What is 9/48 plus 9/21? (Answer: 69/112)

Exact Answer

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Problem: What is 9/48 plus 9/21?
Formula / Expression: 9/48 + 9/21
Final Answer: 69/112
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).
Working: LCD(48, 21) = 336

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 9/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.
Working: 9 × 7/48 × 7 = 63/336 and 9 × 16/21 × 16 = 144/336

Step 3: Add the Numerators
Now add the numerators (63 + 144 = 207) and keep the common denominator 336 unchanged.
Working: 63 + 144/336 = 207/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 207 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 207 ÷ 3/336 ÷ 3 = 69/112

Step 5: Decimal & Percentage Representation
Dividing the numerator 69 by denominator 112 produces a repeating decimal (approximately 0.616071, or 61.6071%).
Working: 69 ÷ 112 = 0.616071 (61.6071%)

Key Values:
- Simplified Fraction: 69/112
- Mixed Number Form: 69/112
- Decimal Value: 0.616071
- Percentage: 61.6071%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-9-48-plus-9-21/
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9/48 + 9/21 = 69/112

Simplified Fraction

69/112

Mixed Number

Proper (69/112)

Decimal Value

0.616071

Percentage

61.6071%

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Step-by-Step Solution: 9/48 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 48 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 336 (which is smaller than their product 48 × 21 = 1008, keeping the calculation simpler).

LCD(48, 21) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

Multiply the numerator and denominator of 9/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.

9 × 7/48 × 7 = 63/336 and 9 × 16/21 × 16 = 144/336

Step 3

Add the Numerators

Now add the numerators (63 + 144 = 207) and keep the common denominator 336 unchanged.

63 + 144/336 = 207/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 207 and 336, which is 3. Divide both the numerator and denominator by 3.

207 ÷ 3/336 ÷ 3 = 69/112

Step 5

Decimal & Percentage Representation

Dividing the numerator 69 by denominator 112 produces a repeating decimal (approximately 0.616071, or 61.6071%).

69 ÷ 112 = 0.616071 (61.6071%)

Visual Representation

The diagram below illustrates 9/48 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`69/112`
Mixed Number Form	`69/112`
Decimal Form	`0.616071`
Percentage	`61.6071%`

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Frequently Asked Questions

What is 9/48 plus 9/21 as a fraction?

9/48 + 9/21 in simplest fraction form is 69/112.

What is 9/48 plus 9/21 as a decimal?

9/48 + 9/21 converted to a decimal is 0.616071.

What is 9/48 plus 9/21 as a percentage?

9/48 + 9/21 expressed as a percentage is 61.6071%.

Does 9/48 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.616071...) because the denominator contains prime factors other than 2 and 5.