Name
class
date
Decimals
You compute with decimals when you shop or when you measure using metric units. Many
statistics including those in sports involve decimals.
To add and subtract with decimals, add and subtract as you would whole numbers. Remember to
align the decimal point in the sum or difference with the decimal points in the numbers you are
adding or subtracting.
Example A
Elliot buys a video game for $24.95 and a pair of headphones for $16.99. He hands the clerk $50.
How much change should Elliot get?
Step 1: Find how much Elliot spends. Add $24.95 and $16.99.
$24.95
1 16.99
$41.94
Step 2: Find the change. Subtract what Elliot spent from $50.00.
$50.00
2 41.94
$8.06
Solution: Elliot should get $8.06 in change.
Multiply decimals as you would whole numbers. When multiplication is complete, place the
decimal point in the product by finding the total number of digits to the right of the decimal points
in the factors. The product will have the same number of places to the right of the decimal point.
Example B
Shauna buys 12.2 gallons of gas for $2.90 per gallon. How much will she spend?
Step 1: Get a good estimate by rounding. Round to the nearest whole number.
12.2 rounds to 12.
2.90 rounds to 3.
12 3 3 5 36
12.2
Step 2: Multiply as you would with whole numbers.
3 2.9
1098
1 2440
3538
Step 3: Count the number of decimal places in the factors. The product will have
the same number of places to the right of the decimal point.
Step 4: Compare your solution to the estimate. Since 35.38 is close to 36, the
solution is reasonable.
12.2 ← 1 decimal place
3 2.9 ← 1 decimal place
1098
1 2440
35.38 ← 2 decimal place
35.38 ≈ 36
Solution: Shauna will spend $35.38 for 12.2 gallons of gas.
© 2014 College Board. All rights reserved.
1
SpringBoard Algebra 1, Unit 1
Decimals (continued)
You can use the distributive property to multiply with decimals. The distributive property states
that to multiply a sum by a number, you can multiply each addend by the number and add the
products.
Example c
Multiply 10.4 3 4.8 using the distributive property.
Step 1: Break one of the decimals into a sum using addition.
10.4 3 4.8 5 (10 1 0.4) 3 4.8
Step 2: Rewrite the expression.
5 (10 3 4.8) 1 (0.4 3 4.8)
Step 3: Multiply inside each set of parentheses.
5 48 1 1.92
Step 4: Add the products.
5 49.92
Solution: 10.4 3 4.8 5 49.92
To divide a decimal by a whole number, place the decimal point in the quotient directly above
the decimal point in the dividend. Then divide as you would whole numbers.
One difference in division with decimals is that you may have to write zeros in the dividend so
that you have enough digits to divide.
Example D
Darby is hiking 6.8 kilometers. She will stop 8 times along her route. If her stops are equally
spaced, how far will she hike before her first rest stop?
Step 1: Place the decimal point in the quotient directly above the decimal point in
the dividend.
.
8 6.8
Step 2: Because 6 , 8, the quotient will be less than 1, so place a 0 before the decimal
point in the quotient.
0.
8 6.8
Step 3: Divide as you would with whole numbers. Add one or more zeros after the
decimal point in the dividend and divide until the decimal in the quotient terminates.
0.85
8 6.80
26 4
40
240
0
Solution: Darby will hike 0.85 kilometer before her first rest stop.
© 2014 College Board. All rights reserved.
2
SpringBoard Algebra 1, Unit 1
Decimals (continued)
To divide by a decimal, you must first write an equivalent expression with a whole-number
divisor. To do this, multiply both the dividend and divisor by a power of 10 (10, 100, 1,000, . . .)
that will make the divisor a whole number.
Example E
Jill earns $9.50 per hour for walking her neighbors’ dogs. Last week, she earned $114.
For how many hours did Jill walk the dogs last week?
Step 1: The divisor has 1 decimal place. So, multiply 9.5 by 10 to make
a whole-number divisor. You must also multiply the dividend by 10.
Step 2: Divide.
$114 49.5
$114 3 10 9.5 3 10
1140 495
12
95 1140
295
190
2190
0
Solution: Jill walked the dogs for 12 hours last week.
PRACTICE
Find each sum, difference, product, or quotient.
1.29.38 1 5.7 2.3.08 1 0.72 1 0.5 3.11.5 2 6.03 4.0.31 2 0.009 5.77 3 1.36 6.0.37 3 1.2 7.1.048 4 4 8.75 4 0.6 9.70.2 4 3.9 10. Kayla is going to Japan for vacation. She will exchange $300 for Japanese yen.
The exchange rate is $1 5 85.74 yen. How many yen will Kayla receive?
11. When you multiply one decimal greater than 1 by one decimal less than one,
how does the product compare to the factors? Illustrate with an example.
12. Mr. Alquist has 448.2 kilograms of clay. Each student needs 5.5 kilograms of clay
for the art project. How many students can Mr. Alquist provide with clay?
13. Jorge bought 3 shirts and 2 pairs of pants. Each shirt cost $21.50 and each pair
of pants cost $34.45. If he had $145 in his wallet, how much money will he have
left after paying for his clothes? Show your work and explain your answer.
© 2014 College Board. All rights reserved.
3
SpringBoard Algebra 1, Unit 1