UNIT 5
^ " " " o o ,
10
Estimating Sums
and Differences
Quick Review
Here are 2 ways t o e s t i m a t e 4.548 + 2.417.
>
W r i t e each d e c i m a l t o t h e nearest w h o l e n u m b e r :
5 + 2 = 7
>
So, 4.548 + 2.417 is a b o u t 7.
W r i t e o n l y 1 d e c i m a l t o t h e nearest w h o l e n u m b e r :
5 4- 2.417 = 7.417
So, 4.548 + 2.417 is a b o u t 7.417.
Here are 2 ways t o e s t i m a t e 4.538 — 2.417.
>
W r i t e t h e s e c o n d d e c i m a l t o t h e nearest w h o l e n u m b e r :
4.538 - 2 = 2.538
>
So, 4.538 - 2.417 is a b o u t 2.538.
W r i t e b o t h decimals t o t h e nearest w h o l e n u m b e r :
5-2 = 3
So, 4.538 - 2.417 is a b o u t 3.
Try These
1.
2.
84
Estimate each s u m .
a) 2.54 + 7.16
b) 4.197 4- 3.864
c) 0.765 + 1.295
d) 5.765 + 3.189
e) 0.473 + 1.697
f)
a) 7.546 - 3.518
b) 2.476 -
c) 7.9 -
d) 3.204 - 0 . 9 3 8
e) 1.497 - 0.126
2.008 + 3.801
Estimate each difference.
1.555
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f)
3.267
12.094 -
8.259
Practice
1.
Estimate each s u m or difference.
2.
a) 27.6 + 49.23
b ) 16.257 - 9.396
c) 4.875 -
d ) 7.596 + 2.17
e) 13.123 - 6.959
f)
2.93
10.67 + 7.834
a) Joline b o u g h t a pair o f skates f o r $79.95.
She also b o u g h t a pullover for $45.25.
Estimate t h e total cost of Joline's purchases.
b) Estimate h o w m u c h m o r e Joline p a i d for t h e skates t h a n t h e pullover.
3.
The table shows t h e masses o f five p u p p i e s .
a) Estimate t h e c o m b i n e d masses of:
Masses of Puppies
Brutus a n d Zeus
Name
Mass (kg)
Tawny a n d Zena
Brutus
3.106
Zeus a n d Zara
Tawny
0.992
Zara
1.935
Zena
2.791
Zeus
1.276
Zara a n d Tawny
b) Estimate t h e difference in masses of:
Zara a n d Zena
Brutus a n d Zeus
Tawny a n d Zara
The heaviest a n d lightest p u p p i e s
4.
Circle t h e better estimate,
a) 3.549 + 6.831
9
or
10
b) 4.316 - 0.135
3 or
4
Stretch Your Thinking
Estimate t h e c o m b i n e d mass o f t h e five p u p p i e s .
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85
Adding Decimals
Quick Review
M a d i s o n rode her bike 11.76 k m o n Saturday a n d 6.18 k m o n Sunday.
W h a t t o t a l distance d i d M a d i s o n ride?
You can use place value t o a d d 11.76 + 6.18.
First estimate.
11.76 is a b o u t 12.
6.18 is a b o u t 6.
12 + 6 = 18
S t e p 1:
Record t h e n u m b e r s .
Tens
A l i g n t h e m as t h e y are
1
Ones < t Tenths
Hundredths
1
i>
7
6
6
<•
1
8
a l i g n e d in t h e
place-value chart.
11.76
+ 6.18
S t e p 2:
A d d as y o u w o u l d w i t h
Add the hcridnedths.
whole numbers.
Regroup IH fxmdnedfhs
11.76
as 1 tenth H ones.
Add the tenths.
+ 6.18
Add the ones.
17.94
Add the tens.
17.94 is close t o t h e e s t i m a t e o f 18, so t h e answer is reasonable.
Try These
%
1.
%
&
*
#
*
Estimate first.Then a d d .
a)
e)
86
&
3.4
b)
6.8
+ 9.3
+4.7
25.2
f) $43.16
+ 13.9
+ $ 8.97
c)
7.54
d)
+ 3.62
g)
0.97
+ 1.23
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$8.09
+ $7.68
h)
18.40
+ 26.60
Practice
1.
A d d . Estimate t o check.
a)
9.7
b)
+ 4.9
e)
35.7
+ 98.6
2.
f)
16.3
c) $4.07
+ 12.8
+ $8.63
$1.54
+ $3.65
g)
6.28
d)
21.60
+ 14.73
h)
+ 12.32
47.37
+ 19.08
Play this g a m e w i t h a partner.
You will n e e d paper, pencils, a n d a n u m b e r cube, labelled 1 t o 6.
The o b j e c t o f t h e g a m e is t o g e t t h e greater s u m .
>
Draw an a d d i t i o n g r i d like this o n y o u r paper:
>
Take t u r n s t o roll t h e n u m b e r c u b e . Record t h e n u m b e r rolled in any box
in y o u r a d d i t i o n g r i d .
>
C o n t i n u e u n t i l all t h e boxes in y o u r g r i d are full.
>
A d d . T h e player w i t h t h e greater s u m scores 1 p o i n t .
>
Play 4 m o r e r o u n d s t o f i n d t h e overall w i n n e r .
>
Play t h e g a m e again.This t i m e , t r y t o g e t t h e lesser s u m .
Stretch Your Thinking
Find 2 decimals w i t h a s u m o f 9.76.
Do this in as m a n y ways as y o u can.
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87
UNIT
5
A2
Subtracting Decimals
<*ssot*
Quick Review
Joline g r e w 2 p u m p k i n s in her g a r d e n .
The masses o f her p u m p k i n s are 7.05 k g a n d 9.84 kg.
W h a t is t h e difference in t h e masses?
You can use place value t o f i n d 9.84 - 7.05.
S t e p 1:
Ones < • Tenths
Record t h e n u m b e r s .
A l i g n t h e m as t h e y are a l i g n e d
Hundredths
9
<»
8
4
7
«
0
5
in t h e place-value chart.
9.84
-7.05
S t e p 2:
Subtract as y o u w o u l d w i t h w h o l e n u m b e r s .
7 14
Regroup 1 tenth as 10 hmdredths.
-7.05
Subtract the hundredths.
Subtract the tenths.
2.79
Subtract the ones.
A d d t o check y o u r answer.
7.05
+ 2.79
9.84
Try These
1.
Estimate first.Then subtract.
a)
6.8
-4.3
88
b)
8.5
-0.9
c)
2.67
-1.38
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d) $12.45
-$
8.68
Practice
1.
Subtract. A d d t o check.
9.4
a)
b)
-6.8
el
i
-
a)
iLi..
J
8.37
25.8
c)
-16.9
f) $ 20.15
-$
g)
9.48
7.04
d)
8.62
-2.13
-5.74
84.08
h) 52.34
-47.16
- 26.89
H o w m u c h m o r e t h a n t h e jacket d o t h e jeans cost?
b) Jerry p a i d for a baseball hat w i t h a $10 bill.
H o w m u c h c h a n g e d i d he get?
c)
Sylvie b o u g h t a shirt a n d a pair o f socks. She gave t h e clerk $20.
H o w m u c h c h a n g e d i d she get?
d) W h a t is t h e difference in price b e t w e e n t h e least expensive a n d m o s t
expensive items?
JC..I
Qjrfij
_
e)
W h i c h 2 items have each difference in price?
"1
$26.30
$15.10
$6.76
Stretch Your Thinking
N a m e 2 decimals w h o s e difference is b e t w e e n 9 a n d 10, b u t closer t o 9.
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89
^""X
13
Adding and Subtracting
Decimals
Quick Review
>
You can use place value t o a d d 5.763 a n d 3.949.
S t e p l : Estimate.
S t e p 2 : A d d as y o u w o u l d w i t h
Write the second decimal to
t h e nearest w h o l e n u m b e r .
whole numbers.
1 11
5.763
A d d : 5.763 + 4 = 9.763
+ 3.949
So, 5.763 + 3.949 is a b o u t 9.763.
9.712
9.712 is close t o t h e e s t i m a t e , so t h e answer is reasonable.
You can use place value t o s u b t r a c t 3.949 f r o m 5.763.
S t e p 1: Subtract as y o u
S t e p 2:
Estimate t o check t h e
would with whole
answer is reasonable.
numbers.
W r i t e 3.949 as 4.
2
-
Subtract: 5.763 - 4 = 1.763
3.949
1.814
1.814 is close t o t h e estimate, so t h e answer is reasonable.
Try These
1.
A d d . Estimate t o check y o u r answers.
a)
4.521
+
2.
3.097
2.168
+
0.948
c)
7.169
+
d)
8.473
6.704
+
0.491
Subtract. Estimate first.Then subtract.
a)
9.732
-
90
b)
0.489
b)
6.371
4.152
1.098
4.097
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d)
3.652
-
1.984
Practice
1.
A d d . Use s u b t r a c t i o n t o check each answer.
a)
4.157
+
d)
12.349
27.309
+
14.167
e)
-
c)
-
0.573
+ 4.497
3.187
+
f)
-
4.679
36.234
+
14.875
Subtract. Use a d d i t i o n t o check each answer.
a)
7.243
-
d)
2.807
b)
+
1 1.431
- 8.763
3.
-
5.138
+
2.
6.346
b)
4.583
-
e)
+
2.338
c)
+
4.010
-
2.862
13.040
-
f)
+
7.862
73.832
-
51.765
The difference in t h e masses of 2 objects is 0.479 kg.
a) W h a t m i g h t t h e mass o f each o b j e c t be?
b) W h a t m i g h t t h e objects be?
4.
Salvatore ran 2.457 k m o n Saturday a n d 3.169 k m o n Sunday.
a) How far d i d Salvatore run in all?
b) H o w m u c h f u r t h e r d i d he run o n Sunday t h a n o n Saturday?
Stretch Your Thinking
Use each of t h e digits 1 t o 8 o n c e
t o m a k e this s u b t r a c t i o n true.
1 . 3 4 7
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