What is 10/49 plus 15/21? (Answer: 45/49)

Exact Answer

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Problem: What is 10/49 plus 15/21?
Formula / Expression: 10/49 + 15/21
Final Answer: 45/49
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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 10/49 by 3, and multiply the numerator and denominator of 15/21 by 7 so both fractions share the common base 147.
Working: 10 × 3/49 × 3 = 30/147 and 15 × 7/21 × 7 = 105/147

Step 3: Add the Numerators
Now add the numerators (30 + 105 = 135) and keep the common denominator 147 unchanged.
Working: 30 + 105/147 = 135/147

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 135 and 147, which is 3. Divide both the numerator and denominator by 3.
Working: 135 ÷ 3/147 ÷ 3 = 45/49

Step 5: Decimal & Percentage Representation
Dividing the numerator 45 by denominator 49 produces a repeating decimal (approximately 0.918367, or 91.8367%).
Working: 45 ÷ 49 = 0.918367 (91.8367%)

Key Values:
- Simplified Fraction: 45/49
- Mixed Number Form: 45/49
- Decimal Value: 0.918367
- Percentage: 91.8367%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-49-plus-15-21/
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10/49 + 15/21 = 45/49

Simplified Fraction

45/49

Mixed Number

Proper (45/49)

Decimal Value

0.918367

Percentage

91.8367%

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Step-by-Step Solution: 10/49 + 15/21

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 10/49 by 3, and multiply the numerator and denominator of 15/21 by 7 so both fractions share the common base 147.

10 × 3/49 × 3 = 30/147 and 15 × 7/21 × 7 = 105/147

Step 3

Add the Numerators

Now add the numerators (30 + 105 = 135) and keep the common denominator 147 unchanged.

30 + 105/147 = 135/147

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 135 and 147, which is 3. Divide both the numerator and denominator by 3.

135 ÷ 3/147 ÷ 3 = 45/49

Step 5

Decimal & Percentage Representation

Dividing the numerator 45 by denominator 49 produces a repeating decimal (approximately 0.918367, or 91.8367%).

45 ÷ 49 = 0.918367 (91.8367%)

Visual Representation

The diagram below illustrates 10/49 plus 15/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`45/49`
Mixed Number Form	`45/49`
Decimal Form	`0.918367`
Percentage	`91.8367%`

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Frequently Asked Questions

What is 10/49 plus 15/21 as a fraction?

10/49 + 15/21 in simplest fraction form is 45/49.

What is 10/49 plus 15/21 as a decimal?

10/49 + 15/21 converted to a decimal is 0.918367.

What is 10/49 plus 15/21 as a percentage?

10/49 + 15/21 expressed as a percentage is 91.8367%.

Does 10/49 plus 15/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.918367...) because the denominator contains prime factors other than 2 and 5.