What is 9/35 plus 3/4? (Answer: 141/140)

Exact Answer

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Problem: What is 9/35 plus 3/4?
Formula / Expression: 9/35 + 3/4
Final Answer: 1 1/140 (141/140)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 35 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 4 = 140.
Working: LCD(35, 4) = 140

Step 2: Convert to Equivalent Fractions with Common Denominator 140
Multiply the numerator and denominator of 9/35 by 4, and multiply the numerator and denominator of 3/4 by 35 so both fractions share the common base 140.
Working: 9 × 4/35 × 4 = 36/140 and 3 × 35/4 × 35 = 105/140

Step 3: Add the Numerators
Now add the numerators (36 + 105 = 141) and keep the common denominator 140 unchanged.
Working: 36 + 105/140 = 141/140

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 141 and 140 is 1, confirming that 141/140 cannot be reduced further—it is already in its simplest irreducible form.
Working: 141/140

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (141) is greater than the denominator (140), divide 141 by 140: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/140.
Working: 141/140 = 1 1/140

Step 6: Decimal & Percentage Representation
Dividing the numerator 141 by denominator 140 produces a repeating decimal (approximately 1.007143, or 100.7143%).
Working: 141 ÷ 140 = 1.007143 (100.7143%)

Key Values:
- Simplified Fraction: 141/140
- Mixed Number Form: 1 1/140
- Decimal Value: 1.007143
- Percentage: 100.7143%

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9/35 + 3/4 = 141/140

Simplified Fraction

141/140

Mixed Number

1 1/140

Decimal Value

1.007143

Percentage

100.7143%

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Step-by-Step Solution: 9/35 + 3/4

Step 1

Find the Least Common Denominator (LCD)

The denominators 35 and 4 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 35 × 4 = 140.

LCD(35, 4) = 140

Step 2

Convert to Equivalent Fractions with Common Denominator 140

Multiply the numerator and denominator of 9/35 by 4, and multiply the numerator and denominator of 3/4 by 35 so both fractions share the common base 140.

9 × 4/35 × 4 = 36/140 and 3 × 35/4 × 35 = 105/140

Step 3

Add the Numerators

Now add the numerators (36 + 105 = 141) and keep the common denominator 140 unchanged.

36 + 105/140 = 141/140

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 141 and 140 is 1, confirming that 141/140 cannot be reduced further—it is already in its simplest irreducible form.

141/140

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (141) is greater than the denominator (140), divide 141 by 140: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/140.

141/140 = 11/140

Step 6

Decimal & Percentage Representation

Dividing the numerator 141 by denominator 140 produces a repeating decimal (approximately 1.007143, or 100.7143%).

141 ÷ 140 = 1.007143 (100.7143%)

Visual Representation

The diagram below illustrates 9/35 plus 3/4 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`141/140`
Mixed Number Form	`1 1/140`
Decimal Form	`1.007143`
Percentage	`100.7143%`

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Frequently Asked Questions

What is 9/35 plus 3/4 as a fraction?

9/35 + 3/4 in simplest fraction form is 141/140 (or 1 1/140 as a mixed number).

What is 9/35 plus 3/4 as a decimal?

9/35 + 3/4 converted to a decimal is 1.007143.

What is 9/35 plus 3/4 as a percentage?

9/35 + 3/4 expressed as a percentage is 100.7143%.

How do you write 9/35 plus 3/4 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 141/140 can be written as the mixed number 1 1/140.

Does 9/35 plus 3/4 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.007143...) because the denominator contains prime factors other than 2 and 5.