In this unit of math, we learned many things. I learned how to isolate the variable, write and solve algebra equations, graph on number lines, and how to solve decimal and fraction equations. For my assignment, I will be showing how to graph an inequality on the number line.

example: x ≥ 2

Step 1: Find out what the signs are saying. In this case, the equation is saying that x is greater than, or equal to 2. So the options are 2,3,4,5,6, through infinity.

Step 2: Find whether the dot should be opened or closed. Closed means  that it includes the value, and open means that it is greater then the value. In our equation, our dot is going to be closed.

Step 3:  Figure out which way the arrow is going to be facing on the graph. Our equation is increasing, so the arrow is going to be going to the right.

Step 4: Place the equation on the graph, I will demonstrate down below.

In our second unit of math, we covered many topics. We learned how to find square roots, determine the length, width, areas, etc of squares, and how to estimate the square root of a irrational number. We also learned what the Pythagorean Theorem is, and how to square root fractions, decimals, positive, and negative numbers. We leaned how to write in exponential form, and how to simplify equations. Lastly, how to add and subtract  exponents. For my assignment, I will be focusing on estimating the square root of an irrational step by step.

Number: √30.

Step 1:

Find whether the number is rational or irrational (rational: stops or has a pattern, irrational: repeating but doesn’t have a pattern). In this case, this number is irrational.

Step 2:

See which 2 square roots 30 falls in between. It is 5 and 6, becuase the Square root of five is 25 and square root of six is 36. 30 is in between 25 and 36.

Step 3:

Seeing which rational number it is closer to. 30 is almost in the middle of 25 and 36 but it is a little bit closer to 25 which means the number is going to be smaller than 5.5.

Step 4:

Lastly, choose a decimal that would fit with this equation, I would choose 5.4. So, √30 is around 5.4

Harder equation:

In our first unit of math, we covered many topics. We worked with multiplying, dividing, adding, and subtracting fractions. As well as converting a mixed fraction to improper, and how to make a decimal a fraction. We also learned how to place numbers and equations on the number line, and what real, rational, integers, whole numbers, and natural numbers are. For my summary, I will be focusing on adding fractions, and converting it from improper to mixed.

There are a few steps with adding fractions, which will be written down below with an example.

3/4 + 1/3

Step 1: The first step is finding the common denominator. Do do this, we need to find multiples of 3 and 4, and see what multiple they have in common. If the denominator is ever the lowest common multiple already, then you don’t need to do anything to that fraction (I will give and example on paper).

4,8,12,16

3,6,9,12

As you can see, 12 is the number they both have in common

Step 2: Now, we change the denominator to 12. To get 4 to 12, we have to multiply 4×3, so whatever we do to the denominator, you always have to do to the numerator, which means multiplying 3×3, so our new fraction is 9/12. Do that to the second fraction as well, making it 4/12.

Step 3: now, we can add the two numerators together, so 9/12 + 4/12 = 13/12

Step 4: The final step is to convert it into a mixed fraction. Firstly, you see how many times 12 goes into 13 (1x), which gives the whole number, and then you see how many remains (1). With this information, all you have to do is  keep the denominator 12, and you are left with 1 1/12.

So, 3/4 + 1/3 = 1 1/12.