1. Bell Work If the radius of a circle is 13 cm, then what is the circumference? If two angles of a triangle are 45 degrees, then what is the 3rd angle measurement?

2. Answer: 2π(13cm) = 2(3.14)(13cm) = 81.64cm 90°

3. Lesson 4: Review of Arithmetic

4. Number. : An idea Numeral
Number*: An idea Numeral*: A symbol that we use to express the idea of a particular number. The value of a numeral is the number represented by the numeral.

5. Easier way to understand this: You are a person, and there is just one of you. But different people call you by different names. Your name isn’t you, it just represents you. It’s the same thing with number and numeral. A number is an idea but a numeral is what is used to represent that idea. For example, there could be three pencils on my desk. I know there are three objects, however a way I could put this down on paper to represent it would be to say there are “3” pencils.

6. Counting Numbers (or Natural Numbers): When we begin counting, we always begin with the number 1 and follow it with the number 2 etc. Thus counting numbers are (1, 2, 3, 4, ……).

7. Real Numbers: A value that represents a quantity or a distance on a number line. This includes all rational (-5, ⅔) and all irrational (√2, π).

8. Number Line: The number line can be used as a graphic aid when discussing positive and negative numbers.

9. To graph a point on the number, we place a closed dot on that corresponding number.

10. Graph the following points on a number line. -5, 1, -2, 3.5, -2.5, 2.5

11. Answer: -5, -2.5, -2, 1, 2.5, 3.5

12. Multiplication of Fractions: Fractions are multiplied by multiplying the numerators to get the new numerator, and by multiplying the denominators to get the new denominator.

13. Example: 4/3 x 7/5 5/7 x 2/3

14. Answer: 4/3 x 7/5 = 4x7/3x5 = 28/15 = 1 13/15 5/7 x 2/3 = 5x2/7x3 = 10/21

15. Diving Fractions: We divide fractions by inverting the divisor and then multiplying.

16. Example: 4/3 ÷ 15/8 5/6 ÷ 3/4

17. Answer: 4/3 ÷ 15/8 = 4/3 x 8/15 = 4x8/3x15 = 32/45 5/6 ÷ 3/4 = 5/6 x 4/3 = 5x4/6x3 = 20/18 = 1 2/18 = 1 1/9

18. If cancellation is possible, it is easier if we cancel before we multiply. Example: solve by cancelling 7/3 x 30/9 3/5 x 5/6 x 21/23

19. Answer: 7/3 x 30/9 = 7/1 x 10/9 = 70/9 = 7 7/9 3/5 x 5/6 x 21/23 = 1/1 x ½ x 21/23 = 21/46

20. Change mixed numbers to improper fractions and then multiply or divide as indicated. Example: 2 ½ x 5 ⅓ 12 ⅓ ÷ 2 ⅙

21. Answer: 2 ½ x 5 ⅓ = 5/2 x 16/3 = 5/1 x 8/3 = 40/3 = 13 ⅓ 12 ⅓ ÷ 2 ⅙ = 37/3 x 6/13 = 37/1 x 2/13 = 74/13 = 5 9/13

22. We use the equals sign to designate two quantities are equal
We use the equals sign to designate two quantities are equal = 7 In the same way we use the ≠ symbol to designate that two quantities are not equal ≠ 11

23. Basic Operations: Addition = Sum Subtraction = Difference Multiplication = Product Division = Quotient

24. Operations with decimal numbers: We must align the decimal points vertically when we add and subtract decimal numbers. Example: –

25. Answer: = – =

26. We do not alight the decimal points when we multiply. Example: 4
We do not alight the decimal points when we multiply. Example: 4.06 x 0.016

27. Answer: 4.06 x =

28. When we divide, we adjust the decimal points as necessary. Example: 6

29. Answer: ÷ 0.03 = ÷ 3 = 201.3

30. Unit Multiplier: 3 ft/1yd and 1yd/3ft are both equal to 1
Unit Multiplier: 3 ft/1yd and 1yd/3ft are both equal to 1. We call these fractions unit multipliers. We can use unit multipliers to change the units of a number.

31. Example: Use one unit multiplier to convert 32 feet to inches
Example: Use one unit multiplier to convert 32 feet to inches (1ft = 12 inches)

32. Answer: = 32 ft / 1 x 12 inches / 1 ft Feet cancel out = 32 x 12 inches / 1 = 384 inches

33. Example: Use one unit multiplier to convert 36 feet to miles
Example: Use one unit multiplier to convert 36 feet to miles (5280 feet = 1 mile)

34. Answer: = 36 feet / 1 x 1 mile / 5280 feet Feet cancel out = 36 miles / 5280 ≈0.0068 miles

35. Equivalent Measures: 1 foot = 12 inches 1 meter = 100 cm 1 yard = 3 feet 1 cm = 10 mm 1 inch = 2.54 cm 1 mile = 5280 feet 1 km = 1000 m

36. Practice: Solve the following without a calculator 4 ½ x 2 ⅘ 3 ¼ ÷ 1 ⅜

37. Answer: 4 ½ x 2 ⅘ = 9/2 x 14/5 = 63/5 = 12 ⅗ 3 ¼ ÷ 1 ⅜ = 13/4 ÷ 11/8 = 13/4 x 8/11 = 26/11 = 2 4/11

38. HW: Lesson 4 #1-30