How to Subtract Mixed Fractions

In order to be able to subtract mixed fractions, you will have to follow the process below. For example, if the equation you want to find out the answer to is:

    \[ 2\frac{3}{4}-6\frac{2}{3} \]

The method in order to answer the equation is:

1. First, add the whole numbers. In this case, you add 2 and 6 which is 8. Leave the 8 until later.

2. Next, convert the two leftover fractions into improper fractions. In this case, the equation will be:

    \[ \frac{3}{4}-\frac{2}{3} \]

3. Next, convert the denominators into the same numbers. In order to do so, you will have to find out the LCM (Least Common Multiple) of the two numbers. In this case, the LCM is 12. Therefore, it will be like the equation below:

    \[ \frac{9}{12}-\frac{8}{12}=\frac{1}{12} \]

4. The sum is not an improper fraction. Therefore, simplifying it to a mixed number is not necessary.

5. When producing the final answer, you have to add the 8, which was left at the start to the sum. Therefore, the equation will be:

    \[ \frac{1}{12}+8=8\frac{1}{12} \]

6. You’re done! The final answer is:

    \[ 8\frac{1}{12} \]

 

How to Add Mixed Numbers

In order to be able to add mixed fractions, you will have to follow the process below. For example, if the equation you want to find out the answer to is:

    \[ 1\frac{1}{2}+2\frac{5}{6} \]

The method in order to answer the equation is:

1. First, add the whole numbers. In this case, you add 1 and 2 which is 3. Leave the 3 until later.

2. Next, convert the two leftover fractions into improper fractions. In this case, the equation will be:

    \[ \frac{1}{2}+\frac{5}{6} \]

3.  Next, convert the denominators into the same numbers. In order to do so, you will have to find out the LCM (Least Common Multiple) of the two numbers. In this case, the LCM is  6. Therefore, it will be like the equation below:

    \[ \frac{3}{6}+\frac{5}{6}=\frac{8}{6} \]

4. The sum is an improper fraction. Therefore, simplifying it to a mixed number is necessary.

    \[ 1\frac{2}{6} \]

Which when simplified further, is:

    \[ 1\frac{1}{3} \]

5. When producing the final answer, you have to add the 3, which was left at the start to the sum. Therefore, the equation will be:

    \[ 1\frac{1}{3}+3=4\frac{1}{3} \]

6. You’re done! The final answer is:

    \[ 4\frac{1}{3} \]

 

How to Subtract Proper Fractions

In order to be able to subtract proper fractions, first you have to convert the denominators into the same number like the other equations. For example, if the equation you want to work out is

    \[ \frac{3}{5}-\frac{1}{4} \]

The method in order to answer the equation is:

1. As mentioned before, convert the denominators into the same number. In order to do so, you will have to find out the LCM (Least Common Multiple) of the two numbers. In this case, the LCM is 20. Therefore, it will be like the equation below:

    \[ \frac{12}{20}-\frac{5}{20}=\frac{7}{20} \]

2. The answer is not an improper fraction and is a proper fraction. Therefore, simplifying it to a mixed number is not necessary. The final answer is written below:

    \[ \frac{7}{20} \]

 

How to Add Proper Fractions

In order to be able to add proper fractions, first you have to convert the denominators into the same number like the other equations. For example, if the equation you want to work out is

    \[ \frac{2}{3}+\frac{3}{5} \]

The method in order to answer the equation is:

1. As mentioned before, convert the denominators into the same number. In order to do so, you will have to find out the LCM (Least Common Multiple) of the two numbers. In this case, the LCM is 15. Therefore, it will be like the equation below:

    \[ \frac{10}{15}+\frac{9}{15}=\frac{19}{15} \]

2. The answer is an improper fraction. Therefore, simplifying it to a mixed number is necessary. The answer is written below:

    \[ 1\frac{4}{15} \]

3. You’re done! The final answer is:

    \[ 1\frac{4}{15} \]

 

How to Add Subtractions

In order to be able to add fractions, first you have to convert the denominators into the same number. For example, if the equation you want to work out is

    \[ \frac{9}{11}+\frac{5}{2} \]

The method in order to answer the equation is:

1. As mentioned before, convert the denominators into the same number. In order to do so, you will have to find out the LCM (Least Common Multiple) of the two numbers. In this case, the LCM is 22. Therefore, it will be like the equation below:

    \[ \frac{18}{22}+\frac{55}{22}=\frac{73}{22} \]

2. The answer is an improper fraction. Therefore, simplifying it to a mixed number is necessary. The answer is written below:

    \[ 3\frac{7}{22} \]

3. You’re done! The final answer is:

    \[ 3\frac{7}{22} \]

 

How to Subtract Fractions

In order to be able to subtract fractions, first you have to convert the denominators into the same number in order to make sure it as a Equivalent Fraction. For example, if the equation you want to work out is

    \[ \frac{9}{4}-\frac{1}{6} \]

The method in order to answer the equation is:

1. As mentioned before, convert the denominators into the same number. In order to do so, you will have to find out the LCM (Least Common Multiple) of the two numbers. In this case, the LCM will be 12. Therefore, it will be like the equation below:

    \[ \frac{27}{12}-\frac{2}{12}=\frac{25}{12} \]

2. The answer is an improper fraction. Therefore, simplifying it to a mixed number is necessary. The answer is written below:

    \[ 2\frac{1}{12} \]

3. You’re done! The final answer is:

    \[ 2\frac{1}{12} \]

 

Comparing Fractions

In order to compare fractions, you have to follow the steps below.

1. For example if the fraction you want to compare is 9/4 and 5/13, you have to make the denominator the same.

    \[ \frac{9}{4} \]

 

 

    \[ \frac{4}{16}=\frac{1}{4} \]

How to Convert Improper Fractions to Mixed Numbers

Steps in order to convert improper fractions to mixed numbers:

1. For example, if the number is 5/13, divide the denominator by the numerator. So that would be… 13÷5=2 r 3.

2. According to the equation, there are 2 fives in 13 and 3 is left over. So… the mixed number will be 2 3/5.

How to convert mixed numbers in to improper fractions:

For example if the number is 3 2/5, the numerator will be 3 * 5 + 2. The denominator will be the same- 5.

 

Criterion D: Reflection of Number Challenge

For the number challenge, I used organising skills, addition skills, subtraction skills, multiplication skills, division skills and so on. As I discovered more new and interesting methods, I explored other ways of getting answers. Using parentheses, square and cubic numbers, and root numbers enabled me to have a wider variety of solutions and possible equations.

One of the challenges I encountered was the fact that it took a long time to figure out the way to correctly express the equation on the computer. The number which was challenging to get was 17 as it took a long time to come up with the idea of using decimal numbers. For example, I thought of this equation for 17.

Screen Shot 2013-10-16 at 6.55.33 PM– decimal number.

Another challenging technique was using root numbers and also negative numbers.

Screen Shot 2013-10-16 at 6.58.47 PM,       Screen Shot 2013-10-16 at 7.00.42 PM

In order to improve my method of getting the answers, maybe I should try to work out answers in order, starting with 0.

For the past few weeks, we learnt about root numbers, square numbers, cubic numbers and such.