3. Warm-Up:
3. Which Fraction is larger: 4/6 or 7/10?
4. 2/5 + 7/8 = 5. 3 3/7 + 2 3/8 =
6. 6/11 - 5/12 = 7. 3 2/7 - 2 1/8 =
8. 8/15 • 3/11 = 9. 3 2/7 • 2 1/8 =
10. 8/15 ÷ 3/11 11. 3 2/7 ÷ 2 1/8 =
=
12. Find the Prime Factorization of 60
13. Simplify, using GCF: 144/150
4. Decimals: Objectives
1. Read decimals 6. Add decimals
2. Write decimals 7. Subtract decimals
3. Compare the size of 8. Multiply decimals
decimals to one 9. Divide decimals
another 10. Round decimals to
4. Convert fractions to nearest tenth
decimals 11. Round decimals to
5. Convert decimals to nearest hundredth
fractions
5. Decimals: Definition
A decimal is a fraction with a denominator that is a
multiple of 10. The decimal (.) is used to indicate place
value. Examples:
3
equals 0.3 stated as "three tenths"
10
18
equals 0.18 stated as "eighteen hundre dths"
100
Caution: each decimal expression with a value
less than 1 is preceded by a leading zero to
emphasize the presence of a decimal. For
example, .7 is correctly written as 0.7
7. Decimals: Reading
Reading
1. Read the whole number on the left
2. Read the decimal point as the word
“and”
3. Read the decimal fraction on the right
Example: 8.3 = “eight and three tenths”
4.06 = “four and six hundredths”
0.5 = “five tenths
8. Decimals: Writing
Write as follows
1. The whole number (if none, then write a zero - (“0”)
2. The decimal point to indicate the place of value
3. The decimal fraction portion of the number
Examples: “Seven and five tenths” = 7.5
“One hundred twenty-five thousandths” = 0.125
9. Decimals: Comparing Values
Zeros do not change the value of the number
whether added at the beginning or the end,
but they are unsafe as trailers.
Ex: .7 is the same numerical value as 0.7
12.6250 is the same value as 12.625
but, 30.0 can be misinterpreted as 300!
Use leading zeros; AVOID trailing zeros
10. Decimals: Comparing Values (cont’d)
Zeros added within a decimal number
change the value dramatically
Example: 0.375 is NOT the same as 0.0375
2.025 is NOT the same as 20.025
11. Decimals: Comparing Values (cont’d)
Different whole numbers
Ifwhole numbers are present and different,
whole numbers are compared to determine
largest
Example: 4.8 is greater than 2.9
Same or no whole number
The number in the tenths place determines
largest
Example: 0.45 is larger than 0.37
12. Decimals: Comparing Values (cont’d)
Same or no whole number, and the number
in the tenths place is the same
The decimal with the highest number in the
hundredths place is the largest
Examples: 0.67 is larger than 0.66
0.17 is larger than 0.14
0.09 is larger than 0.08
13. Decimals: Adding and Subtracting
Place the numbers in the columns so the decimals
are lined up. Add or subtract from left to right.
Examples:
16.4 .7
21.8 .750 .7
+ 3.0 + .324 - .050
Safety Point: Zeros may be added to help line up
decimals – don’t include in final answer!
14. Decimals: Multiplying
Place decimal correctly!
Multiply numbers; in the product (answer), count
decimal places right to left equal to the total
decimal places in the numbers being multiplied.
Example:
1.2
.7
x 3.2
x .050
24
36
384. = 3.84
15. Decimals: Multiplying (cont’d)
Add zeros where needed to ensure correct
placement of decimal in answer
Example: 0.11 x .33
0.11
.12
x 0.33
x .14
33
33
0363. = 0.0363
16. Multiplying by Decimal Movement
Multiplying by 10, 100, 1,000 can be done by
moving decimal to the right one space for each
zero in the number by which multiplying
Example: 1.6 x 10 = 1.6 = 16
5.2 x 100 = 5.20 = 520
.7 • 10 = .8 • 100 =
17. Decimals: Dividing
Same as for whole numbers
Q uotient
Divisor Dividend
Example: 9 27 = 27 divided by 9
18. Decimals: Dividing a Decimal
To divide by a whole number, place decimal in
quotient directly above decimal in dividend
3 .5
5 1 7 .5
8 22.3
- 15
25 4 35.7
- 25
0
19. Decimals: Dividing by a Decimal
Move the decimal in the divisor to the right
until the number is a whole number. Then move
the decimal in the dividend the same number of
spaces. 2 3 .2
. 3 6 9 .6
0.3 6.96 - 6
9
- 9
.8 12.1 6
-6
0
20. Class Work:
Decimal Handout:
Every Other Problem
Girls: Begin with First Problem
Gents: Begin with Second
Problem
21.
22. Decimals: Changing from Fractions
Rewrite fraction in division format
Divide the numerator by the denominator and add
zeros as needed
Method can be used to compare fraction size
0.4
2 1 1
5 2.0 0.333... and 0.166...
5 3 6
1 1
Therefore is larger than
3 6
