 93 by 70: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/70.
Working: 93/70 = 1 23/70

Step 6: Decimal & Percentage Representation
Dividing the numerator 93 by denominator 70 produces a repeating decimal (approximately 1.328571, or 132.8571%).
Working: 93 ÷ 70 = 1.328571 (132.8571%)

Key Values:
- Simplified Fraction: 93/70
- Mixed Number Form: 1 23/70
- Decimal Value: 1.328571
- Percentage: 132.8571%

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Solved with FractionsCalc:
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3/7 + 9/10 = 93/70

Simplified Fraction

93/70

Mixed Number

1 23/70

Decimal Value

1.328571

Percentage

132.8571%

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Step-by-Step Solution: 3/7 + 9/10

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 9/10 by 7 so both fractions share the common base 70.

3 × 10/7 × 10 = 30/70 and 9 × 7/10 × 7 = 63/70

Step 3

Add the Numerators

Now add the numerators (30 + 63 = 93) and keep the common denominator 70 unchanged.

30 + 63/70 = 93/70

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 93 and 70 is 1, confirming that 93/70 cannot be reduced further—it is already in its simplest irreducible form.

93/70

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (93) is greater than the denominator (70), divide 93 by 70: it goes in 1 whole time(s) with a remainder of 23, giving the mixed number 1 23/70.

93/70 = 123/70

Step 6

Decimal & Percentage Representation

Dividing the numerator 93 by denominator 70 produces a repeating decimal (approximately 1.328571, or 132.8571%).

93 ÷ 70 = 1.328571 (132.8571%)

Visual Representation

The diagram below illustrates 3/7 plus 9/10 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`93/70`
Mixed Number Form	`1 23/70`
Decimal Form	`1.328571`
Percentage	`132.8571%`

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Frequently Asked Questions

What is 3/7 plus 9/10 as a fraction?

3/7 + 9/10 in simplest fraction form is 93/70 (or 1 23/70 as a mixed number).

What is 3/7 plus 9/10 as a decimal?

3/7 + 9/10 converted to a decimal is 1.328571.

What is 3/7 plus 9/10 as a percentage?

3/7 + 9/10 expressed as a percentage is 132.8571%.

How do you write 3/7 plus 9/10 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 93/70 can be written as the mixed number 1 23/70.

Does 3/7 plus 9/10 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.328571...) because the denominator contains prime factors other than 2 and 5.