Pretest Ch. 10
Estimate each sum or difference. Name the method you used. (My solutions are possible solutions.)
1.
½ + 9/10
½=½
9/10 is about 1, so 1 ½ is my solution. I used rounding.
2. 11/12 - 1/9
11/12 is about 1 1/9 is about 0, so my solution is 1. I used rounding.
3. 23 1/5 – 12 ¾
20 – 10 = 10; I used front-end to get my estimate of 10.
4. 5/7 + 8/9
5/7 is close to 1
5. 32 2/3 + 14 ½
30 + 10 = 40; I used front-end to get my estimate of 40.
Add. Write each sum in simplest form.
6. 7/8 + 3/8
=1¼
7. 4/12 + 4/12
= 2/3
8. 1 2/3 + 2 2/6
=4
9. 4 ¾ + 1 4/5
= 6 11/20
10. 5 ¾ + 2 1/9
= 7 31/36
Subtract. Write each difference in simplest form.
11. 7/10 – 3/10
= 2/5
12. 1 1/3 – 2/3
= 2/3
13. 4 3/8 - 1 ¼
= 3 1/8
14. 5 1/6 – 2 2/5
= 2 23/30
8/9 is close to 1, so 2 is my solution. I used rounding.
15. 2 ½ - 1 2/3
= 5/6
Solve.
16. Tony worked 9/10 of an hour on a technology project. That is three times as long as Bill worked.
How many hours did they work in all?
Tony ‘s work = 9/10 of an hour
T
T T
That is 3 times as long as Bill’s work
B B B
T T
T T T T
In all, they worked 12/10ths hours which is 1 and 1/5 hours. You may also write this as 1 hour and 12
min.
17. A farm has 60 cows, pigs, and horses. There are four times as many cows and pigs as horses.
How many horses are there?
Cow and pigs
12
Horses
12
12
12
12
There are 60 in
total, so 60
divided into 5
parts = 12
animals in each
part.
Each part represents 12 animals, so there are 12 horses.
18. Alex and Tim rode their bikes from their houses to the library. Alex rode 1 ¾ miles and Tim rode
2/3 miles farther than Alex. How many miles did the two boys ride in all?
We want the distance
both boys rode in all.
Alex’s bike distance
1 ¾ miles
Tim rode further than
Alex. The blocks help us
Tim’s bike distance
2/3 miles
to see we need to add
1 ¾ + 1 ¾ + 2/3 miles
Solution: The two boys rode 4 1/6 miles in all.
Here is how we would calculate (I’m sorry, it is too difficult to show equivalent blocks by typing,
but I will explain with words. You can draw the blocks to see it more clearly, however.).
Tim rode 2/3 miles farther than Alex. The blocks help us to see the equation we need is
1 ¾ + 1 ¾ + 2/3
If we get common denominators to add, we see we need 12ths.
Our equation will be:
1 9/12 + 1 9/12 + 8/12
= 2 26/12 which can be written as 4 2/12 and
simplified further to 4 and 1/6.
19. Alicia cut a pie into 7 equal pieces. She gave two pieces to her grandmother and twice as much to
Billie. What fractional part of the pie was left?
Alicia’s “pie” is in 7 equal pieces
G
G
B
B
B
B
Grandmother got 2 pieces. Billie got twice as much. The amount of the pie that is left is 1/7.
20. A hardware store has a display of 75 screwdrivers. For every 7 flat-head screwdrivers, there are 8
Phillips-head screwdrivers. How many screwdrivers are there of each type?
Flat-head screwdrivers
7
7
7
7
7
= 35
Phillips-head screwdrivers
8
8
8
8
8
= 40
Solution: There will be 35 flat-head screwdrivers and
40 Phillips-head screwdrivers in the hardware store display
of 75 screwdrivers.
Because of the words “for
every” I made my boxes
equal. I know there are 15
screwdrivers (7 + 8) at a
time when I am displaying
both. 75 divided by 15 = 5.
There will be five times I
will have 7 flat heads and 5
times there are 8 Phillipshead screw drivers if there
are to be 75 screwdrivers
total.