What is 4/16 plus 7/9? (Answer: 37/36)

Exact Answer

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Problem: What is 4/16 plus 7/9?
Formula / Expression: 4/16 + 7/9
Final Answer: 1 1/36 (37/36)
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 16 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 9 = 144.
Working: LCD(16, 9) = 144

Step 2: Convert to Equivalent Fractions with Common Denominator 144
Multiply the numerator and denominator of 4/16 by 9, and multiply the numerator and denominator of 7/9 by 16 so both fractions share the common base 144.
Working: 4 × 9/16 × 9 = 36/144 and 7 × 16/9 × 16 = 112/144

Step 3: Add the Numerators
Now add the numerators (36 + 112 = 148) and keep the common denominator 144 unchanged.
Working: 36 + 112/144 = 148/144

Step 4: Simplify the Fraction to Lowest Terms
Find the Greatest Common Divisor (GCD) of 148 and 144, which is 4. Divide both the numerator and denominator by 4.
Working: 148 ÷ 4/144 ÷ 4 = 37/36

Step 5: Convert Improper Fraction to a Mixed Number
Since the numerator (37) is greater than the denominator (36), divide 37 by 36: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/36.
Working: 37/36 = 1 1/36

Step 6: Decimal & Percentage Representation
Dividing the numerator 37 by denominator 36 produces a repeating decimal (approximately 1.027778, or 102.7778%).
Working: 37 ÷ 36 = 1.027778 (102.7778%)

Key Values:
- Simplified Fraction: 37/36
- Mixed Number Form: 1 1/36
- Decimal Value: 1.027778
- Percentage: 102.7778%

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Solved with FractionsCalc:
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4/16 + 7/9 = 37/36

Simplified Fraction

37/36

Mixed Number

1 1/36

Decimal Value

1.027778

Percentage

102.7778%

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Step-by-Step Solution: 4/16 + 7/9

Step 1

Find the Least Common Denominator (LCD)

The denominators 16 and 9 are coprime (they share no common factors other than 1). Therefore, their Least Common Denominator (LCD) is simply their direct product: 16 × 9 = 144.

LCD(16, 9) = 144

Step 2

Convert to Equivalent Fractions with Common Denominator 144

Multiply the numerator and denominator of 4/16 by 9, and multiply the numerator and denominator of 7/9 by 16 so both fractions share the common base 144.

4 × 9/16 × 9 = 36/144 and 7 × 16/9 × 16 = 112/144

Step 3

Add the Numerators

Now add the numerators (36 + 112 = 148) and keep the common denominator 144 unchanged.

36 + 112/144 = 148/144

Step 4

Simplify the Fraction to Lowest Terms

Find the Greatest Common Divisor (GCD) of 148 and 144, which is 4. Divide both the numerator and denominator by 4.

148 ÷ 4/144 ÷ 4 = 37/36

Step 5

Convert Improper Fraction to a Mixed Number

Since the numerator (37) is greater than the denominator (36), divide 37 by 36: it goes in 1 whole time(s) with a remainder of 1, giving the mixed number 1 1/36.

37/36 = 11/36

Step 6

Decimal & Percentage Representation

Dividing the numerator 37 by denominator 36 produces a repeating decimal (approximately 1.027778, or 102.7778%).

37 ÷ 36 = 1.027778 (102.7778%)

Visual Representation

The diagram below illustrates 4/16 plus 7/9 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`37/36`
Mixed Number Form	`1 1/36`
Decimal Form	`1.027778`
Percentage	`102.7778%`

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Frequently Asked Questions

What is 4/16 plus 7/9 as a fraction?

4/16 + 7/9 in simplest fraction form is 37/36 (or 1 1/36 as a mixed number).

What is 4/16 plus 7/9 as a decimal?

4/16 + 7/9 converted to a decimal is 1.027778.

What is 4/16 plus 7/9 as a percentage?

4/16 + 7/9 expressed as a percentage is 102.7778%.

How do you write 4/16 plus 7/9 as a mixed number?

Because the numerator is greater than the denominator, the improper fraction 37/36 can be written as the mixed number 1 1/36.

Does 4/16 plus 7/9 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 1.027778...) because the denominator contains prime factors other than 2 and 5.