Adding and Subtracting Rules for All Rational Numbers
1. Change all subtraction problems to addition using the additive inverse.
2. Find the number with the biggest absolute value and use its sign (+ or -) for your answer.
3. Same signs? Add the numbers. Different signs? Subtract the numbers. (Remember that you subtract like normal, only using the absolute values of each number.)
4. Use the rule for the type of rational number you have. Fractions must have common denominators. Decimals must be lined up according to the decimal place.
Multiplying and Dividing Rules for All Rational Numbers
Count the number of negative signs in the expression. You can use EPON if the expression consists only of multiplication or division. EPON = Even number of negatives means a Positive answer. Odd number of negatives means a Negative answer.
You can also use same signs will produce a positive answer, and different signs will produce a negative answer.
Classwork - Word Problems
1) A balloon descends at a rate of 2.3m/s. After 2 minutes, how many meters has the balloon descended?
2) A taxi driver charges $3.15 when you get in the cab as well as $0.35 per mile traveled. If you have $25 to spend on your taxi ride, how many miles can you travel?
3) Suzanne is making a pound cake. The recipe calls for 2/3 cups of sugar per 5 servings. If 20 of her friends are coming for dinner, how much sugar will Suzanne need?
4) During science, students conducted a lab of how far a turtle can travel. The students collected the following data: 0.25m, 0.0145m, 1.25m, and 5.091m.
What is the total distance traveled?
5) A rope is 72 yards long. John needs to mark the rope every 2.75 yards. How many marks need to be made?
6) What is the value of the following:
(-9/3 - 2.15) x (-1.02 / .04)
1. About eleven twelfths of a golf course is in the fairways, one-eighteenth in the greens, and the rest in the trees. What part of the golf course is in the trees?
2. David is having trouble when subtracting mixed numbers. The problem he was given was -3 ⅖ - ⅗. So he converted 3 ⅗ = 2 12/5. He then subtracted and found that 2 9/5 was his difference. He converted from an improper fraction to a mixed number and his solution was 3 ⅘. Was he correct? How can you tell? What might be his difficulty? How might you help David?
3. John spent a quarter of his life as a boy growing up, one- sixth of his life in college, and one-half of his life as a teacher. He spent the last 6 years in retirement. How old was he when he died?
4. Rafael ate one fourth of a pizza and Donatello ate one third of it. What fraction of the pizza did they eat? Create and solve a similar problem.
Some of the items listed here have been done in class.
Here is a PDF form that works with all operations with decimals here.
To change a fraction into a decimal, sometimes you may be able to set up a proportion to get the fraction to a denominator of a multiple of 10. For example, 3/5 can be changed into 6/10, which is an equivalent fraction by a factor of 2. 6/10 is the same as 0.6.
Other times you will need to divide the numerator by the denominator to get a decimal. This way will work every time. If your fraction can not be equivalent to a denominator of 10, simply divide it. 5/8 can't evenly go into a denominator of 10 (without doing extra steps), so divide 5 by 8 to get 0.625.
To remember which number get divided, you can remember the shortcut in/out or you can note that a proper fraction will always be a number less than one.
To change a terminating decimal into a fraction, note the place value of the decimal and make that the denominator. Put the number that you see as the numerator. Then simplify
How do you know if a fraction is a repeating or terminating decimal?
If its denominator has a factor of 2 or 5, it will be a terminating decimal.
Video Links provide notes as well as example problems - Converting Decimals, Converting Fractions
Worksheet on Converting Fractions and Decimals (shown below)
Worksheet on Ordering Rational Numbers (linked and shown below)