What is 4/8 plus 9/14? (Answer: 8/7)

Exact Answer

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Problem: What is 4/8 plus 9/14?
Formula / Expression: 4/8 + 9/14
Final Answer: 1 1/7 (8/7)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 8 and 14 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 56 (which is smaller than their product 8 × 14 = 112, keeping the calculation simpler).
Working: LCD(8, 14) = 56

Step 2: Convert to Equivalent Fractions with Common Denominator 56
Multiply the numerator and denominator of 4/8 by 7, and multiply the numerator and denominator of 9/14 by 4 so both fractions share the common base 56.
Working: 4 × 7/8 × 7 = 28/56 and 9 × 4/14 × 4 = 36/56

Step 3: Add the Numerators
Now add the numerators (28 + 36 = 64) and keep the common denominator 56 unchanged.
Working: 28 + 36/56 = 64/56

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 64 and 56, which is 8. Divide both the numerator and denominator by 8.
Working: 64 ÷ 8/56 ÷ 8 = 8/7

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.
Working: 8/7 = 1 1/7

Step 6: Decimal & Percentage Representation
Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).
Working: 8 ÷ 7 = 1.142857 (114.2857%)

Key Values:
- Simplified Fraction: 8/7
- Mixed Number Form: 1 1/7
- Decimal Value: 1.142857
- Percentage: 114.2857%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-4-8-plus-9-14/
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4/8 + 9/14 = 8/7

Simplified Fraction

8/7

Mixed Number

1 1/7

Decimal Value

1.142857

Percentage

114.2857%

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Step-by-Step Solution: 4/8 + 9/14

Step 1

Find the Least Common Denominator (LCD)

The denominators 8 and 14 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 56 (which is smaller than their product 8 × 14 = 112, keeping the calculation simpler).

LCD(8, 14) = 56

Step 2

Convert to Equivalent Fractions with Common Denominator 56

Multiply the numerator and denominator of 4/8 by 7, and multiply the numerator and denominator of 9/14 by 4 so both fractions share the common base 56.

4 × 7/8 × 7 = 28/56 and 9 × 4/14 × 4 = 36/56

Step 3

Add the Numerators

Now add the numerators (28 + 36 = 64) and keep the common denominator 56 unchanged.

28 + 36/56 = 64/56

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 64 and 56, which is 8. Divide both the numerator and denominator by 8.

64 ÷ 8/56 ÷ 8 = 8/7

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (8) is greater than the denominator (7), divide 8 by 7: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/7.

8/7 = 11/7

Step 6

Decimal & Percentage Representation

Dividing the numerator 8 by denominator 7 produces a repeating decimal (approximately 1.142857, or 114.2857%).

8 ÷ 7 = 1.142857 (114.2857%)

Visual Representation

The diagram below illustrates 4/8 plus 9/14 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`8/7`
Mixed Number Form	`1 1/7`
Decimal Form	`1.142857`
Percentage	`114.2857%`

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Frequently Asked Questions

What is 4/8 plus 9/14 as a fraction?

4/8 + 9/14 in simplest fraction form is 8/7 (or 1 1/7 as a mixed number).

What is 4/8 plus 9/14 as a decimal?

4/8 + 9/14 converted to a decimal is 1.142857.

What is 4/8 plus 9/14 as a percentage?

4/8 + 9/14 expressed as a percentage is 114.2857%.

How do you write 4/8 plus 9/14 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 8/7 can be written as the mixed number 1 1/7.

Does 4/8 plus 9/14 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.142857...) because the denominator contains prime factors other than 2 and 5.