What is 3/8 plus 9/21? (Answer: 45/56)

Exact Answer

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Problem: What is 3/8 plus 9/21?
Formula / Expression: 3/8 + 9/21
Final Answer: 45/56
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.
Working: LCD(8, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 3/8 by 21, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.
Working: 3 × 21/8 × 21 = 63/168 and 9 × 8/21 × 8 = 72/168

Step 3: Add the Numerators
Now add the numerators (63 + 72 = 135) and keep the common denominator 168 unchanged.
Working: 63 + 72/168 = 135/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 168, which is 3. Divide both the numerator and denominator by 3.
Working: 135 ÷ 3/168 ÷ 3 = 45/56

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 56 produces a repeating decimal (approximately 0.803571, or 80.3571%).
Working: 45 ÷ 56 = 0.803571 (80.3571%)

Key Values:
- Simplified Fraction: 45/56
- Mixed Number Form: 45/56
- Decimal Value: 0.803571
- Percentage: 80.3571%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-3-8-plus-9-21/
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3/8 + 9/21 = 45/56

Simplified Fraction

45/56

Mixed Number

Proper (45/56)

Decimal Value

0.803571

Percentage

80.3571%

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Step-by-Step Solution: 3/8 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 21 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 8 × 21 = 168.

LCD(8, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 3/8 by 21, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.

3 × 21/8 × 21 = 63/168 and 9 × 8/21 × 8 = 72/168

Step 3

Add the Numerators

Now add the numerators (63 + 72 = 135) and keep the common denominator 168 unchanged.

63 + 72/168 = 135/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 168, which is 3. Divide both the numerator and denominator by 3.

135 ÷ 3/168 ÷ 3 = 45/56

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 56 produces a repeating decimal (approximately 0.803571, or 80.3571%).

45 ÷ 56 = 0.803571 (80.3571%)

Visual Representation

The diagram below illustrates 3/8 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/56`
Mixed Number Form	`45/56`
Decimal Form	`0.803571`
Percentage	`80.3571%`

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Frequently Asked Questions

What is 3/8 plus 9/21 as a fraction?

3/8 + 9/21 in simplest fraction form is 45/56.

What is 3/8 plus 9/21 as a decimal?

3/8 + 9/21 converted to a decimal is 0.803571.

What is 3/8 plus 9/21 as a percentage?

3/8 + 9/21 expressed as a percentage is 80.3571%.

Does 3/8 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.803571...) because the denominator contains prime factors other than 2 and 5.