What is 15/48 plus 7/21? (Answer: 31/48)

Exact Answer

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Problem: What is 15/48 plus 7/21?
Formula / Expression: 15/48 + 7/21
Final Answer: 31/48
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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 15/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.
Working: 15 × 7/48 × 7 = 105/336 and 7 × 16/21 × 16 = 112/336

Step 3: Add the Numerators
Now add the numerators (105 + 112 = 217) and keep the common denominator 336 unchanged.
Working: 105 + 112/336 = 217/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 217 and 336, which is 7. Divide both the numerator and denominator by 7.
Working: 217 ÷ 7/336 ÷ 7 = 31/48

Step 5: Decimal & Percentage Representation
Dividing the numerator 31 by denominator 48 produces a repeating decimal (approximately 0.645833, or 64.5833%).
Working: 31 ÷ 48 = 0.645833 (64.5833%)

Key Values:
- Simplified Fraction: 31/48
- Mixed Number Form: 31/48
- Decimal Value: 0.645833
- Percentage: 64.5833%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-15-48-plus-7-21/
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15/48 + 7/21 = 31/48

Simplified Fraction

31/48

Mixed Number

Proper (31/48)

Decimal Value

0.645833

Percentage

64.5833%

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Step-by-Step Solution: 15/48 + 7/21

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 15/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.

15 × 7/48 × 7 = 105/336 and 7 × 16/21 × 16 = 112/336

Step 3

Add the Numerators

Now add the numerators (105 + 112 = 217) and keep the common denominator 336 unchanged.

105 + 112/336 = 217/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 217 and 336, which is 7. Divide both the numerator and denominator by 7.

217 ÷ 7/336 ÷ 7 = 31/48

Step 5

Decimal & Percentage Representation

Dividing the numerator 31 by denominator 48 produces a repeating decimal (approximately 0.645833, or 64.5833%).

31 ÷ 48 = 0.645833 (64.5833%)

Visual Representation

The diagram below illustrates 15/48 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`31/48`
Mixed Number Form	`31/48`
Decimal Form	`0.645833`
Percentage	`64.5833%`

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Frequently Asked Questions

What is 15/48 plus 7/21 as a fraction?

15/48 + 7/21 in simplest fraction form is 31/48.

What is 15/48 plus 7/21 as a decimal?

15/48 + 7/21 converted to a decimal is 0.645833.

What is 15/48 plus 7/21 as a percentage?

15/48 + 7/21 expressed as a percentage is 64.5833%.

Does 15/48 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.645833...) because the denominator contains prime factors other than 2 and 5.