What is 5/56 plus 7/21? (Answer: 71/168)

Exact Answer

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Problem: What is 5/56 plus 7/21?
Formula / Expression: 5/56 + 7/21
Final Answer: 71/168
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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 5/56 by 3, and multiply the numerator and denominator of 7/21 by 8 so both fractions share the common base 168.
Working: 5 × 3/56 × 3 = 15/168 and 7 × 8/21 × 8 = 56/168

Step 3: Add the Numerators
Now add the numerators (15 + 56 = 71) and keep the common denominator 168 unchanged.
Working: 15 + 56/168 = 71/168

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 71 and 168 is 1, confirming that 71/168 cannot be reduced further—it is already in its simplest irreducible form.
Working: 71/168

Step 5: Decimal & Percentage Representation
Dividing the numerator 71 by denominator 168 produces a repeating decimal (approximately 0.422619, or 42.2619%).
Working: 71 ÷ 168 = 0.422619 (42.2619%)

Key Values:
- Simplified Fraction: 71/168
- Mixed Number Form: 71/168
- Decimal Value: 0.422619
- Percentage: 42.2619%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-5-56-plus-7-21/
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5/56 + 7/21 = 71/168

Simplified Fraction

71/168

Mixed Number

Proper (71/168)

Decimal Value

0.422619

Percentage

42.2619%

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Step-by-Step Solution: 5/56 + 7/21

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 5/56 by 3, and multiply the numerator and denominator of 7/21 by 8 so both fractions share the common base 168.

5 × 3/56 × 3 = 15/168 and 7 × 8/21 × 8 = 56/168

Step 3

Add the Numerators

Now add the numerators (15 + 56 = 71) and keep the common denominator 168 unchanged.

15 + 56/168 = 71/168

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 71 and 168 is 1, confirming that 71/168 cannot be reduced further—it is already in its simplest irreducible form.

71/168

Step 5

Decimal & Percentage Representation

Dividing the numerator 71 by denominator 168 produces a repeating decimal (approximately 0.422619, or 42.2619%).

71 ÷ 168 = 0.422619 (42.2619%)

Visual Representation

The diagram below illustrates 5/56 plus 7/21 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`71/168`
Mixed Number Form	`71/168`
Decimal Form	`0.422619`
Percentage	`42.2619%`

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Frequently Asked Questions

What is 5/56 plus 7/21 as a fraction?

5/56 + 7/21 in simplest fraction form is 71/168.

What is 5/56 plus 7/21 as a decimal?

5/56 + 7/21 converted to a decimal is 0.422619.

What is 5/56 plus 7/21 as a percentage?

5/56 + 7/21 expressed as a percentage is 42.2619%.

Does 5/56 plus 7/21 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.422619...) because the denominator contains prime factors other than 2 and 5.