What is 20/48 plus 9/21? (Answer: 71/84)

Exact Answer

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Problem: What is 20/48 plus 9/21?
Formula / Expression: 20/48 + 9/21
Final Answer: 71/84
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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 20/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.
Working: 20 × 7/48 × 7 = 140/336 and 9 × 16/21 × 16 = 144/336

Step 3: Add the Numerators
Now add the numerators (140 + 144 = 284) and keep the common denominator 336 unchanged.
Working: 140 + 144/336 = 284/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 284 and 336, which is 4. Divide both the numerator and denominator by 4.
Working: 284 ÷ 4/336 ÷ 4 = 71/84

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 84 produces a repeating decimal (approximately 0.845238, or 84.5238%).
Working: 71 ÷ 84 = 0.845238 (84.5238%)

Key Values:
- Simplified Fraction: 71/84
- Mixed Number Form: 71/84
- Decimal Value: 0.845238
- Percentage: 84.5238%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-20-48-plus-9-21/
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20/48 + 9/21 = 71/84

Simplified Fraction

71/84

Mixed Number

Proper (71/84)

Decimal Value

0.845238

Percentage

84.5238%

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Step-by-Step Solution: 20/48 + 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 20/48 by 7, and multiply the numerator and denominator of 9/21 by 16 so both fractions share the common base 336.

20 × 7/48 × 7 = 140/336 and 9 × 16/21 × 16 = 144/336

Step 3

Add the Numerators

Now add the numerators (140 + 144 = 284) and keep the common denominator 336 unchanged.

140 + 144/336 = 284/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 284 and 336, which is 4. Divide both the numerator and denominator by 4.

284 ÷ 4/336 ÷ 4 = 71/84

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 84 produces a repeating decimal (approximately 0.845238, or 84.5238%).

71 ÷ 84 = 0.845238 (84.5238%)

Visual Representation

The diagram below illustrates 20/48 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/84`
Mixed Number Form	`71/84`
Decimal Form	`0.845238`
Percentage	`84.5238%`

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Frequently Asked Questions

What is 20/48 plus 9/21 as a fraction?

20/48 + 9/21 in simplest fraction form is 71/84.

What is 20/48 plus 9/21 as a decimal?

20/48 + 9/21 converted to a decimal is 0.845238.

What is 20/48 plus 9/21 as a percentage?

20/48 + 9/21 expressed as a percentage is 84.5238%.

Does 20/48 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.845238...) because the denominator contains prime factors other than 2 and 5.