Download Fraction and Decimal Notes Unit 2 Workbook 1 Fraction and Decimals

Fraction and Decimal Notes
Unit 2 Workbook 1
.
Fraction and Decimals
.
Things That Make You Go Hmm…..
How can a visual model of an equation be created to demonstrate the
process of division of fractions?
Why does the process of invert and multiply work when dividing
fractions?
When I divide one number by another number, do I always get a
quotient smaller than my original number?
When I divide a fraction by a fraction what does the dividend, quotient,
and divisor represent?
I CAN
_____ I can compute and solve word problems involving division of fractions.
_____ I can fluently divide multi-digit numbers using the standard algorithm.
_____ I can fluently add multi-digit decimals using the standard algorithm for each operation.
_____ I can fluently subtract multi-digit decimals using the standard algorithm for each operation.
_____ I can fluently multiply multi-digit decimals using the standard algorithm for each operation.
_____ I can fluently divide multi-digit decimals using the standard algorithm for each operation.
Table of Contents
Multiplication of Fraction .......................Page 4
Division of Fractions with Models.............Page 5
Division of Fractions...............................Page 6
Key Phrases for Fraction Word Problems...Page 7
Addition and Subtraction of Decimals.......Page 8
Multiplication of Decimals......................Page 9
Division of Decimals...............................Page 10
Multiplication with Model
1
2
𝑜𝑓
1
3
1
The area of shaded overlap
is your numerator, and the
amount of total boxes is
your denominator.
2
means 2 x 3
Step 1: Draw a unit
rectangle and divide it into
3 pieces vertically. Lightly
shade 2 of those pieces.
Step 2: Use horizontal line
and divide the unit
rectangle in half
2
6
1
2
2
2
x3=6
Multiplication of Fractions
You can also cross cancel numbers.
Multiplication of Fractions
3
7
x
2
3𝑥2
3
7𝑥3
=
6
21
Step 1: Multiply the numerators
Step 2: Multiply the denominators
Step 3: Simplify Answer
Both the 5 and 10 are
divisible by 5. Therefore
you can simplify these
two numbers by dividing
each by 5.
Multiplication of Mixed Numbers
You MUST change a
mixed number into
an improper
fraction and then
multiply.
Dividing Fractions with Visual Models
Divide a whole by a fraction
How many 1/3 of a cup are in 2 cups? 2 ÷
1. Draw 2
cups
2. Divide
each cup
into thirds.
𝟏
𝟑
1
4
2
5
3
6
3. There are 6 thirds
in 2 cups.
1
Therefore 2÷3 = 6
Divide a fraction by a whole
2
5
÷4
1. Draw a model of two-fifths.
2. Highlight the portion that
needs to be divided that is 2
squares out of 5
3. Then divide the
highlighted area into 4
pieces
One row of the shaded area is the answer. 2 pieces
out of a total of 20.
𝟐
=
𝟐𝟎
𝟏
𝟏𝟎
Division of Fractions
Choosing what method depends on the numbers you are dealing with.
Method 1: Divide Across
If the numbers allow, you can divide across the numerator and divide across the denominator.
𝟖
Example:
𝟐
𝟖÷𝟐
𝟒
÷ = 𝟐𝟏÷𝟑 = 𝟕
𝟐𝟏 𝟑
Method 2: Common Denominators
You can find a common denominator, and then divide across the numerator
1
2
÷
9 3
Example
Step 1: Find a common Denominator and equivalent fractions
1
9
÷
2
1
=
3
9
÷
6
9
Step 2: Divide across and rewrite numerator
1Anything
6 over ( 1÷6
divided by) 11÷6
is
÷ =
=
that number therefore we can
9
9
9÷9
simplify the denominator.
Therefore
1
9
=
1
2
1
3
6
÷ =
1 ÷6
can be written as
1
6
Method 3: Multiply by the Inverse
Find the inverse (recipricol) of the second fraction and multiply
Example:
𝟑
𝟏
÷
𝟖 𝟑
Step 1: Find the inverse of the 2nd fraction
Step 2: Multiply by the inverse
𝟑
𝟏
𝟑
𝟑
𝟖
𝟏
𝟑
𝟗
𝟏
𝟏
𝟖
𝟖
x = =1
ALL MIXED NUMBERS MUST BE CHANGED IT IMPROPER FRACTIONS
BEFORE APPLYING ANY METHOD
Key words that Signal a Multiplication of Fractions Problems
Part OF a whole/part
1
1
Example: I had 2 a tray of brownies and ate 3 of it.
Situation suggest repeated addition.
1
Example: Each block is 42 inches long. If I have 7 block, how long is my row?
Find the total
3
Example: I made 5 batched of cookie. Each batch uses 4 cup of sugar. How much sugar do I need?
Find the Product
1
3
Example: What is the product of 3 and 4?
Times
1
Example: 56 times 5
Key words that Signal Division of Fractions Problem
Sharing/Separating/Cutting/Slicing
3
8
Example: There are 4 pizza pies left over. Six people are going to split the leftovers. How much will each
person take home?
How Many are in…
1
2
Example: I have 42 pound of dog food. If I feed my dog 3 cups each day, how many days will the
food last?
Addition and Subtraction with Decimals
DUDE!!!!!
When adding or subtracting with decimals, remember…
Decimal
Under
Decimal
Exactly
Example 1: .034 + 1.4
Step 1: Rewrite vertically and line up the decimals
.034
+1.4
Step 2: You may add zeros to hold a place and it does not change the value.
.034
+1.400
Step 3. Bring down the decimal and add normally
.034
+1.400
1.734
**If you have a whole number the decimal point is to the right of the number.
Example 12 you would put the decimal point at the end 12.
Multiplication
CHA CHA SLIDE
When multiplying numbers you DO NOT line up your decimals!
Example 1:
1.59 x .5
Step 1: Write the problem vertically. Do not line up decimals.
1.59
x .5
Step 2: Multiply normally
1.59
x .5
7 95
Step 3: Cha Cha Slide.
Slide the decimal in the top factor right.
Slide the decimal in the bottom factor right.
Slide the decimal the same number of places in the product to the
left.
1.59 2 spaces
x .5 1 space
.7 95
3 spaces
Division
Decimal ÷ Whole Number
Step 1:Bring up the decimal
Step 2: Divide normally
Decimal ÷ Decimal
Whole Number ÷ Decimal
Step 1: Outside number- move decimal right.
Step 2: Inside number- place decimal point after number then move
right same number of spaces.
Step 3: Divide normally
Multiplication of
Fractions
Computations
NAME ________________________________________ DATE _____________ PERIOD _____
Homework Practice
Multiply Fractions
Multiply. Write in simplest form.
3
1
× −
1. −
7
1
2. −
×−
3
1
3. −
× −
2
2
4. −
× −
1
5. −
× 11
1
6. −
× 12
5
7. −
× 21
3
8. −
× 10
1
4
9. −
× −
3
4
10. −
× −
7
4
11. −
× −
3
5
12. −
× −
6
1
13. −
× −
9
4
14. −
× −
8
9
15. −
× −
4
3
5
8
9
7
8
10
8
11
4
21
5
15
9
3
3
2
17. −
× −
× −
5
4
8
5
12
10
2
12
1
18. −
× −
× −
3
3
17
4
4
19. SPORTS Of the sixth graders in a school, −
play at least one sport.
5
2
play on a team. What fraction of the sixth graders play
Of those, −
3
a sport on a team?
2
20. AQUARIUM A model of the ocean floor takes up −
of the space in an
5
3
of the model is coral, what fraction of the space in the
aquarium. If −
8
aquarium is taken up by coral?
Get ConnectED
For more practice, go to www.connected.mcgraw-hill.com.
Course 1 • Multiply and Divide Fractions
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
4
4
2
4
1
1
1
16. −
× −
× −
3
2
3
6
9
3
NAME ________________________________________ DATE _____________ PERIOD _____
Homework Practice
Multiply Mixed Numbers
Multiply. Write in simplest form.
4
1
× 3−
1. −
9
1
2. −
× 3−
3
3
3. 1 −
×−
5
2
4. 2 −
×−
2
1
5. −
× 3−
3
2
6. −
× 2−
5
8
8
10
3
3
3
5
4
4
5
3
1
2
7. 1 −
× 2−
1
1
8. 5 −
× 2−
1
1
9. 2 −
× 1−
4
2
10. 6 −
× 1−
3
1
11. 3 −
× 5−
3
1
12. 8 −
× 4−
4
3
5
3
3
7
3
2
1
13. −
× −
× 2−
9
4
4
4
5
8
4
1
1
1
14. 5 −
× 3−
× −
2
3
6
4
5
1
1
1
15. 1 −
× 2−
× 1−
2
6
5
4
1
inches. What is the area of the plywood?
by 41 −
5
2
1
17. LANDSCAPING A planter box in the city plaza measures 3 −
feet by 4 −
feet
1
feet. Find the volume of the planter box.
by 2 −
3
8
2
Get ConnectED
For more practice, go to www.connected.mcgraw-hill.com.
Course 1 • Multiply and Divide Fractions
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
3
16. LUMBER A lumber yard has a scrap sheet of plywood that is 23 −
inches
Division
of
Fractions
Making Visual Models
for a
Whole Number Divided By A Fraction
;
Name:____________________________
Date:________________________
Dividing Whole Numbers by Fractions
Think about it!
!
!
Morgan bought 3 cups of juice. She wants to pour it into "- cup servings. How many "- cup
servings can she make?
Visual Model:
Number Sentence: _______________________
Answer: ____________________________________
DividingFractionsusingModels
Name:________________Block_________
DivisionProblem
WorkArea:Createamodelforeachdivisionproblemtoarriveatyour
answer.Circleyourfinalanswer.
3 ÷ 1/4
(Howmany1/4sarein3
wholes?)
5 ÷ 1/3
(Howmany1/3sarein5
wholes?)
3 ÷ 1/4
(Howmany1/4sarein3
wholes?)
5 ÷ 2/3
(Howmany2/3sarein5
wholes?)
8 ÷ 2/5
(Howmany2/5sarein8
wholes?)
¾ ÷3/8
(Howmany3/8sarein
3/4 ?)
Name:
Writeitasadivisionquestion.
M akearoughdraftofam odeltorepresentthequestion
Exercises1–5
1.
Aconstructioncompanyissettingupsignson milesoftheroad.Ifthecompanyplacesasignevery ofamile,
howmanysignswillitneed?
2.
Georgebought
feedwith
pizzasforabirthdayparty.Ifeachpersonwilleat ofapizza,howmanypeoplecanGeorge
pizzas?
3.
TheLopezfamilyadopted milesoftrailontheErieCanal.Ifeachfamilymembercancleanup
ofamile,how
manyfamilymembersareneededtocleantheadoptedsection?
4.
Margoisfreezing cupsofstrawberries.Ifthisis ofthetotalstrawberriesthatwerepicked,howmanycupsof
Name:
strawberriesdidMargopick?
5.
Reginaischoppingupwood.Shehaschopped
logssofar.Ifthe
logsrepresent ofallthelogsthatneedto
bechopped,howmanylogsneedtobechoppedinall?
ProblemSet
Rewriteeachproblemasamultiplicationquestion.Modelyouranswer.
1.
Nicolehasused feetofribbon.Thisrepresents ofthetotalamountofribbonshestartedwith.Howmuch
ribbondidNicolehaveatthestart?
2.
Howmanyquarterhoursarein hours?
Making Visual Models
For
Fractions Divided by a Whole Number
Name:
M akearoughdraftofam odeltorepresentthequestion
Example1(fractiondividedbyawhole) Mariahas lb.oftrailmix.Sheneedstoshareitequallyamong friends.Howmuchwilleachfriendbegiven?Whatis
thisquestionaskingustodo?Howcanthisquestionbemodeled?
Example2 Let’slookataslightlydifferentexample.Imaginethatyouhave ofacupoffrostingtoshareequallyamongthree
desserts.Howwouldwewritethisasadivisionquestion?
Wecanstartbydrawingamodeloftwo-fifths.
Howcanweshowthatwearedividingtwo-fifthsintothreeequalparts?Whatdoesthispartrepresent?
Name:
Exercises1–7
Foreachquestionbelow,modelandgivetheanswer.
1.
2.
3.
4.
5.
6.
7.
Division of Fractions
Computations
Fraction Word Problems
Keywords or Signs it is a Multiplication Problem
Keywords of Signs it is a Division Problem
Decimals
.
Review Topics
1
Place Value
The position of a digit in a number reflects the "place value" of that digit. In
the following table, the number represented has value according to the place
the digit "1" holds in each case. (Note the use of commas.)
1,
0
1
0
0
1
0,
0,
0,
1,
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
.
.
.
.
.
.
.
.
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
Etc.
Ten Millionths
Millionths
Hundred-Thousandths
Ten-Thousandths
Thousandths
Hundredths
Tenths
Decimal Point (and)
Units (Ones)
Tens
Hundreds
Thousands,
Ten Thousands
Hundred Thousands
Millions,
Ten Millions
Etc.
In the following chart, note the similarity of place value names on both sides
of the decimal. Those places to the right of the decimal end in "ths"
indicating that they are fractional.
Whole Numbers
Decimal Fractions
1
In a spoken or written number, the word "and" reflects placement of a
decimal point. Although each number uses the same digits, (ones and
zeros), the value of each number in the chart above is very different. The
numbers, in order of the chart, are read:
one million and one millionth
one hundred thousand and one hundred-thousandth
ten thousand and one ten-thousandth
one thousand and one thousandth
one hundred and one hundredth
ten and one tenth
one and no tenths, or more commonly, one
one tenth
7
Writing Decimals
Place value is reflected when writing and reading decimal numbers in words.
In writing the decimal is represented by the word "and."
Example:
4.7
is written
"four and seven tenths."
70.024
is written
"seventy and twenty-four thousandths."
Write the following in words as you would write the number. (Use the
chart at the end of the booklet to aid with number placement.)
1)
20.15
6)
4.05
2)
45.21
7)
278.54
3)
15.196
8)
7.0007
4)
2,049.009
9)
1.1
5)
0.005
10)
1928.07
2
Translating Numerical Expressions
3
To translate written numerical expressions, place the last written number in
the correct place value.
Example:
Six, (6) the last digit belongs in the thousandths place.
Twenty and ninety(Third place to the right from the decimal point.)
six thousandths
20.096
20.096
Zero must be entered in the tenths place.
Write the following using digits. (Use a chart if needed)
1) four and five tenths
2) fourteen hundredths
3) one thousand nine hundred seventy-two ten thousandths
4) four hundred seven and three hundred twenty-eight thousandths
5) one tenth
6) seven and nine hundredths
7) one hundred seventy-two ten-thousandths
8) twenty-two and five tenths
9) twenty and four hundred ninety-six thousandths
10)
three hundred and three hundredths
9
Decimal Fractions
A decimal number is another way to write a fraction with a denominator of
a multiple of ten, (i.e., denominators equal to 10; 100; 1,000; 10,000; etc.)
To convert a fraction with a denominator of a multiple of ten to a decimal,
read the fraction and write as a decimal number.
Example:
3
7
10
3.7
Example:
15
234
1000
15.234
is read " three and seven tenths"
expressed with digits
is read " fifteen and two hundred thirty-four
thousandths"
expressed with digits
Example:
5
100
0.05
is read " five hundredths"
expressed with digits. Note the zero placement.
Write as a decimal number.
1)
19
72
100
4)
2)
7
301
1000
5)
6
1
100
3)
17
100
6)
24
1000
10
1276
3
10
4
Comparing Decimals
5
To compare decimals, write the decimal numbers with the same number of
decimal places and decide which is larger.
Example:
Which is greater:
0.9 or 0.91?
0.90 ? 0.91
Example:
Write the following from
smallest to largest:
0.78006, 0.7845,
0.7851, 0.785, 0.78
To compare write both numbers with two decimal
places. Note zeros may be added or deleted from
the right and after the decimal point.
Compare digits in hundredths place. 1 is greater
than 0; therefore, 0.91 is greater. (hint: Consider
money)
Write the list adding zeros to hundred thousandths
place as needed.
0.78006, 0.78450,
0.78510, 0.78500,
0.78000
Since the digits in the tenths and hundredths
places are the same, compare the digits in the
thousandths place first. Then compare the digits
in the remaining places.
0.78000, 0.78006,
0.78450, 0.78500,
0.78510
Re-write the list from smallest to largest.
Write from smallest to largest:
1) 12.34, 1.234, 0.1234
5) 0.935, 1.2, 0.6, 0.56
2) 0.1, 0.01, 1.001
6) 0.12, 0.16, 0.2, 0.48, 0.054
3) 3.1, 0.031, 0.331
7) 5.038, 5.0382, 50.382, 0.5382
4) 0.06, 0.4, 0.9
8) 0.08, 8.08, 8.808, 8.888, 0.088, 0.8
11
Rounding
To round numbers for estimation:
1. Identify the place value to be rounded. All digits to the left of that place
remain the same.
2. Check the number to the immediate right of the place to be rounded:
a. If the digit in that place is 5 or greater, add one to the digit in
the place to be rounded.
OR
b. If the digit in that place is 4 or less, do not change the digit in
the place to be rounded.
3. Fill in the remaining place values to the right of the place to be rounded
with zeros, or drop the digits after the decimal point.
Example:
Round 1792 to the Identify the place value to be rounded, (7 hundred).
Write the digit(s) to the left (1). Identify the number to
hundreds place.
the right (9).
9 is greater than 5; add one to 7, (7+1=8), enter 8 in
18 _ _
the hundreds place.
Fill in all the places to the right with zeros.
18 0 0
Example:
Round 73.64 to
the tenths place.
Identify the place value to be rounded, (6 tenths).
Write the digits to the left (73). Identify the number to
the right (4).
73.6 _
4 is less than 5, 6 remains in the tenths place.
73.60 = 73.6
It is not need to fill in all the places to the right with
zeros; rounding to tenths place.
Example:
Round 49.897 to
the hundredths
place.
Identify the place value to be rounded, (9 hundredths).
Write the digits to the left (49.8). Identify the number
to the right, (7).
49. 8 10 _
7 is greater than 5, add one to 9. Since 9 + 1 = 10, a
zero is entered in the hundredths place, and the 1 is
carried to the tenths place.
49.(8+1) 0 _
The 1 is added to 8.
49.90
The zero is needed to represent the hundredths place.
12
6
7
Round these numbers as indicated.
1)
Tenths
62.87
9)
2)
Units
14.45
10) Hundredths
49.995
3)
Ten thousandths
3.56906
11) Thousandths
5.0074
4)
Tenths
3.1416
12) Thousandths
0.6739
5)
Hundreds
459.326
13) Tenths
1.98
6)
Tenths
19.77
14) Ten thousandths 0.01704
7)
Thousandths
0.0067
15) Hundredths
0.01011
8)
Tens
389.88
16) Thousandths
0.0007
13
Units
33.97
Addition
To add decimals, write the numbers vertically with the decimal points
directly under each other, then add the digits.
Note: When the decimal points are lined up, the digits are
automatically lined up in the correct place value.
Example:
13.2 + 1.57
13.20
+ 1.57
14.77
Example:
$437 + $41.56 + $0.18
$437.00
41.56
+ 0.18
$478.74
Find the Sum (Add):
1) 0.03 + 0.4
Write the problem vertically. Line up the decimal
points.
Note the additional zero. Adding zeros to the right
of the final digit after the decimal does not change
the value of the number.
Dollar values are the most familiar decimal values.
Write the problem vertically. Line up the decimal
points.
The additional zeros are optional, but help with
placement. Note dollar sign use.
6)
48 + 0.84
2)
0.3 + 0.03 + 0.003
7)
10 + 9.6 + 3.76 + 8.451
3)
2.05 + 0.561 + 43.9 + 17.32
8)
$3.06 + $2.13 + $4.89
4)
$4 + $14.01
9)
2,134.07 + 306.5 + 2.109
5)
8.0632 + 0.234 + 0.81 + 0.064
10) 56.3701 + 0.268 + 4.2
14
8
Subtraction
9
To subtract decimals, write the numbers vertically with decimal points
directly under each other, and add zeros when needed, then subtract the
digits.
Note: When the decimal points are lined up, the digits are automatically
lined up in the correct place value.
Example:
42.63 - 18.275
42.630
- 18.275
24.355
Example:
$23 - $0.13
Write the problem vertically. Line up the decimals.
Remember: always write the first number on the top.
Add zeros to the number with fewer places to the right of the
decimal point. Subtract.
Write the problem vertically. Line up the decimals.
Insert the decimal point and two zeros.
$23.00
- 0.13
Subtract; borrow if necessary.
$22.87
Find the Difference (Subtract):
5) 4.355 - 1.647
1) 8.4 - 7.35
2)
12.5 - 8.7
6)
60.54 - 0.928
3)
$17.50 - $6.25
7)
89. - 58.46
4)
$18 - $5.63
8)
104.003 - 21.78
Find the Sum and Difference as indicated, (in the order indicated):
9) 14.6 - 1.98 + 3.7
11) 0.19 + 2.34 - 1.003
10) 5.67 + 0.34 - 2.05
12) $21.90 - $0.45 - $ 2.34
15
Multiplication with Decimals
10
Multiplication
To multiply decimals, write the problem and multiply as you would a
whole number multiplication problem. The product (answer) of two
decimal numbers has the same number of decimal places after the
decimal point as the total number of decimal places in the two numbers
being multiplied.
Example:
0.19 x 0.4
0.19
x 0.4
0.076
Write vertically. (The decimal points do not have to line
up.)
2 decimal places (Decimal points not lined up.)
+ 1 decimal place
3 decimal places
Count from right to left; add a zero before the decimal
point.
Example:
708
x 0.32
1416
21240
226.56
0 decimal places
+ 2 decimal places
2 decimal places
(Decimal points not lined up.)
Count from right to left to place decimal point.
Find the Product (multiply):
1)
0.32
x 0.6
4)
5.048
x 2.03
7)
0.075
x 5.4
2)
1.9
x 0.05
5)
0.15
x 0.15
8)
99
x 1.1
6)
2.4
x .013
9)
2.029
x 10.8
3)
400
x 0.17
16
Multiplying Decimals (A)
Find each product.
99.1
× 0.16
614
× 4.0
8.41
× 30
56.3
× 3.9
616
× 23
0.817
× 1.5
90.0
× 0.55
0.203
× 12
1.63
× 0.78
430
× 4.6
3.59
× 5.0
0.361
× 8.4
520
× 0.97
388
× 5.5
1.60
× 0.82
91.7
× 3.8
934
× 0.58
0.423
× 0.41
0.240
× 9.9
80.3
× 0.58
Math-Drills.Com
Multiplying Decimals (B)
Find each product.
43.7
× 0.77
11.1
× 16
265
× 1.3
866
× 68
71.7
× 0.68
6.38
× 8.5
667
× 1.9
0.941
× 9.1
10.5
× 40
0.307
× 6.1
0.649
× 9.9
0.589
× 21
6.93
× 46
6.88
× 7.4
0.607
× 24
36.4
× 14
6.66
× 6.5
82.3
× 0.71
29.7
× 1.7
0.475
× 0.39
Math-Drills.Com
11
Multiplication by Multiples of 10
To multiply by a multiple of ten, move the decimal point RIGHT as many
places as there are zeros in the multiplier.
Example:
24.6 x 10
= 246.0
There is one zero in the multiplier (10); therefore, the
decimal point moves right one place.
Example:
0.048 7 x 1000 There are three zeros in the multiplier (1000); therefore,
= 48.7 the decimal point movers right three places.
Example:
24.6_ x 100
= 2,460.0
There are two zeros in the multiplier, (100); therefore, the
decimal point moves right two places. Note the
additional zeros.
Multiply:
1)
4.83 x 10 =
7)
35.961 x 100 =
2)
83.5 x 1000 =
8)
82.6 x 1000 =
3)
90.2 x 100 =
9)
7.007 x 100 =
4)
10.37 x 10 =
10) 72.953 x 10 =
5)
0.76 x 1000 =
11) 0.987 x 1000 =
6)
0.08 x 10 =
12) 476.098 x 10,000 =
17
Division with Decimals
Division by Whole Numbers
13
To divide a decimal by a whole number, place the decimal point in the
quotient directly above the decimal point in the dividend to ensure the
correct place value. Divide as with whole numbers.
Example:
.
Write the problem with a "division house," placing the
quotient's (answer's) decimal point directly over the
decimal point of the dividend.
5.5 ÷ 5 = 5 5.5
1 .1
5 5 .5
5
5
5
0
Example:
.
22 . 5
= 3 22.5
3
7 .5
3 22 . 5
21___
15
15
0
Divide:
1)
1 .8 ÷ 6 =
A fraction is another way to express a division problem.
The divisor is the denominator and the dividend is the
numerator.
Write the problem with a "division house," placing the
quotient's (answer's) decimal point directly over the
decimal point of the dividend.
4)
0 . 264 ÷ 4 =
7)
0 . 32 ÷ 5 =
2)
0 . 84
4
5)
3.96
9
8)
34 . 5
5
3)
0.096
8
6)
0.016 ÷ 2 =
9)
1.49
2
19
14
Division by Decimals
In division, the divisor must be a whole number. To convert a decimal
divisor to a whole number, multiply the divisor and the dividend by a
multiple of ten. Then divide as usual.
Example:
4.9 ÷ 0.7
(4.9 x 10) ÷ (0.7 x 10)
49 ÷ 7 = 7
Example:
8.505 100 850.5
x
=
0.05 100
5
170.1
5 850.5
5
35
35
00 5
5
0
The divisor (0.7) has one decimal place. To
change the divisor to a whole number, multiply
the divisor and the dividend by 10.
Divide as usual.
The divisor (0.05) has two decimal places. To
change the divisor to a whole number, multiply
the divisor and the dividend by 100.
Divide as usual. Place the decimal point for the
quotient (170.1) directly above the decimal point in
the dividend (850.5)
.
Divide:
1)
574.0 ÷ 0.7
4)
35.1 ÷ 2.7
7)
82.8 ÷ 0.03
2)
0.4 6.988
5)
2.4 77.04
8)
0.41 205
3)
0.0144
1.2
6)
0.132
0.011
9)
0.6832
0.004
20
Dividing Decimals (A)
Find each quotient.
0.2 ) 1.64
0.3 ) 1.65
0.2 ) 0.5
0.6 ) 0.84
0.9 ) 7.02
0.1 ) 0.85
0.5 ) 1.5
0.7 ) 3.01
0.2 ) 0.56
0.4 ) 3.32
0.9 ) 1.44
0.6 ) 4.86
Math-Drills.Com
Dividing Decimals (A)
Find each quotient.
2 ) 155.2
5.1 ) 499.29
7.8 ) 467.22
4.2 ) 171.36
7 ) 694.4
6.2 ) 95.48
9.4 ) 223.72
1.3 ) 53.69
9.2 ) 367.08
7.4 ) 142.08
5.4 ) 109.08
7.6 ) 405.08
Math-Drills.Com
(
Division by Multiples of 10
To divide by a multiple of ten, (10; 100; 1,000; etc.), move the decimal
point to the LEFT as many places as there are zeros in the divisor.
Example:
7 8.2 ÷ 10 =
= 7.82
Example:
_ _ _0.32
There is one zero in the divisor (10), therefore the
decimal point moves left one place.
There are three zeros in the divisor (1000), therefore
÷ 1000 the decimal point moves left three places.
= 0.00032 Note the additional zeros.
Divide:
1)
82.5 ÷ 100 =
6)
78.567 ÷ 10 =
2)
923.8 ÷ 1000 =
7)
54.87 ÷ 1000 =
3)
0.754 ÷ 10 =
8)
20.35 ÷ 10 =
4)
0.845 ÷ 100 =
9)
540.8 ÷ 100 =
5)
63.8 ÷ 100 =
10) 6200 ÷ 10,000 =
18
2
Converting Fraction to
Decimals
15
eg.
Converting Fractions to Terminating Decimals
To convert a fraction to a decimal, divide. Some fractions will convert
to a decimal representation with a remainder of zero, called a
terminating decimal.
Example:
Convert to a Decimal
0 .25
3
= 12 3 .00
12
24
60
60
0
Divide 3 by 12.
The decimal equivalent to three twelfths is twentyfive hundredths.
3
= 0.25
12
Example:
Convert to a Decimal
0.20
5
11 = 11 + 25 5.00
25
50
0
11
5
= 11.20
25
The whole number portion of the number will remain
the same. The fraction will convert to a decimal.
Divide 5 by 25.
The decimal equivalent to eleven and five twentyfifths is eleven and two tenths.
Convert to a Decimal:
9
1)
6)
19
40
48
32
18
2)
15
30
7)
3)
6
16
8)
4)
9
20
9)
5)
13
50
10)
21
5
2
20
77
7
40
47
37
50
Converting to Repeating Decimals
ra
16
To convert a fraction to a decimal, divide. Some fractions will convert to a
decimal representation with pattern, called a repeating decimal.
Example:
0.666...
2
= 3 2.000...
3
18
20
20
20
0.666... = 0.6
Example:
3 . 0909 ...
34
= 11 34 . 0000 ...
11
33
100
99
100
99
1
3.0909... = 3.09
Convert:
1) 1
Divide two by three. Note that the remainder will
continue to be two; therefore, the decimal answer is a
repeating decimal.
Repeating decimals are written with a bar over the
repeating digits in the pattern.
Divide 34 by 11. Since 11 does not divide 10, there is a
need to bring down an additional zero. Note that there is
a portion of the quotient that does not repeat.
The bar indicates that only the 09 repeats.
6)
1
8
11
1
3
2)
1
33
7)
3)
4
9
8)
7
33
4)
1
3
9)
7
42
5)
3
22
10)
22
4
1
6
2
3
17
13
Converting Decimals to Fractions
To convert a terminating decimal to a fraction, write the decimal with the place
value multiple of ten as a denominator and reduce to simplest terms.
Example:
2
The decimal fraction portion of the number terminates in the
3.2 = 3
tenths place; therefore the denominator will be 10.
10
3
2
1
=3
10
5
This fraction is not in lowest terms, therefore must be
reduced. Divide numerator and denominator by 2.
To convert a repeating decimal to a fraction, use a value of 9 as the
denominator.
Example:
9
The repeating pattern ends in the hundredths place,
3.09 = 3
therefore the denominator will have two nines, or be 99.
99
3
This fraction is not in lowest terms, therefore must be
reduced. Divide numerator and denominator by 9
1
9
=3
11
99
Convert:
1)
7.85
6)
34.0102
2)
10.3
7)
7.7
3)
2.08
8)
10.425
4)
0.45
9)
0.006
5)
0.360
10)
2.360
23
Decimals word
problems
.
.
Student Name: __________________________
Score:
Decimals Subtraction Word Problems
Questions
Katherine bought cosmetic items which cost
$78.12 in total. She gave $100 to the shop
keeper. How much does she receive as
change?
Answer:
Kelly scored 56.73 points and Karen scored
74.92 points on a University exam. How many
points less did Kelly score than Karen?
Answer:
A mixture is obtained by mixing two products
A and B respectively. Product A weighs 234.56
grams and the mixture weighs 988.76 grams.
How much does Product B weigh?
Answer:
David’s home is 12.53 miles away from the
lake and 16.73 miles away from his school.
How far is David’s school from the lake?
Answer:
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Workspace
:
19
re
Solve the following.
1) The $146.35 cost of a party was shared by 10 people. How much did each
person have to pay? (Be sure to round your answer to the nearest cent.)
2) 537 people attended a $100 dollar a plate fund raising dinner for the NSCC
Foundation. How much money did this dinner raise?
3) At the beginning of the month, Jim's bank balance was $275.38. During the
month he wrote the following checks: $174.89, $68, and $57.76. He made
deposits of $250 and $350. Find his bank balance at the end of the month.
4) Rudy drove his car 9,600 miles last year. His total car expenses were $625
for the year. Find the average cost per mile. (Round off your answer to the
nearest hundredth)
25
20
saga
5)
A garden is 33.75 feet long and 21.6 feet wide. Draw a diagram of the
garden with the lengths written on all four sides. What is the total
distance around the garden?
6)
A car traveled at 50 miles an hour for 2.5 hours. How far did it go?
7)
A can of ham weighing 7.75 pounds costs $ 11.86. What does the ham
cost per pound? (Round to the nearest cent.)
8)
A park is 4.6 miles long and 2.7 miles wide.
a. What is the total distance around the park?
b. If a racecar drove 50 times around the park, how far will it have to
go?
26
2
as
Name__________________________
Solve all problems on a separate piece of paper.
ORGANIZE YOUR WORK!
3
Bad
1. Joseph runs each morning before school. On Monday he ran 1.34 miles. On Tuesday he ran
2.456 miles. On Wednesday he ran 2.5 miles. On Thursday he ran 0.375 miles. On Friday he ran
0.25 miles. His goal for the week was to run 10 miles. Did Joseph meet his running goal for the
week? How do the miles he ran compare to his goal?
2. Sarah and three of her classmates entered a story they wrote into a contest at the mall. The
team won the contest, and their prize was money. Each person on the team received $21.25.
How much money did the team win altogether?
3. Bobby bought the following items at the school store: 10 pencils for $0.21 each, 8 pens for
$0.45 each, and 2 posters for $0.55 each. How much money did Bobby spend in all?
4. Betsy made ribbons for school spirit day. Her roll of ribbon was 30 ft. long. For each
individual ribbon she needed 0.625 ft. How many ribbons could she make from her roll?
5. L.B. Johnson Middle School held a track and field event during the school year. Miguel took
part in a four-person shot put team. Shot put is a track and field event where athletes throw
(or “put”) a heavy sphere, called a “shot,” as far as possible. To determine a team score, the
distances of all team members are added. The team with the greatest score wins first place.
The current winning team’s final score at the shot put is 52.08 ft. Miguel’s teammates threw
the shot put the following distances: 12.26 ft., 12.82 ft., and 13.75 ft. Exactly how many feet
will Miguel need to throw the shot put in order to tie the current first place score?
6. Suzy took a cab from the airport. Her total fare, not including tip, was $21.50. The cab driver
charged $1.00 for the first .2 mile, and $.25 for each additional .2 mile traveled. The fare
included a charge of $2.50 for being picked up at the airport.
How many miles was the cab ride? Explain your answer.
4
a.
Patricia earned $4.00 working. Gregory works at the
same store and earns $12.00 per hour. If she worked
for 2 hours, how much money does Patricia earn per
hour?
Richard worked to earn $280.00. Howard worked for
$15.00 hours. If he earns $4.00 per hour, how many
hours did Richard work?
Frank has $11.00. Stephanie gives with $4.37 to Frank.
If Stephanie started with $57.00, how much money
does she have left?
Ralph has $60.00. crayons cost $2.00 each. pencils cost
$13.00 each. How many crayons can Ralph buy?
Deborah has $23.00. Craig has $7.87. Janet has $9.00.
How much more does Deborah have than Craig?
Susan earns $9.00 per hour working. She wants to earn
$14.00 to buy erasers. If Susan worked for 10 hours,
how much money did she earn?
Each egg costs $8.00 and each apple costs $11.00. How
much do 70 eggs cost?
Rachel earns $2.00 per hour working. She wants to
earn $9.00 to buy Skittles. If Rachel worked for 8 hours,
how much money did she earn?
Martin has $6.21. Heather has $3.00. Lori has $7.00.
How much more does Martin have than Heather?
5
eae
Eugene has $400.00. pencils cost $5.00 each. Skittles
cost $13.00 each. How many pencils can Eugene buy?
Christine has $80.00. Sarah has $37.69. Gerald has
$9.00. How much more does Christine have than
Sarah?
James has $41.00. Anna has $8.48. Kathy has $6.00.
How much more does James have than Anna?
Antonio has $27.00. erasers cost $9.00 each. stickers
cost $9.00 each. How many erasers can Antonio buy?
Carl starts with $71.00 and spends $9.48 on bananas.
Walter spends $12.00 on bananas. How much money
does Carl have left?
Roy spends $640.00 on candies. Joyce buys 13 candies.
Each candy costs $8.00. How many candies did Roy
buy?
6
§
Student Name: __________________________
or7
Score:
Decimals Multiplication Word Problems
Questions
Hamlet ordered 9 pizzas. Each pizza costs
$13.95. How much does he need to pay?
Answer:
A broken scale is used to measure the height
of the plant. The length of the broken scale is
12 cm. The height of the plant is 14.15 times
greater than the broken scale. What is the
height of the plant?
Answer:
The height and volume of a rectangular box is
one inch and 56.23 inch3 respectively. What is
the volume of the box if the height is
increased to 13 inches?
Answer:
David and Dora are close friends studying in
the same school. David’s home is 6.87 miles
away from school. Dora’s home is 7 times as
far as David’s home from school. Find the
distance between Dora’s school and her
home.
Answer:
Free Math Worksheets @ http://www.mathworksheets4kids.com
Workspace
Student Name: __________________________
8
gas
Score:
Decimals Division Word Problems
Questions
Catherine split rope that was 49.4 inches into
4 equal parts. What is the length of each part?
Answer:
Serene paid $35.01 to buy 9 hot dogs. How
much did each hot dog cost?
Answer:
Diana sells 12 garlands for $12.12. What is the
cost of each garland?
Answer:
A shop keeper bought 26 apples from a fruit
vendor for $37.70. How much did each apple
cost?
Answer:
Free Math Worksheets @ http://www.mathworksheets4kids.com
Workspace
Name: ________________________________________________________________________ Date: ________________
Solve the following problems.
1. At the marketplace, 5 pounds of oranges
are selling for $3.15.
a. What is the unit price for oranges?
b. To the nearest dollar, what is the cost of
buying 10.5 pounds of oranges?
3. You have one chocolate bar that you want
to divide equally among 5 crying babies.
a. Write and solve a problem to find the
amount, as a decimal number, that
each baby will get.
9
e.
2. A recipe requires 0.5 stick of butter. Find
the amount of butter needed for one
quarter of the recipe by:
a. Using division
b. Using multiplication
4. I borrowed $12.75 from Keysha. Later on I
borrowed an additional $6.15.
a. What is the amount of my debt?
b. If my sister gives me $20 and I pay
all my debt, how much money will I
be left with?
b. What does your answer mean?
5. How many groups of 15 cents are in
$14.25?
6. How many feet are in 66.75 inches? Hint:
7. I paid $39.90 to fill up my car with 10
gallons of gas. What is the unit price of
gas? Hint: just move the decimal point.
8. Ethan is trying to draw one row of
congruent squares on a 8.5 inch wide
paper. If each square is 0.85 inch wide.
How many squares will Ethan be able to fit
in the row?
Student Accessible – studentaccessible.com – Maya Khalil
the quotient will terminate after 4 decimal places.
10
Ear
_________ Problems Wrong
Name _______________________________
_________ Points Missed
Math 7, Period 1, 2, 3, 4, 5, 6, 7
_________ Grade
AC
All Decimal Operations with Word Problems
1) Ellen wanted to buy the following items:
A DVD player for $49.95
A DVD holder for $19.95
Personal stereo for $21.95
Does Ellen have enough money to buy all three items if she has $90.
2) Melissa purchased $39.46 in groceries at a store. The cashier gave her $1.46 in change from a $50
bill. How much change should the cashier have given Melissa?
3) If a 10-foot piece of electrical tape has five pieces that are each 1.25 feet cut from it, what is the
new length of the tape?
4) Patricia has $425.82 in her checking account. How much does she have in her account after she
makes a deposit of $120.75 and a withdrawal of $185.90?
5) The mass of a jar of sugar is 1.9 kg. What is the total mass of 13 jars of sugar?
6) Carpeting costs $9.99 a yard. If Jan buys 17.4 yards, how much will it cost her? (Round your answer
to the nearest hundredth)
are
7) If your weekly salary is $1,015.00, how much do you have left each week after you pay for the
following?
Rent - $443.50
Cable TV -$23. 99
Electricity - $45.62
Groceries - $124.87
11
8) Brad studied a total of 24.4 hours over a period of four days. On average, how many hours did
Brad study each day?
9) Find the perimeter of the rectangle below.
10) Samantha paid $26.25 for three books that all cost the same amount. What was the cost per
book?
11) While at the grocery store, Mrs. Martin noticed that there were two different sized bottles of hot
sauce, one was 16.9 ounces and the other 32.55 ounces. What is the difference in weight of the two
bottles of hot sauce?
12) Larry paid $11.20 for four gallons of gas. How much was each gallon of gas?
12
BE
Use the table below to answer #13-15.
Item
Movie Ticket
Medium Popcorn
Medium Soda
Candy
Cost
$8.25
$6.00
$4.75
$3.50
13) Find the total cost of two Medium Sodas, two Medium Popcorns, and two Movie tickets.
14) If Marty spent $66 on Movie tickets, how many tickets did he buy?
15) Find the total cost of four bags of candy and two movie tickets.
16) Leon bough a dozen daisies for $3.75. Which is the closest to the amount Leon paid for each
daisy?
A. $0.25
B. $ 0.29
C. $0.31
D. $0.38
17) Dolores bough 15 party hats priced at $0.75 each and 15 noisemakers priced at $1.25 each. How
much did Dolores spend in all?
​At a display booth at an amusement park, every visitor gets a gift bag.
8.
Some of the bags have items in
them as shown in this table.
​
Items in the Gift Bags
Items
Bags
Hat
Every 2nd visitor
T-shirt
Every 7th visitor
Backpack Every 10th visitor
​How often will a bag contain all three items?
​A.
9.
Every 14 bags
B. Every 19 bags
C. Every 70 bags
D. Every 140 bags
​Bridget has swimming lessons every fifth day and diving lessons every third day.
If she had
​a swimming lesson and a diving lesson on May 5, when will be the next date on which she
​has both swimming and diving lessons?
10.
​Hot dogs come in packages of 8. Hot dog buns come in packages of 12. If Grace wants to
​have enough to serve 24 people and have none left over, how many packages of hot dogs and
​hot dog buns should she purchase?
11.
​There are 40 girls and 32 boys who want to participate in 6
th
grade intramurals. If each
​team must have the same number of girls and the same number of boys, what is the
​At a display booth at an amusement park, every visitor gets a gift bag.
8.
Some of the bags have items in
them as shown in this table.
​
Items in the Gift Bags
Items
Bags
Hat
Every 2nd visitor
T-shirt
Every 7th visitor
Backpack Every 10th visitor
​How often will a bag contain all three items?
​A.
9.
Every 14 bags
B. Every 19 bags
C. Every 70 bags
D. Every 140 bags
​Bridget has swimming lessons every fifth day and diving lessons every third day.
If she had
​a swimming lesson and a diving lesson on May 5, when will be the next date on which she
​has both swimming and diving lessons?
10.
​Hot dogs come in packages of 8. Hot dog buns come in packages of 12. If Grace wants to
​have enough to serve 24 people and have none left over, how many packages of hot dogs and
​hot dog buns should she purchase?
11.
​There are 40 girls and 32 boys who want to participate in 6
th
grade intramurals. If each
​team must have the same number of girls and the same number of boys, what is the