Download Math 7 Challenge, Unit 1: Rational Numbers, Study Guide Name

Math 7 Challenge, Unit 1: Rational Numbers, Study Guide
Name: _______________________________ Period: __________
Target 1: I can identify and classify numbers within the subsets of the real number system.
Natural Numbers (Counting Numbers): 1, 2, 3, …
Whole Numbers: 0, 1, 2, 3, …
Integers: All whole numbers AND their opposites
Rational Numbers: All integers and all of the numbers in between (fractions and decimals.)
1) The number (-2) is NOT in which subset(s)?
a. Natural Numbers
b. Whole Numbers
c. Integers
d. Rational Numbers
2) All Whole Numbers are also:
a. Natural Numbers
b. Integers
c. Rational Numbers
d. All of the above
3) All Integers are also:
a. Natural Numbers
b. Whole Numbers
c. Rational Numbers
d. All of the above
2
Math 7 Challenge, Unit 1: Rational Numbers, Study Guide
Target 2: I can convert a fraction to a decimal to determine whether it is a terminating or
repeating decimal using long division.
5
8
𝟖
Divide the numerator by the denominator.
Divide the numerator by the denominator.
𝟏𝟓
0.625
8 ) 5.000
-48
20
-16
40
-40
0 The remainder is zero and there
are not any parts of the original
numerator to bring down. So,
this decimal terminates.
3
4) Without a calculator, find the decimal equivalent for 8.
15
5) Does the fraction 24 convert to a terminating or repeating decimal? How do you know?
Target 3: I can approximate the value of an irrational number and locate it on a number line.
Approximate the square root of the following. If using a decimal approximation, estimate to the
nearest tenth. If using a fractional approximation, simplify the fraction.
6)
√114
8)
Place the following numbers in their appropriate location on the number line.
√2.25
−√7
− 1.7
7)
√7
Math 7 Challenge, Unit 1: Rational Numbers, Study Guide
Name: _______________________________ Period: __________
Target 4: I can convert a decimal to a fraction.
Find the fraction equivalent for each decimal. Simplify.
9) 0.48
10)
̅̅̅̅
−0. 45
Target 5: I understand the absolute value of a rational number as its distance from 0 in the
number line.
11)
|−4| =
12)
|4| =
13)
|𝑥| = 7
14)
|−4| − |9| =
Target 6: I can add and subtract integers.
8) −3 + 4
10) −3 − 4
9) −3 + − 4
12) −3 − (−4)
10) 3 + 4
Adding Integers with the Same Sign:
1) Add the absolute values
2) Keep the sign the same
13) 3 − 4
Adding Integers with Different Signs:
1) Find the difference of the absolute
values.
2) Use the sign of the integer with the
larger absolute value.
Subtracting Integers:
1) To subtract an integer, add the opposite.
4
Math 7 Challenge, Unit 1: Rational Numbers, Study Guide
Target 7: I can multiply and divide integers.
 If the signs of the integers are the same, then the product (or quotient) is positive.
 If the signs of the integers are different, then the product (or quotient) is negative.
14)
−3 × 4 =
15)
3 × (−4) =
16)
−3 × (−4) =
17)
−15 ÷ 3 =
18)
15 ÷ (−3) =
19)
−15 ÷ (−3) =
Target 8: I can add and subtract signed fractions and decimals (rational numbers).
20)
1
2
+ (−
1
4
)
21)
−2.35 − (−1)
Target 9: I can multiply and divide signed fractions and decimals (rational numbers).
2
4
22)
−3 × 5
24)
−3 ÷ 4
2
4
23)
1.5 × (− 15)
25)
−0.6 ÷ (−0.3)
Math 7 Challenge, Unit 1: Rational Numbers, Study Guide
Name: _______________________________ Period: __________
Target 10: I can solve real-world problems using rational numbers including fractions, decimals
and integers.
26) It was −3° in Columbia, MO when Shari got on a plane for Florida. There was a temperature
increase of 60° when she got off of the plane in Miami, Florida.
a. Write this as a number sentence.
b. What was the temperature in Miami?
27) Five friends went to play golf. Jon shot a −2, Kaleb shot a 3, Carey shot a 4. What was the
mean score for the four players?
28) Find the mean of these five daily temperatures: −4°, −6°, 2°, −5°, 3°. Show your work.