Answer:
Explanation:
Summer Mathematics Packet
IM Page 1
Rename Fractions, Percents, and Decimals
Hints/Guide:
To convert fractions into decimals, we start with a fraction, such as
5
3
, and divide the numerator
(the top number of a fraction) by the denominator (the bottom number of a fraction). So:
and the fraction
5
3
is equivalent to the decimal 0.6
To convert a decimal to a percent, we multiply the decimal by 100 (percent means a ratio of a
number compared to 100). A short-cut is sometimes used of moving the decimal point two
places to the right (which is equivalent to multiplying a decimal by 100, so 0.6 x 100 = 60 and
5
3 = 0.6 = 60%
To convert a percent to a decimal, we divide the percent by 100, 60% ÷ 100 = 0.6 so 60% = 0.6
To convert a fraction into a percent, we can use a proportion to solve,
5 100
3 x
= , so 5x = 300 which means that x = 60 = 60%
Exercises: No Calculators!
Rename each fraction as a decimal:
1.
=
5
1
2.
=
4
3
3.
=
2
1
4.
=
3
1
5.
=
10
8
6.
=
3
2
Rename each fraction as a percent:
7.
=
5
1
8.
=
4
3
9.
=
2
1
10.
=
3
1
11.
=
10
8
12.
=
3
2
Rename each percent as a decimal:
13. 8% = 14. 60% = 15. 11% =
16. 12% = 17. 40% = 18. 95% =
6
5 | 3.0
- 30
0
0.2 0.3333...
0.75 0.8 0.5 0.6666.... 20% 33.33...% 75%80% 50% 66.66....% 0.08 0.12 0.6 0.4 0.11
0.95
Summer Mathematics Packet
IM Page 2
Fraction Operations
Hints/Guide:
When adding and subtracting fractions, we need to be sure that each fraction has the same
denominator, then add or subtract the numerators together. For example:
8
7
8
1 6
8
6
8
1
4
3
8
1
=
+
+ = + =
That was easy because it was easy to see what the new denominator should be, but what about if
it is not so apparent? For example:
15
8
12
7
+
For this example we must find the Lowest Common Denominator (LCM) for the two
denominators. 12 and 15
12 = 12, 24, 36, 48, 60, 72, 84, ....
15 = 15, 30, 45, 60, 75, 90, 105, .....
LCM (12, 15) = 60
So,
60
7
1
60
67
60
35 32
60
32
60
35
15
8
12
7
= =
+
+ = + = Note: Be sure answers are in lowest terms
To multiply fractions, we multiply the numerators together and the denominators together, and
then simplify the product. To divide fractions, we find the reciprocal of the second fraction (flip
the numerator and the denominator) and then multiply the two together. For example:
9
8
3
4
3
2
4
3
3
2 and 6
1
12
2
4
1
3
2
• = = ÷ = • =
Exercises: Perform the indicated operation: No calculators!
SHOW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.
1.
+ =
5
3
4
1
2.
+ =
3
2
7
6
3.
+ =
9
8
5
2
4.
! =
3
2
4
3
5.
! =
9
2
5
2
6.
! =
5
2
11
9
7.
• =
3
2
3
1
8.
• =
5
3
4
3
9.
• =
5
2
8
7
10.
÷ =
4
3
8
3
11.
÷ =
4
1
4
1
12.
÷ =
5
3
11
7
Summer Mathematics Packet
IM Page 3
Multiply Fractions and Solve Proportions
Hints/Guide:
To solve problems involving multiplying fractions and whole numbers, we must first place a one
under the whole number, then multiply the numerators together and the denominators together.
Then we simplify the answer:
7
3
3
7
24
1
4
7
6
4
7
6
• = • = =
To solve proportions, one method is to determine the multiplying factor of the two equal ratios.
For example:
x
24
9
4
=
since 4 is multiplied by 6 to get 24, we multiply 9 by 6, so
54
24
9
4
= .
Since the numerator of the fraction on the right must be multiplied by 6 to get the numerator on
the left, then we must multiply the denominator of 9 by 6 to get the missing denominator, which
must be 54.
Exercises: Solve (For problems 8 - 15, solve for N): No Calculators!
SHOW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.
1.
• =
4
3
4 2.
• 7 =
5
1
3.
• =
5
1
8
4.
• =
7
3
6
5.
• 4 =
5
4
6.
• 6 =
3
2
7.
• =
4
1
7
8. 5 20
1 n
=
9. 28
3 12
=
n
10. 25
1 5
=
n 11. 12
3
4
=
n
12. n
12
7
3
=
13. 27
12
9
=
n
14. n
18
3
2
=
15. 7 21
2 n