What is 5/7 plus 9/12? (Answer: 41/28)

Exact Answer

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Problem: What is 5/7 plus 9/12?
Formula / Expression: 5/7 + 9/12
Final Answer: 1 13/28 (41/28)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 7 and 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 12 = 84.
Working: LCD(7, 12) = 84

Step 2: Convert to Equivalent Fractions with Common Denominator 84
Multiply the numerator and denominator of 5/7 by 12, and multiply the numerator and denominator of 9/12 by 7 so both fractions share the common base 84.
Working: 5 × 12/7 × 12 = 60/84 and 9 × 7/12 × 7 = 63/84

Step 3: Add the Numerators
Now add the numerators (60 + 63 = 123) and keep the common denominator 84 unchanged.
Working: 60 + 63/84 = 123/84

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 123 and 84, which is 3. Divide both the numerator and denominator by 3.
Working: 123 ÷ 3/84 ÷ 3 = 41/28

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (41) is greater than the denominator (28), divide 41 by 28: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/28.
Working: 41/28 = 1 13/28

Step 6: Decimal & Percentage Representation
Dividing the numerator 41 by denominator 28 produces a repeating decimal (approximately 1.464286, or 146.4286%).
Working: 41 ÷ 28 = 1.464286 (146.4286%)

Key Values:
- Simplified Fraction: 41/28
- Mixed Number Form: 1 13/28
- Decimal Value: 1.464286
- Percentage: 146.4286%

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Solved with FractionsCalc:
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5/7 + 9/12 = 41/28

Simplified Fraction

41/28

Mixed Number

1 13/28

Decimal Value

1.464286

Percentage

146.4286%

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Step-by-Step Solution: 5/7 + 9/12

Step 1

Find the Least Common Denominator (LCD)

The denominators 7 and 12 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 7 × 12 = 84.

LCD(7, 12) = 84

Step 2

Convert to Equivalent Fractions with Common Denominator 84

Multiply the numerator and denominator of 5/7 by 12, and multiply the numerator and denominator of 9/12 by 7 so both fractions share the common base 84.

5 × 12/7 × 12 = 60/84 and 9 × 7/12 × 7 = 63/84

Step 3

Add the Numerators

Now add the numerators (60 + 63 = 123) and keep the common denominator 84 unchanged.

60 + 63/84 = 123/84

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 123 and 84, which is 3. Divide both the numerator and denominator by 3.

123 ÷ 3/84 ÷ 3 = 41/28

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (41) is greater than the denominator (28), divide 41 by 28: it goes in 1 whole time(s) with a remainder of 13, giving the mixed number 1 13/28.

41/28 = 113/28

Step 6

Decimal & Percentage Representation

Dividing the numerator 41 by denominator 28 produces a repeating decimal (approximately 1.464286, or 146.4286%).

41 ÷ 28 = 1.464286 (146.4286%)

Visual Representation

The diagram below illustrates 5/7 plus 9/12 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`41/28`
Mixed Number Form	`1 13/28`
Decimal Form	`1.464286`
Percentage	`146.4286%`

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Frequently Asked Questions

What is 5/7 plus 9/12 as a fraction?

5/7 + 9/12 in simplest fraction form is 41/28 (or 1 13/28 as a mixed number).

What is 5/7 plus 9/12 as a decimal?

5/7 + 9/12 converted to a decimal is 1.464286.

What is 5/7 plus 9/12 as a percentage?

5/7 + 9/12 expressed as a percentage is 146.4286%.

How do you write 5/7 plus 9/12 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 41/28 can be written as the mixed number 1 13/28.

Does 5/7 plus 9/12 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.464286...) because the denominator contains prime factors other than 2 and 5.