What is 9/21 plus 14/32? (Answer: 97/112)

Exact Answer

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Problem: What is 9/21 plus 14/32?
Formula / Expression: 9/21 + 14/32
Final Answer: 97/112
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 21 and 32 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 32 = 672.
Working: LCD(21, 32) = 672

Step 2: Convert to Equivalent Fractions with Common Denominator 672
Multiply the numerator and denominator of 9/21 by 32, and multiply the numerator and denominator of 14/32 by 21 so both fractions share the common base 672.
Working: 9 × 32/21 × 32 = 288/672 and 14 × 21/32 × 21 = 294/672

Step 3: Add the Numerators
Now add the numerators (288 + 294 = 582) and keep the common denominator 672 unchanged.
Working: 288 + 294/672 = 582/672

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 582 and 672, which is 6. Divide both the numerator and denominator by 6.
Working: 582 ÷ 6/672 ÷ 6 = 97/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 97 by denominator 112 produces a repeating decimal (approximately 0.866071, or 86.6071%).
Working: 97 ÷ 112 = 0.866071 (86.6071%)

Key Values:
- Simplified Fraction: 97/112
- Mixed Number Form: 97/112
- Decimal Value: 0.866071
- Percentage: 86.6071%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-21-plus-14-32/
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9/21 + 14/32 = 97/112

Simplified Fraction

97/112

Mixed Number

Proper (97/112)

Decimal Value

0.866071

Percentage

86.6071%

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Step-by-Step Solution: 9/21 + 14/32

Step 1

Find the Least Common Denominator (LCD)

The denominators 21 and 32 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 21 × 32 = 672.

LCD(21, 32) = 672

Step 2

Convert to Equivalent Fractions with Common Denominator 672

Multiply the numerator and denominator of 9/21 by 32, and multiply the numerator and denominator of 14/32 by 21 so both fractions share the common base 672.

9 × 32/21 × 32 = 288/672 and 14 × 21/32 × 21 = 294/672

Step 3

Add the Numerators

Now add the numerators (288 + 294 = 582) and keep the common denominator 672 unchanged.

288 + 294/672 = 582/672

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 582 and 672, which is 6. Divide both the numerator and denominator by 6.

582 ÷ 6/672 ÷ 6 = 97/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 97 by denominator 112 produces a repeating decimal (approximately 0.866071, or 86.6071%).

97 ÷ 112 = 0.866071 (86.6071%)

Visual Representation

The diagram below illustrates 9/21 plus 14/32 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`97/112`
Mixed Number Form	`97/112`
Decimal Form	`0.866071`
Percentage	`86.6071%`

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Frequently Asked Questions

What is 9/21 plus 14/32 as a fraction?

9/21 + 14/32 in simplest fraction form is 97/112.

What is 9/21 plus 14/32 as a decimal?

9/21 + 14/32 converted to a decimal is 0.866071.

What is 9/21 plus 14/32 as a percentage?

9/21 + 14/32 expressed as a percentage is 86.6071%.

Does 9/21 plus 14/32 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.866071...) because the denominator contains prime factors other than 2 and 5.