What is 10/48 plus 7/21? (Answer: 13/24)

Exact Answer

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Problem: What is 10/48 plus 7/21?
Formula / Expression: 10/48 + 7/21
Final Answer: 13/24
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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 7/21 by 16 so both fractions share the common base 336.
Working: 10 × 7/48 × 7 = 70/336 and 7 × 16/21 × 16 = 112/336

Step 3: Add the Numerators
Now add the numerators (70 + 112 = 182) and keep the common denominator 336 unchanged.
Working: 70 + 112/336 = 182/336

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 182 and 336, which is 14. Divide both the numerator and denominator by 14.
Working: 182 ÷ 14/336 ÷ 14 = 13/24

Step 5: Decimal & Percentage Representation
Dividing the numerator 13 by denominator 24 produces a repeating decimal (approximately 0.541667, or 54.1667%).
Working: 13 ÷ 24 = 0.541667 (54.1667%)

Key Values:
- Simplified Fraction: 13/24
- Mixed Number Form: 13/24
- Decimal Value: 0.541667
- Percentage: 54.1667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-48-plus-7-21/
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10/48 + 7/21 = 13/24

Simplified Fraction

13/24

Mixed Number

Proper (13/24)

Decimal Value

0.541667

Percentage

54.1667%

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Step-by-Step Solution: 10/48 + 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 10/48 by 7, and multiply the numerator and denominator of 7/21 by 16 so both fractions share the common base 336.

10 × 7/48 × 7 = 70/336 and 7 × 16/21 × 16 = 112/336

Step 3

Add the Numerators

Now add the numerators (70 + 112 = 182) and keep the common denominator 336 unchanged.

70 + 112/336 = 182/336

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 182 and 336, which is 14. Divide both the numerator and denominator by 14.

182 ÷ 14/336 ÷ 14 = 13/24

Step 5

Decimal & Percentage Representation

Dividing the numerator 13 by denominator 24 produces a repeating decimal (approximately 0.541667, or 54.1667%).

13 ÷ 24 = 0.541667 (54.1667%)

Visual Representation

The diagram below illustrates 10/48 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`13/24`
Mixed Number Form	`13/24`
Decimal Form	`0.541667`
Percentage	`54.1667%`

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Frequently Asked Questions

What is 10/48 plus 7/21 as a fraction?

10/48 + 7/21 in simplest fraction form is 13/24.

What is 10/48 plus 7/21 as a decimal?

10/48 + 7/21 converted to a decimal is 0.541667.

What is 10/48 plus 7/21 as a percentage?

10/48 + 7/21 expressed as a percentage is 54.1667%.

Does 10/48 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.541667...) because the denominator contains prime factors other than 2 and 5.