What is 9/21 plus 21/48? (Answer: 97/112)

Exact Answer

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Problem: What is 9/21 plus 21/48?
Formula / Expression: 9/21 + 21/48
Final Answer: 97/112
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Step-by-Step Solution:

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

Step 2: Convert to Equivalent Fractions with Common Denominator 336
Multiply the numerator and denominator of 9/21 by 16, and multiply the numerator and denominator of 21/48 by 7 so both fractions share the common base 336.
Working: 9 × 16/21 × 16 = 144/336 and 21 × 7/48 × 7 = 147/336

Step 3: Add the Numerators
Now add the numerators (144 + 147 = 291) and keep the common denominator 336 unchanged.
Working: 144 + 147/336 = 291/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 291 and 336, which is 3. Divide both the numerator and denominator by 3.
Working: 291 ÷ 3/336 ÷ 3 = 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-21-48/
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9/21 + 21/48 = 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 + 21/48

Step 1

Find the Least Common Denominator (LCD)

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

LCD(21, 48) = 336

Step 2

Convert to Equivalent Fractions with Common Denominator 336

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

9 × 16/21 × 16 = 144/336 and 21 × 7/48 × 7 = 147/336

Step 3

Add the Numerators

Now add the numerators (144 + 147 = 291) and keep the common denominator 336 unchanged.

144 + 147/336 = 291/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 291 and 336, which is 3. Divide both the numerator and denominator by 3.

291 ÷ 3/336 ÷ 3 = 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 21/48 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 21/48 as a fraction?

9/21 + 21/48 in simplest fraction form is 97/112.

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

9/21 + 21/48 converted to a decimal is 0.866071.

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

9/21 + 21/48 expressed as a percentage is 86.6071%.

Does 9/21 plus 21/48 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.