Representation and Comparison of Rational Numbers
What is the absolute value of -5?
5 because absolute value is the distance from 0. This means that -5 is really 5 units away from 0 on the number line.
Use PEMDAS to solve the following expression
4(-2) + (-10)
-18
In this problem, we see only multiplication and addition. According to PEMDAS, we multiply first and then we add.
4 x -2 = -8
-8 + -10 = -18
What percent is 1/8?
12.5%
Use TIBO to turn your fraction into a decimal and then move your decimal point 2 places to the right to get your percent.
Omar has a new credit card. He earns 300 reward points for every $100 dollars he spends.
If Omar earned 1,800 reward points, how much money did he spend?
$600
Step 1: Set up your two equivalent rates (fractions) *Make sure units match*
Step 2: Look to see how you went from one rate to the other rate (Did you multiply or divide? What did you multiply or divide by?)
What is the opposite of 21?
-21 because opposite integers are positioned on the opposite side of 0 on the number line.
Use PEMDAS to solve the following expression
4(-2) + (-10) + 3
-15
In this problem, we see only multiplication and addition. According to PEMDAS, we multiply first and then we add.
4 x -2 = -8
-8 + -10 = -18
-18 + 3
**TO ADD integers with DIFFERENT SIGNS, we must first find the absolute value of integers.
The absolute value of -18 is 18
The absolute value of 3 is 3
Then, we subtract our absolute values:
18 -3 = 15
Finally, we take the original sign of the bigger number. 18 was the bigger number and originally, its sign was negative. So our answer would be -15
True or False
14/20 = .07 as a decimal
FALSE
14/20 , when you use T.I.B.O. is .7 as a decimal.
It costs $3.99 for 25 fl. oz. of detergent or $6.99 for 90 fl. oz. Which is a better buy?
$6.99 for 90 fl. oz. is the better buy.
Step 1: Set up two fractions. Money always goes on top!!!
Step 2: Use T.I.B.O. to find your unit rate for each fraction
Step 3: Compare the unit rates and see which is the better buy!
Solve the following problem
|-21| + |52|
73 because the absolute value of -21 is 21. So you add 21 + 52 and get 73.
Use PEMDAS to solve the following expression
4(-2) + (-10) + 3(-8)
-42
In this problem, we see only multiplication and addition. According to PEMDAS, we multiply first and then we add.
4 x -2 = -8
3 x -8 = -24
-8 + -10 -24
First, we add -8 + -10 to get -18.
Then, we subtract -18 - 24.
**TO SUBTRACT integers with DIFFERENT SIGNS, we must change the subtraction sign to ADDITION.
-18 + - 24 = -42
A waiter earned a 21% tip. What decimal is equivalent to 21%?
.21 To turn a percent into a decimal, you must move the decimal point 2 places to the left.
21% is a whole number percent, meaning the decimal point is located behind 21. So we move the decimal point 2 places to the left and get .21
If Ms. Alma travels 100 miles in 4 hours, how many miles does she travel per hour?
25 miles per hour
100 miles divided by 4 hours will give you 25. Which means Ms. Alma traveled 25 miles per hour
-1/2, -3.5, 2, 5/8
-3.5, -1/2, 2, 5/8
Convert all the rational numbers into the same form (decimals). Then, compare your decimals.
-1/2 = -0.5
-3.5 = -3.5
2 = 2.0
5/8 = 0.625
The further left of the number line, the smaller the number is. The further right of the number line, the bigger the number is. -3.5 is the furthest left on the number line. As we move to the right, next is -1/2, 5/8, 2.
True or False:
-4 + (-3) = -7
True
When adding integers with the SAME sign, we just add them as is and keep the sign
Timmy spent $15 out of the $20 in his wallet. What decimal represents the fraction of the $20 Timmy spent?
.75
Step 1: Set up your fraction
Step 2: Use T.I.B.O to get your decimal
4 packets contain 2000 paperclips. How many paperclips are there per packet?
500 paperclips per packet.
The question is asking for you to find paperclips per packet. So you divide 2000 paperclips by 4 packets and get 500 paperclips per packet.
Which is bigger?
17/20 or 3/5
17/20. There are two ways you can find the answer.
Option 1: Find the Common Denominator by identifying the largest denominator. Then look to see if your small denominator is a factor of the largest denominator. Finally, create equivalent fractions
17/20 = 17/20
3/5 = 12/20
Option 2: Convert the fractions into decimals by using T.I.B.O. Then, compare
17/20 = .85
3/5 = .6
*You can add a 0 to .6 to make it .60 so it is easier to compare.
17/20 is the bigger rational number.
Solve using PEMDAS
50 -(14 + 12 + 2(5) + 2(2) + 3)
Answer: 7
Step 1: Start with inside the parenthesis
50 - (14 + 12 + 2(5) + 2(2) + 3)
We must multiply first because multiplication comes before addition
2(5) = 10
2(2) = 4
50 - (14 + 12 + 10 + 4 + 3)
Step 2: Let's add everything in our parenthesis
50 - (43)
Step 3: Subtract 50 - 43
Your answer is 7.
A farmer watered 3/8 of a field. What percentage is equivalent to the fraction of the field the farmer watered?
37.5%
Step 1: Turn fraction into decimal using T.I.B.O.
Step 2: Move decimal point 2 places to the right & add your percent sign
For every touchdown scored by the Timberwolves, the mascot does 3 back flips and the cheerleaders set off 6 confetti cannons.
How many TOUCHDOWNS did the Timberwolves score if the cheerleaders set off 18 confetti cannons?
3
Step 1: Set up your two equivalent rates (fractions)
1 touchdown ? touchdown
-------------- = --------------
6 cannons 18 cannons
To get from 6 cannons to 18 cannons, we multiplied by 3. What we do to the bottom we must do to the top. So we must multiply the top by 3 as well. 1 x 3 is 3 So the Timberwolves scored 3 touchdowns.