What is 6/45 plus 7/21? (Answer: 7/15)

Exact Answer

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Problem: What is 6/45 plus 7/21?
Formula / Expression: 6/45 + 7/21
Final Answer: 7/15
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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 6/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.
Working: 6 × 7/45 × 7 = 42/315 and 7 × 15/21 × 15 = 105/315

Step 3: Add the Numerators
Now add the numerators (42 + 105 = 147) and keep the common denominator 315 unchanged.
Working: 42 + 105/315 = 147/315

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 147 and 315, which is 21. Divide both the numerator and denominator by 21.
Working: 147 ÷ 21/315 ÷ 21 = 7/15

Step 5: Decimal & Percentage Representation
Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).
Working: 7 ÷ 15 = 0.466667 (46.6667%)

Key Values:
- Simplified Fraction: 7/15
- Mixed Number Form: 7/15
- Decimal Value: 0.466667
- Percentage: 46.6667%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-6-45-plus-7-21/
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6/45 + 7/21 = 7/15

Simplified Fraction

7/15

Mixed Number

Proper (7/15)

Decimal Value

0.466667

Percentage

46.6667%

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Step-by-Step Solution: 6/45 + 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 6/45 by 7, and multiply the numerator and denominator of 7/21 by 15 so both fractions share the common base 315.

6 × 7/45 × 7 = 42/315 and 7 × 15/21 × 15 = 105/315

Step 3

Add the Numerators

Now add the numerators (42 + 105 = 147) and keep the common denominator 315 unchanged.

42 + 105/315 = 147/315

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 147 and 315, which is 21. Divide both the numerator and denominator by 21.

147 ÷ 21/315 ÷ 21 = 7/15

Step 5

Decimal & Percentage Representation

Dividing the numerator 7 by denominator 15 produces a repeating decimal (approximately 0.466667, or 46.6667%).

7 ÷ 15 = 0.466667 (46.6667%)

Visual Representation

The diagram below illustrates 6/45 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`7/15`
Mixed Number Form	`7/15`
Decimal Form	`0.466667`
Percentage	`46.6667%`

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Frequently Asked Questions

What is 6/45 plus 7/21 as a fraction?

6/45 + 7/21 in simplest fraction form is 7/15.

What is 6/45 plus 7/21 as a decimal?

6/45 + 7/21 converted to a decimal is 0.466667.

What is 6/45 plus 7/21 as a percentage?

6/45 + 7/21 expressed as a percentage is 46.6667%.

Does 6/45 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.466667...) because the denominator contains prime factors other than 2 and 5.