Why is there a 2 in this fraction problem?

  • Thread starter jim1174
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In summary, the original problem was 8 5/6 - 1 1/3 and the answer was 7 1/2. However, in a later post, the problem was revised to 8 5/6 - 1 2/3. This change is a result of multiplying the fraction 1/3 by 2 to make it equivalent to 2/6, which matches the denominator of the first fraction in the problem. Ultimately, there is no difference in the value of these fractions and the decision to convert the denominator was simply for convenience.
  • #1
jim1174
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I need some help with this fraction problem. 8 5/6 - 1 1/3 you Need to rewrite the problem as 8 5/6 - 1 2/3 where did the two come from ?
 
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  • #2
Can you show the whole text of this problem and supposed solution?
 
  • #3
The problem is 8 5/6 - 1 1/3 the answer is 8 5/6 - 1 2/6 answer 7 1/2 I just want to know how they got the 2 in 2/6
 
  • #4
jim1174 said:
The problem is 8 5/6 - 1 1/3 the answer is 8 5/6 - 1 2/3 answer 7 1/2
The expression is either 8 5/6 - 1 1/3 or 8 5/6 - 1 2/3. The two are not the same.

Since the answer is 7 1/2, the problem must have been 8 5/6 - 1 1/3. The only explanation for 8 5/6 - 1 2/3 is that it's a typo.

Edit: Jim, I didn't notice that you revised what you wrote in your later post. 1 1/3 is the same as 1 2/6.
 
  • #5
They changed 1/3 to 2/6 by multiplying the top and bottom of the fraction 1/3 by the number 2.
 
  • #6
The question is 8 5/6 - 1 1/3 you are supposed to re write the problem as 8 5/6 - 1 2/6 what I want to know is when they changed the 1/3 to 2/6 where did the two come from
 
  • #7
You can multiply the top of a fraction by any number so long as you multiply the bottom of that fraction by the same AND THIS DOESN'T CHANGE THE VALUE of that fraction.

So 1/3 is equivalent to 2/6 in all regards.

QUESTION: Would you prefer 1 slice of a pie after the pie was cut up into 3 equal pieces, or
would you prefer 2 slices of the same pie after it had been cut into 6 pieces?

ANS: there is no difference!

The decision to convert the denominator into a 6 was so that it matched the denominator of the first fraction in the problem.
 
Last edited:
  • #8
If I may propose a different way of seeing it: any number multiplied by 1 is the same number. Therefore, you can always multiply any fraction by ##n/n## (provided ##n## is not zero!):

$$
\frac{1}{3} = \frac{1}{3} \times 1 = \frac{1}{3} \times \frac{2}{2} = \frac{2}{6}
$$
 

1. Where did the 2 come from in mathematics?

In mathematics, the number 2 is one of the basic building blocks of the number system and is derived from the ancient Hindu-Arabic numeral system. It represents a quantity or value that is double of 1 and half of 4. The concept of 2 can also be seen in nature, such as two eyes, two hands, and two legs, making it a fundamental concept in mathematics.

2. What is the history of the number 2?

The concept of 2 has been around for thousands of years and can be traced back to ancient civilizations such as the Egyptians, Babylonians, and Mayans. It was later introduced into the Hindu-Arabic numeral system by the Indian mathematician Brahmagupta in the 7th century. Throughout history, the number 2 has been used in various mathematical operations, including addition, subtraction, multiplication, and division.

3. How is the concept of 2 applied in science?

The number 2 has numerous applications in science, including in physics, chemistry, and biology. In physics, the concept of 2 can be seen in Newton's Second Law of Motion, which states that force is equal to mass times acceleration (F=ma). In chemistry, the periodic table is organized into groups of elements that share similar properties, with each group containing 2 elements. In biology, the human body is made up of two sets of 23 chromosomes, one from each parent.

4. Can the number 2 be written in different forms?

Yes, the number 2 can be written in different forms, including as a whole number, fraction, decimal, and percent. It can also be expressed in various numeral systems, such as binary (base 2), octal (base 8), and hexadecimal (base 16). Additionally, 2 can be represented as a square root (√2), cube root (³√2), or in exponential form (2^x).

5. What is the significance of the number 2 in mathematics and science?

The number 2 has significant meaning in mathematics and science. In mathematics, it is the first and only even prime number, making it a crucial component in number theory. In science, 2 is a symbol of balance and symmetry, as seen in the structures of molecules and organisms. It is also used to represent binary code, which is the basis of all computer operations. Overall, the number 2 is an essential element in understanding and solving mathematical and scientific problems.

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