1. Rounding and Estimating Whole Numbers and Decimals
Reviewing the Basics
Rounding and Estimating
Whole Numbers and Decimals

2. Rounding and Estimation
Rounding and estimation are used to express a number to the nearest ten, hundred, thousand, and so forth
It may be helpful to review the diagram below to help determine decimal place value

3. Example 1: Round 93 to the nearest ten.
A number line is a good visual aid for the student to see that a number is closer to a certain ten, hundred, thousand, and so forth.

4. Practice
Text page 3 #’s 1-17
Review answers

5. Using Addition and Subtraction
Adding two decimal numbers with more than one digit (columns of numbers) is very similar to adding whole numbers. Like whole numbers, addition of decimals often requires regrouping (carrying, trading, renaming). Regrouping occurs when the total of the numbers in a column (i.e., ones position) is equal to or greater than ten. Problems are presented in both vertical and horizontal formats

6. Example 2: Solve = ?
Step 1: Rewrite the problem vertically. Always line up the decimal points. Step 2: Add the numbers in the hundredths position (7 + 6 = 13). Write the 3 in the hundredths position. Carry the 1 to the next column (tenths). Step 3: Add the numbers in the tenths column, including the number carried over from the previous column ( = 13). Write the 3 in the tenths position. Carry the 1 to the next column (ones). Bring the decimal point down. Step 4: Add the numbers in the ones position, including the number carried over from the previous column ( = 14). Write the 14 to the left of the decimal point.

7. Exercises on page 5 #’s 1-9 together on board
#’s 10 – 30 (Odd) independently
Review answers

8. x 1 2 3 4 5 6 7 8 9 10

9. Multiply Decimal and Whole Numbers
Multiplying a decimal number by a whole number (23 x 3.2) requires a strong understanding of multiplication skills, specifically with multiple digit numbers.

10. Example 3: Solve: 23 x 3.2 = ? Step 1: Rewrite the problem vertically.
Step 2: Multiplication follows the same format as with whole numbers. Please refer to multiplication of whole numbers for more information.
Step 3: Place the decimal point. Each place to the right of the decimal point is a decimal place. Count the number of decimal places in the factors (1). Place the decimal point in that position in the product. The number of decimal places in the product equals the sum of the decimal places in the factors.

11. Divide Decimals by Whole Number
Dividing a decimal number by a whole number is very similar to dividing whole numbers. The decimals point must remain in the same position in the answer.

12. Example 4: Solve 18.9 divided by 9 = ?
Step 1: Write the problem in long division format.
Step 2: Division follows the same format as with whole numbers. 9 goes into 18 two times because 9 x 2 = 18. Place 2 in the ones position. Subtract 18 from 18 resulting in 0. Bring down the 9.
Step 3: Place the decimal point.
Step 4: 9 goes into 9 one time because 9 x 1 = 9. Place 1 in the tenths position. Subtract 9 from 9 resulting in 0.

13. Exercises #’s 1-6 together on board #’s 15-18 independently
Review problems

14. Add Fractions: Different Denominator
A fraction is comprised of two parts: a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 2/3, the "2" is the numerator and the "3" is the denominator. In order to add fractions, you must have a common denominator. A common denominator is a whole number that is a common multiple of the denominators of two or more fractions. For example, 12 and 24 are both common denominators for 3/4 and 5/6, because 4 and 6 will both divide into 12 and into 24.

15. Example 5: Reduce all fractions to lowest terms. 1/5 + 4/9 = ?
Step 1: Rewrite horizontal problems vertically. (This step is not necessary, but many students find it easier to add fractions when the problems are written vertically.)
Step 2: Find a common denominator (a common multiple of the denominators of two or more fractions). For this problem, the common denominator is 45, because 9 and 5 will both divide into 45.
Step 3: Multiply 1/5 by 9/9. Rewrite the first fraction as 9/45. Multiply 4/9 by 5/5. Rewrite the second fraction as 20/45.
Step 4: Add the numerators together ( = 29). The denominator (45) remains the same.

16. Subtract Fractions: Mixed Numbers
Subtracting mixed fractions requires a solid understanding of adding fractions and the multiplication table. If the numerator of a fraction is less than the denominator, the fraction is called a proper fraction. If the numerator is equal to or greater than the denominator, the fraction is called an improper fraction. An improper fraction can be rewritten as a mixed fraction. For example, 5/3 is an improper fraction. It can be rewritten as 1 2/3, which is a mixed fraction. The following is a step-by-step example of subtracting two mixed fractions.

17. Example 6: 7 4/5 - 3 2/9 = ? Step 1: Write the problem vertically.
Step 2: Separate the problem into subtraction of whole numbers and subtraction of fractions.
Step 3: Find a common denominator (a common multiple of the denominators of two or more fractions) for the fractions. For this problem, the common denominator is 45. Multiply 4/5 by 9/9 to get 36/45. Multiply 2/9 by 5/5 to get 10/45.
Step 4: Subtract the whole numbers (7 - 3 = 4). Subtract the numerators ( = 26). The denominator remains the same (45).

18. Practice
Text page 15 #’s 1-10
Review Problems

19. Multiply Fractions: Mixed Numbers
Multiplying mixed fractions involves a solid understanding of the multiplication table.

20. Example 7: 7 2/3 x 4 5/6 = ? Step 1: Rewrite the problem vertically.
Step 2: Rewrite the mixed fraction as an improper fraction. For example, to change 7 2/3 into a fraction multiply the denominator with the whole number (3 x 7 = 21). Then add the product with the numerator ( = 23). The denominator remains the same.
Step 3: Multiply the numerators and denominators.
Reduce

21. Example 8:
Step 1: Rewrite the problem as a multiplication problem. There is a rhyme to help remember how to complete this process: Dividing fractions is easy as pie, Flip the second and multiply. Using this rhyme, the second fraction (8/9) becomes 9/8, and the ÷ symbol becomes a x symbol.
Step 2: Multiply the numerators (2 x 9 = 18) and the denominators (5 x 8 = 40).
Step 3: Reduce the fraction to lowest terms. A fraction is in lowest terms when the numerator and denominator do not have a common factor greater than one. Eighteen and 40 can both be divided by 2, so complete this division to reduce the fraction.

22. Exercises
Text page 17 #’s 1-12
Review on board

23. Ratio/ Proportion
A ratio is a comparison of two numbers expressed as a quotient. They can be written in three ways: a fraction (3/5), a ratio (3:5), or a phrase (3 to 5). Like fractions, ratios refer to a specific comparison. The ratios 3/5, 3:5, and 3 to 5 (as in "the ratio of cellos to violins was 3 to 5") all express the same ratio or comparison. A proportion reflects the equivalency of two ratios. The ratio 3/5 expresses the same proportion as the ratio 15/25.

24. Example 9: Sandra has 15 lollipops and 25 jellybeans
Example 9: Sandra has 15 lollipops and 25 jellybeans. What is the ratio of lollipops to jellybeans?
There are 15 lollipops to 25 jellybeans, so the ratio of lollipops to jellybeans is 15:25.
How else can this ratio be written?

25. Example 10: Is the following proportion True or False? 1/3 = 3/9
The cross products are both equal to 9, so the proportion is TRUE. If the cross products are not equal, the proportion is false.
Sometimes you must find the value of a variable in a proportion. To solve the proportion, you must find the value of the variable that makes both ratios equal

26. Example 11: 9/12 = a/48
Step 1: Find the cross products. Multiply 48 by 9 and 12 by 'a'.
Step 2: 48 x 9 = 432 and 12 x a = 12a. Rewrite the equation with the new products.
Step 3: Divide each side of the equation by 12 to isolate the variable 'a'.
Step 4: Divide 432 by 12 to get a = 36.

27. Exercises Text page 21 #’s 1-8 together #’s 9-18 Independent

28. Calculating Percentages
Percent is a way to express a number as it compares to Percent means "per one hundred." If 7 out of 100 students ate pizza for lunch, then 7% of the students ate pizza for lunch.

29. if you knew that 35 out of 50 students had eaten tacos for dinner.
How would you calculate the percentage of students who ate tacos for dinner?
if you knew that 35 out of 50 students had eaten tacos for dinner.
Percent is "per one hundred."
first set up the ratios: 35/50 =?/ multiplied by 2 is 100, so 35 should be multiplied by 2 to make the ratios equal. The result is 70/100 which translates into 70%. 70% of the students ate tacos for dinner.

30. Example 12: Find 25% of 48
Step 1: Change the percent amount to a fraction (remember percent means "per one hundred").
Step 2: Multiply 25/100 by 48. Change 48 into a fraction by making its denominator 1. Multiply numerator by numerator (25 x 48 = 1200). Multiply denominator by denominator (100 x 1 = 100).
Step 3: Reduce the product to its lowest terms (1200 ÷ 100 = 12).

31. Exercises Text page 23 #’s 1-3 together on board
#’s 4- 7 Independently
Review problems

32. Perimeter, Area, Volume Perimeter is the measurement around a figure
Area is the measurement of the interior of a two-dimensional region. Area measurements are in square units
Volume is the measurement of a three-dimensional figure's interior space. Volume is measured in cubic units

33. Area The formula for calculating area of a square or rectangle is:
Area = length x width.
Area = ½ base x height

34. Example 13: A figure has a width of 7 inches and a length of 3 inches
Example 13: A figure has a width of 7 inches and a length of 3 inches. What is the area of the figure?
Step 1: Multiply the width and the length
Area = 7 x 3 = 21

35. Perimeter
To calculate the perimeter of a figure, add the lengths of all the sides of the figure
P = = 20

36. Volume
Volume is the measurement of a three-dimensional figure's interior space. Volume is measured in cubic units.
The formula for calculating the volume of a rectangular solid is length multiplied by width multiplied by height.
Volume = length x width x height

37. Example 14: A What is the volume of the figure?
The volume of the figure is the length multiplied by the width multiplied by the height
V = 2 x 4 x 6 = 48

38. Exercise
Text page 27 #’s 1-9
Review