## Science Fundamentals: Chapter 1

**Arithmetic**** **

## In this unit, we will talk about different mathematical operations and how to apply them to whole numbers. __Skip to quiz!__

**Overview**

Whole numbers are counting numbers from zero to infinity. Examples of whole numbers would be 0, 1, 2, 3 and so on. Numbers like -1, 7.5, -3 or 1.2 are not whole numbers. We will learn how to do addition, subtraction, multiplication, and division using whole numbers in this topic.

**Addition**

Addition keeps track of the amount of something we have after combining them. We use the plus sign “+” for addition.

There are two methods you can use to do basic addition. The methods are called the **drawing **and the **number line **method. Let’s look at how to use the two methods one by one.

The drawing and the number line methods are the **traditional **ways of doing addition. However, there are some **shortcuts **you can take to make addition faster and easier.

**Subtraction**

Subtraction is when we remove something from a whole. The minus sign “ - ” is used for subtraction.

Say I start with eight slices of pizza, and I ate two slices. That leaves me with six slices of pizza. Subtraction lets me see how many pizza slices I have left after taking away two slices.

Similar to addition, we can use the **drawing **and the **number line** method to subtract. Now one by one, let's look at how we can use the two methods to subtract.

** **

Using the drawing and the number line can take time when subtracting big numbers. Instead, we can use the borrowing method to make this easier. It is the most common method for doing subtraction.

**Multiplication**

Multiplication is adding groups of equal sizes together. We use the times’ sign “ x” or a dot “●” for multiplication. Let’s look at an example of multiplication in the following video.

Say we are multiplying 324 by 46. Here using the addition method to solve will take a long time. Let's look at how to multiply when we have large whole numbers.

When multiplying whole numbers, it might take some time to solve. One way to make multiplying whole numbers easier is by using the base ten methods.

Another way we can make multiplication easy is by following two important rules. Any number multiplied by 0 is 0. For example 4 x 0 = 0.

The second rule: any number multiplied at 1 is equal to that number. For example, 178 x 1 = 178.

**Division**

Division is when we break something into equal parts. We use the slash line “ / ” or a division symbol “ ÷ ” for division. Let’s look at how division is done most commonly.

Sometimes the traditional method of dividing can be time-consuming. In some cases, we can use shortcuts to make division simpler. Let’s look at them one at a time.

In this module, we talked about addition, subtraction, multiplication and division. We also learned how to use shortcuts to make the calculations easy for us.

**Fractions, Decimals, and Percentages**

## In this unit we will learn about fractions, decimals, and percentages. __Skip to quiz!__

**Introduction**

Fractions represent parts of a whole number. We write fractions in “a/b” form. Here, a is the **numerator **and b is the **denominator**.

Imagine a pizza is cut into 4 slices and I ate 1 of the slice. The slice I ate can be represented as ¼ . The fraction ¼ is a smaller part of the whole pizza.

We use a decimal point “ . ” to write decimal numbers. Anything to the right of the point is a whole number. Anything to the left is a part of a whole.

The ¼ fraction of the pizza from the previous example can also be written as 0.25. Here, zero is the whole number and 25 is a part of the whole. Recall that the whole numbers are counting numbers, and fractions are a part of the whole numbers.

A percent is a part out of 100. We use the percent sign “%.” for percentages. For example, I get a 87% on my exam. It means that I got 87 points on the exam out of the total 100 points.

**Adding Fractions **

When adding two fractions together, we first need to check if the denominator is the same or different. The steps for adding fractions changes depending on the denominator.

If we add fractions with the same denominators, that means the two fractions are a part of the same whole. Let us see how we add fractions with the same denominator.

If we add fractions with different denominators, that means the two fractions are not a part of the same whole. In this case, we have to make the fractions be part of the same whole. Let us look at how to do this with an example.

The most important thing to remember when adding decimals is making sure the decimal point in the two numbers are lined up. Let’s look at an example of how to line up the decimals and add the decimal numbers together.

**Conversion**

Recall from the pizza example that fractions can also be written as decimal numbers. We can convert fractions to decimal numbers by **dividing** the numerator and the denominator of the fraction. This acts just like the division operator.

When converting decimals to fractions, we only convert the numbers on the right side of the decimal. We do this by writing the number in terms of what place it is in after the decimal.

When converting fractions to percentages, we first get the fraction into decimal form. Then, we multiply the decimal by 100 to get it into a percentage. In the following example, we will see how this is done.

When converting percentages to fractions, we have to put the percentage over 100 and simplify. Let’s look at an example of how this works.

** Ratio and Proportion**

Ratio compares two numbers. We write ratios with a colon “: ” or a with a dash “/.”

Say, I have five watermelons and three mangos. My ratio of watermelons compared to mangos will be 5:3.

There is no need to convert ratios to fractions because ratios are the simplest forms fractions. We can write the watermelon and mango example from the previous slide as 5/3 instead of 5:3.

Say I have ten watermelons and four mangos. My ratio of watermelons with relation to the mangos will be 10:4. But, it can be simplified by dividing 10/4 that is 5/2 So, we get the ratio as 5:2.

Proportions compare two fractions. We use double colon ‘::’ or equal sign ‘=’ for proportions. Let’s look at how we can figure out if two fractions or ratios are proportional to each other.

Say, we are given a true proportion with a missing number. Here we are given the following proportion. Let’s look at how to find the missing value of n.

In this module, we learned about fractions, decimals, and percentages. We also learned how to convert between fractions, decimals, and percentages.

**Question #1: Find the whole number from the following set of numbers: -1, 1.5, -3, 1**

-1

1.5

-3

1

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Answer: **1**

*Except for 1, all the other numbers in the set are either negative numbers or decimal numbers. *

**Question #2: Use the drawing method to add 5 sodas with 4 more. What is the answer?**

8

1

10

9

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Answer: **9**

*5 + 4 = 9 because if I have 5 sodas and get 4 more, in total, I will have 9 sodas. *

**Question #3: Use the number line method to add 6 sodas with 3 more. What is the answer?**

8

1

10

9

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Answer: **9**

*On the number line, if I go three times to the right from 6, I will end up at 9.*

**Question #4: Subtract 9 from 12 using the borrowing method. What is the answer?**

-3

3

1

0

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Answer: **3**

*When we take away 9 from 12, we are left with 3.*

**Question #5: What is 1200 multiplied by 0?**

1200

12

0

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Answer: **0**

*Remember, anything multiplied by 0 is equal to zero. *

**Question #6: What is 1200 multiplied by 1?**

1200

12

0

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Answer: **1200**

*Remember, any number multiplied by 1 is equal to the number itself.*

**Question #7: The denominator of a fraction is the number on the bottom. **

True

False

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Answer: **True**

*Denominator is the number below the line in a faction. *

**Question #8: What does the number(s) before the decimal represent?**

Fractions

Whole Numbers

None of the above

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Answer:** Whole Numbers **

*The number(s) that comes before the decimal is always a whole number.*

**Question #9: Add the following fraction: 1/7 + 4/7 **

5/14

7/14

5/7

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Answer: **5/7**

*Add the numerator together.*

*= 1/7 + 4/7*

*= (1+4)/7*

*= 5/7 *

**Question #10: Add the following fraction: 1/2 + 1/4 **

2/6

3/4

1/6

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Answer: **3/4**

*Remember, anything multiplied by 0 is equal to zero. *

**Question #11: What is 1.2 + 2.3 ? **

3.5

35

3.2

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Answer: **3.5**

*Line the points up and apply addition property. *

* 1.2*

*+ *__2.3__

* 3.5*

**Question #12: How to convert fraction “a/b” into decimal? **

Multiply a by b

Divide a by b

None of the above

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Answer:** Divide a by b **

*Fractions are represented in the same way division is represented with a slash “/.” When you divide two whole numbers, the result is in decimal form. *

**Question #13: What is 5/2 converted into decimal? **

10

2.5

3.5

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Answer: **2.5**

*Divide 5 by 2.*

**Question #14: What is the fractional form of 1.25 **

1.00

¼

1 ¼

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Answer: **1 ¼**

*Recall from the video, the 2 to the right of the decimal is in 10th place. The 5 is in the 100th place.*

*So, 2 is written as 2/10, or **20/100**, and 5 is written as **5/100**. *

*The fractional form is *

*1 + (25/100)**. When simplified, it becomes *** 1 ¼**.

**Question #15: Convert 75% into the simplest fraction. **

75/100

¾

75

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Answer: **¾**

*Put the 75 over 100 and simply.*

**Question #16: Ratios and fractions are the same thing. **

True

False

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Answer: **True**

*Ratios are another way of representing the fractions.*

**Question #17: ¼ is proportional to 25/100? **

True

False

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Answer: **True**

*25/100 simplified is equal to ¼. This makes the statement true. *

**Question #18: Find the missing value in the following proportion: **

**4/6 = x/15 **

10

6

60

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Answer: **10**

*Cross Multiply and we get 6x = 60. Divide 60 by 6 and we get 10.*