What is 10/45 plus 7/21? (Answer: 5/9)

Exact Answer

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Problem: What is 10/45 plus 7/21?
Formula / Expression: 10/45 + 7/21
Final Answer: 5/9
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).
Working: LCD(45, 21) = 315

Step 2: Convert to Equivalent Fractions with Common Denominator 315
Multiply the numerator and denominator of 10/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.
Working: 10 × 7/45 × 7 = 70/315 and 7 × 15/21 × 15 = 105/315

Step 3: Add the Numerators
Now add the numerators (70 + 105 = 175) and keep the common denominator 315 unchanged.
Working: 70 + 105/315 = 175/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 175 and 315, which is 35. Divide both the numerator and denominator by 35.
Working: 175 ÷ 35/315 ÷ 35 = 5/9

Step 5: Decimal & Percentage Representation
Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).
Working: 5 ÷ 9 = 0.555556 (55.5556%)

Key Values:
- Simplified Fraction: 5/9
- Mixed Number Form: 5/9
- Decimal Value: 0.555556
- Percentage: 55.5556%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-45-plus-7-21/
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10/45 + 7/21 = 5/9

Simplified Fraction

5/9

Mixed Number

Proper (5/9)

Decimal Value

0.555556

Percentage

55.5556%

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Step-by-Step Solution: 10/45 + 7/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 45 and 21 share a common factor (GCD = 3). Finding their Least Common Multiple gives an LCD of 315 (which is smaller than their product 45 × 21 = 945, keeping the calculation simpler).

LCD(45, 21) = 315

Step 2

Convert to Equivalent Fractions with Common Denominator 315

Multiply the numerator and denominator of 10/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.

10 × 7/45 × 7 = 70/315 and 7 × 15/21 × 15 = 105/315

Step 3

Add the Numerators

Now add the numerators (70 + 105 = 175) and keep the common denominator 315 unchanged.

70 + 105/315 = 175/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 175 and 315, which is 35. Divide both the numerator and denominator by 35.

175 ÷ 35/315 ÷ 35 = 5/9

Step 5

Decimal & Percentage Representation

Dividing the numerator 5 by denominator 9 produces a repeating decimal (approximately 0.555556, or 55.5556%).

5 ÷ 9 = 0.555556 (55.5556%)

Visual Representation

The diagram below illustrates 10/45 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`5/9`
Mixed Number Form	`5/9`
Decimal Form	`0.555556`
Percentage	`55.5556%`

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Frequently Asked Questions

What is 10/45 plus 7/21 as a fraction?

10/45 + 7/21 in simplest fraction form is 5/9.

What is 10/45 plus 7/21 as a decimal?

10/45 + 7/21 converted to a decimal is 0.555556.

What is 10/45 plus 7/21 as a percentage?

10/45 + 7/21 expressed as a percentage is 55.5556%.

Does 10/45 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.555556...) because the denominator contains prime factors other than 2 and 5.