Fractions on a number line

When placing a fraction on a number line you place positive fractions to the right and negative fractions to the left. To place a number on the number line you have to split the denominator into pieces between two whole numbers.

For example if you have you find 3 and 4 on a number line. Then you split the section between 3 and 4 into 3 pieces. Then you place the fraction on the 2nd line.

If you want to order the fractions from least to greatest you have to find the lowest common denominator for all the fractions before you can start to place them on the number line.

Comparing Fractions

Numerator and Denominator

The Numerator is the top number and the Denominator is bottom number.

 

To compare 2 fractions you need to make sure that both fractions have the same denominator. If the denominators are different you need to find the lowest common denominator to make sure the fractions have the same denominator. Once both denominators are the same you can compare the numerators. The fraction with the biggest numerator is the bigger fraction.

For example if you have and you will multiply each one by itself to get the lowest common denominator. Once you have the lowest common denominator you can see which numerator is the highest and find out which fraction is bigger.

If the two numerators are negative, the smaller negative is the bigger number

Adding/Subtracting Fractions

When adding and subtracting fractions you need to make sure that both denominators are the same before you add. If the denominators are different you need to find the lowest common denominator to make sure the fractions have the same denominator. Once both denominators are the same you can add or subtract the numerators to get your answer.

You can use the tug a war question method when adding and subtracting fractions. The three steps to a tug a war question are Sort, Combine, and Answer.

Multiplying/Dividing Fractions

When you are multiplying fractions you don’t need both fractions to have the same common denominator, you can just multiply straight across. This is called a just do it question. If you have a denominator and numerator that divide by the same number you can cross simplify to make the fractions easier to multiply.

For example if you had x you could cross simplify the 2 and the 8 and the 4 and the 4 to make the fractions easier to multiply

When you are dividing fractions you don’t need to have the same common denominator. To make a division question easier you could turn it into a multiplication question by reciprocating the second fraction. You reciprocate a fraction by flipping it over.

For example if you have divided by you can reciprocate the and turn it into . Now your question looks like x . From here you can now cross simplify if necessary, multiply and get your answer.

Square Roots

To find the square root of a number you need to find the number that multiples by itself. For example, to find the square root of you need to find the number that times itself equals 25. In this case it would 5. 5 x 5 = 25. = 5

If a number does not have a number that multiplies by itself than it’s not a proper square. In this case, you will need to estimate the square root by finding the 2 whole numbers your number is in between and estimate the decimal value from there.

For example if you have . You know 39 is not a perfect square because 6 x 6 = 36 and 7 x 7 = 49. This means that you know the is going to be between 6 and 7. Now you can estimate the decimal value and get your answer