What is 23/49 plus 10/21? (Answer: 139/147)

Exact Answer

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Problem: What is 23/49 plus 10/21?
Formula / Expression: 23/49 + 10/21
Final Answer: 139/147
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).
Working: LCD(49, 21) = 147

Step 2: Convert to Equivalent Fractions with Common Denominator 147
Multiply the numerator and denominator of 23/49 by 3, and multiply the numerator and denominator of 10/21 by 7 so both fractions share the common base 147.
Working: 23 × 3/49 × 3 = 69/147 and 10 × 7/21 × 7 = 70/147

Step 3: Add the Numerators
Now add the numerators (69 + 70 = 139) and keep the common denominator 147 unchanged.
Working: 69 + 70/147 = 139/147

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 139 and 147 is 1, confirming that 139/147 cannot be reduced further—it is already in its simplest irreducible form.
Working: 139/147

Step 5: Decimal & Percentage Representation
Dividing the numerator 139 by denominator 147 produces a repeating decimal (approximately 0.945578, or 94.5578%).
Working: 139 ÷ 147 = 0.945578 (94.5578%)

Key Values:
- Simplified Fraction: 139/147
- Mixed Number Form: 139/147
- Decimal Value: 0.945578
- Percentage: 94.5578%

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Solved with FractionsCalc:
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23/49 + 10/21 = 139/147

Simplified Fraction

139/147

Mixed Number

Proper (139/147)

Decimal Value

0.945578

Percentage

94.5578%

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Step-by-Step Solution: 23/49 + 10/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 49 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 147 (which is smaller than their product 49 × 21 = 1029, keeping the calculation simpler).

LCD(49, 21) = 147

Step 2

Convert to Equivalent Fractions with Common Denominator 147

Multiply the numerator and denominator of 23/49 by 3, and multiply the numerator and denominator of 10/21 by 7 so both fractions share the common base 147.

23 × 3/49 × 3 = 69/147 and 10 × 7/21 × 7 = 70/147

Step 3

Add the Numerators

Now add the numerators (69 + 70 = 139) and keep the common denominator 147 unchanged.

69 + 70/147 = 139/147

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 139 and 147 is 1, confirming that 139/147 cannot be reduced further—it is already in its simplest irreducible form.

139/147

Step 5

Decimal & Percentage Representation

Dividing the numerator 139 by denominator 147 produces a repeating decimal (approximately 0.945578, or 94.5578%).

139 ÷ 147 = 0.945578 (94.5578%)

Visual Representation

The diagram below illustrates 23/49 plus 10/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`139/147`
Mixed Number Form	`139/147`
Decimal Form	`0.945578`
Percentage	`94.5578%`

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Frequently Asked Questions

What is 23/49 plus 10/21 as a fraction?

23/49 + 10/21 in simplest fraction form is 139/147.

What is 23/49 plus 10/21 as a decimal?

23/49 + 10/21 converted to a decimal is 0.945578.

What is 23/49 plus 10/21 as a percentage?

23/49 + 10/21 expressed as a percentage is 94.5578%.

Does 23/49 plus 10/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.945578...) because the denominator contains prime factors other than 2 and 5.