What is 10/56 plus 9/21? (Answer: 17/28)

Exact Answer

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Problem: What is 10/56 plus 9/21?
Formula / Expression: 10/56 + 9/21
Final Answer: 17/28
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 56 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 56 × 21 = 1176, keeping the calculation simpler).
Working: LCD(56, 21) = 168

Step 2: Convert to Equivalent Fractions with Common Denominator 168
Multiply the numerator and denominator of 10/56 by 3, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.
Working: 10 × 3/56 × 3 = 30/168 and 9 × 8/21 × 8 = 72/168

Step 3: Add the Numerators
Now add the numerators (30 + 72 = 102) and keep the common denominator 168 unchanged.
Working: 30 + 72/168 = 102/168

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 102 and 168, which is 6. Divide both the numerator and denominator by 6.
Working: 102 ÷ 6/168 ÷ 6 = 17/28

Step 5: Decimal & Percentage Representation
Dividing the numerator 17 by denominator 28 produces a repeating decimal (approximately 0.607143, or 60.7143%).
Working: 17 ÷ 28 = 0.607143 (60.7143%)

Key Values:
- Simplified Fraction: 17/28
- Mixed Number Form: 17/28
- Decimal Value: 0.607143
- Percentage: 60.7143%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-10-56-plus-9-21/
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10/56 + 9/21 = 17/28

Simplified Fraction

17/28

Mixed Number

Proper (17/28)

Decimal Value

0.607143

Percentage

60.7143%

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Step-by-Step Solution: 10/56 + 9/21

Step 1

Find the Least Common Denominator (LCD)

The denominators 56 and 21 share a common factor (GCD = 7). Finding their Least Common Multiple gives an LCD of 168 (which is smaller than their product 56 × 21 = 1176, keeping the calculation simpler).

LCD(56, 21) = 168

Step 2

Convert to Equivalent Fractions with Common Denominator 168

Multiply the numerator and denominator of 10/56 by 3, and multiply the numerator and denominator of 9/21 by 8 so both fractions share the common base 168.

10 × 3/56 × 3 = 30/168 and 9 × 8/21 × 8 = 72/168

Step 3

Add the Numerators

Now add the numerators (30 + 72 = 102) and keep the common denominator 168 unchanged.

30 + 72/168 = 102/168

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 102 and 168, which is 6. Divide both the numerator and denominator by 6.

102 ÷ 6/168 ÷ 6 = 17/28

Step 5

Decimal & Percentage Representation

Dividing the numerator 17 by denominator 28 produces a repeating decimal (approximately 0.607143, or 60.7143%).

17 ÷ 28 = 0.607143 (60.7143%)

Visual Representation

The diagram below illustrates 10/56 plus 9/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`17/28`
Mixed Number Form	`17/28`
Decimal Form	`0.607143`
Percentage	`60.7143%`

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Frequently Asked Questions

What is 10/56 plus 9/21 as a fraction?

10/56 + 9/21 in simplest fraction form is 17/28.

What is 10/56 plus 9/21 as a decimal?

10/56 + 9/21 converted to a decimal is 0.607143.

What is 10/56 plus 9/21 as a percentage?

10/56 + 9/21 expressed as a percentage is 60.7143%.

Does 10/56 plus 9/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.607143...) because the denominator contains prime factors other than 2 and 5.