Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
(For help, go to Skills Handbook page 730.)
Simplify.
1. 2.8 + 7.06
2. 0.65 + 1.8
3. 4.52 – 2.48
4. 3.7 – 0.62
Check Skills You’ll Need
3-5
Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
Solutions
1.
2.80
+ 7.06
9.86
2.
0.65
+ 1.80
2.45
3.
4.52
– 2.48
2.04
4.
3.70
– 0.62
3.08
3-5
Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
Solve 6.8 + p = –9.7.
6.8 + p = –9.7
6.8 – 6.8 + p = –9.7 – 6.8
p = –16.5
Check
Subtract 6.8 from each side.
Simplify.
6.8 + p = –9.7
6.8 + (–16.5)
–9.7
Replace p with –16.5.
–9.7 = –9.7
Quick Check
3-5
Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
Ping has a board that is 14.5 ft long. She saws off a
piece that is 8.75 ft long. Use the diagram below to find the
length of the piece that is left.
x + 8.75 = 14.5
x + 8.75 – 8.75 = 14.5 – 8.75
Subtract 8.75 from each side.
x = 5.75
Simplify.
The length of the piece that is left is 5.75 ft.
3-5
Quick Check
Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
Solve –23.34 = q – 16.99.
–23.34 = q – 16.99
–23.34 + 16.99 = q – 16.99 + 16.99
–6.35 = q
Add 16.99 to each side.
Simplify.
Quick Check
3-5
Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
Quick Check
Alejandro wrote a check for $49.98. His new account
balance is $169.45. What was his previous balance?
Words previous balance minus check is new balance
Let p = previous balance.
Equation
p
–
$49.98 =
$169.45
p – 49.98 = 169.45
p – 49.98 + 49.98 = 169.45 + 49.98
p = 219.43
Add 49.98 to each side.
Simplify.
Alejandro had $219.43 in his account before he wrote the check.
3-5
Solving Equations by Adding or Subtracting Decimals
PRE-ALGEBRA LESSON 3-5
Solve each equation.
2. –1.01 = c – 9
1. a + 10 = 7.9
– 2.1
7.99
3. s – (–2.6) = 1.6
4. 3.02 + d = 2.91
–1
– 0.11
5. –23.7 = 13.3 + g
– 37
3-5
Solving Equations by Multiplying or Dividing Decimals
PRE-ALGEBRA LESSON 3-6
Every day the school cafeteria uses about 85.8
gallons of milk. About how many days will it take for the
cafeteria to use the 250 gallons in the refrigerator?
Words
daily milk
consumption
times
number
of days
is
250 gallons
=
250
Let x = number of days.
Equation
85.8
•
x
3-6
Solving Equations by Multiplying or Dividing Decimals
PRE-ALGEBRA LESSON 3-6
(continued)
85.8x = 250
85.8x
250
=
85.8
85.8
Divide each side by 85.8.
x = 2.914 . . . Simplify.
x
3
Round to the nearest whole number.
The school will take about 3 days to use 250 gallons of milk.
Quick Check
3-6
Solving Equations by Multiplying or Dividing Decimals
PRE-ALGEBRA LESSON 3-6
Solve –37.5 =
–37.5 =
–37.5(–1.2) =
c
.
–1.2
c
–1.2
c
(–1.2)
–1.2
45 = c
Multiply each side by –1.2.
Simplify.
Quick Check
3-6
Solving Equations by Multiplying or Dividing Decimals
PRE-ALGEBRA LESSON 3-6
A little league player was at bat 15 times and had
a batting average of 0.133 (rounded to the nearest thousandth). The
batting average formula is a = h , where a is the batting average, h is
n
the number of hits, and n is the number of times at bat. Use the
formula to find the number of hits she made.
h
a= n
h
0.133 = 15
Replace a with 0.133 and n with 15.
3-6
Solving Equations by Multiplying or Dividing Decimals
PRE-ALGEBRA LESSON 3-6
(continued)
h
0.133(15) = 15 (15)
1.995 = h
2
h
Multiply each side by 15.
Simplify.
Since h (hits) represents an integer,
round to the nearest integer.
The little league player made 2 hits.
Quick Check
3-6
Solving Equations by Multiplying or Dividing Decimals
PRE-ALGEBRA LESSON 3-6
Solve each equation.
p
1. 9b = –30.6
2. –10.8 = –2.5
–3.4
27
3. 2.45 = –0.7k
4.
–3.5
t
= 240
3.7
888
5. y ÷ (–0.3) = 146.7
– 44.01
3-6