What is 10/48 plus 15/21? (Answer: 155/168)

Exact Answer

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Problem: What is 10/48 plus 15/21?
Formula / Expression: 10/48 + 15/21
Final Answer: 155/168
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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 10/48 by 7, and multiply the numerator and denominator of 15/21 by 16 so both fractions share the common base 336.
Working: 10 × 7/48 × 7 = 70/336 and 15 × 16/21 × 16 = 240/336

Step 3: Add the Numerators
Now add the numerators (70 + 240 = 310) and keep the common denominator 336 unchanged.
Working: 70 + 240/336 = 310/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 310 and 336, which is 2. Divide both the numerator and denominator by 2.
Working: 310 ÷ 2/336 ÷ 2 = 155/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 155 by denominator 168 produces a repeating decimal (approximately 0.922619, or 92.2619%).
Working: 155 ÷ 168 = 0.922619 (92.2619%)

Key Values:
- Simplified Fraction: 155/168
- Mixed Number Form: 155/168
- Decimal Value: 0.922619
- Percentage: 92.2619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-48-plus-15-21/
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10/48 + 15/21 = 155/168

Simplified Fraction

155/168

Mixed Number

Proper (155/168)

Decimal Value

0.922619

Percentage

92.2619%

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Step-by-Step Solution: 10/48 + 15/21

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 10/48 by 7, and multiply the numerator and denominator of 15/21 by 16 so both fractions share the common base 336.

10 × 7/48 × 7 = 70/336 and 15 × 16/21 × 16 = 240/336

Step 3

Add the Numerators

Now add the numerators (70 + 240 = 310) and keep the common denominator 336 unchanged.

70 + 240/336 = 310/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 310 and 336, which is 2. Divide both the numerator and denominator by 2.

310 ÷ 2/336 ÷ 2 = 155/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 155 by denominator 168 produces a repeating decimal (approximately 0.922619, or 92.2619%).

155 ÷ 168 = 0.922619 (92.2619%)

Visual Representation

The diagram below illustrates 10/48 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`155/168`
Mixed Number Form	`155/168`
Decimal Form	`0.922619`
Percentage	`92.2619%`

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Frequently Asked Questions

What is 10/48 plus 15/21 as a fraction?

10/48 + 15/21 in simplest fraction form is 155/168.

What is 10/48 plus 15/21 as a decimal?

10/48 + 15/21 converted to a decimal is 0.922619.

What is 10/48 plus 15/21 as a percentage?

10/48 + 15/21 expressed as a percentage is 92.2619%.

Does 10/48 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.922619...) because the denominator contains prime factors other than 2 and 5.