Download Chapter 30 Math skills worksheet

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Skills Worksheet
Math Skills – Chapter 30
Order of Operations and Distances from Stars to Planets
When solving long mathematical problems, you need to do the operations in the
correct order, called the order of operations. To remember the correct order,
parenthesis, exponents, multiplication, division, addition, and subtraction, you can
use the acronym “PEMDAS.” The following rules summarize the correct order of
operations for long mathematical problems:
Order of Operations
1. Simplify groups inside parentheses. Start with the innermost group and work
out.
2. Simplify all exponents.
3. Perform multiplication and division in order from left to right.
4. Perform addition and subtraction in order from left to right.
SAMPLE PROBLEM
Imagine you are an astronomer trying to determine the distance in lightminutes from an imaginary star to planets in its orbit. A light-minute is the
distance light travels in 1 min. The speed of light is 300,000 km/s.
In an imaginary example, Planet A is 48 light-minutes from the star.
Another 24 light-minutes beyond Planet A is Planet B. A third planet, Planet
C, is half the distance of Planet B from the star. You want to know how many
kilometers Planet C is from the star. The equation for this problem might
look like this: [(48 + 24) ÷ 2]  [(3  105)  60]  ?
SOLUTION
Step 1: Because there is an exponent inside parentheses, simplify it first:
105  100,000
Step 2: Simplify groups inside the inner parentheses:
48  24  72
3  100,000  300,000
Step 3: Simplify groups inside the outer parentheses:
72  2  36
300,000  60  18,000,000
Step 4: Perform multiplication:
36  18,000,000  648,000,000
Step 5: Write the answer:
Planet C is 648,000,000 km from the star.
Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
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Stars, Galaxies and the Universe
Name ______________________________ Class ___________________ Date __________________
Math Skills continued
PRACTICE
Using the sample problem as a guide, answer the following questions. Remember
to show your work.
1. Planet X is 21 light-minutes from a star. Another 33 light-minutes beyond that
is Planet Y. A third planet, Planet Z, is one-third the distance of Planet Y from
the star. How many kilometers is Planet Z from the star? Write and solve the
equation.
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2. Planet D is 95 light-hours from a star. Another 15 light-hours beyond that is
Planet E. A third planet, Planet F, is twice the distance of Planet E from the
star. How many kilometers is Planet F is from the star? Write and solve the
equation.
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3. Assume you have worked out the following equation to find the distance in
kilometers of Planet L to a star. Solve this equation.
[(63  30)  2]  [(3  105)  60 60]  ?.
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4. Assume you have worked out the following equation to find the distance in
kilometers of Planet M to a star. Solve this equation.
[(22  11)  4]  [(3  105)  60]  ?.
5. Assume you have worked out the following equation to find the distance in
kilometers of Planet N to a star. Solve this equation.
[(19  4)  2]  [(3  105)  60]  ?.
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Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
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Stars, Galaxies and the Universe
ANSWER KEY
Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.
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Stars, Galaxies and the Universe