Ratios and Proportional Relationships
You and your friend are making lemonade. You decide to use a recipe that calls for 2 cup of lemon juice for every 10 cups of water. What is the ratio of lemon juice to water?
2:10
Find the sum: 2/5 + 1/6
1. Find a common denominator
2. Create equivlant fractions
12/30 + 5/30
2. Add the numerators.
17/30
Describe the difference between 23 and 2 x 3.
23 equals 2 to the power of 3, or 2 cubed, which means 2 multiplied by itself 3 times.
2 x 3 = 6, or 2 being added to itself 3 times.
Find the area and the perimeter of the shape.
Area: l x w = 32 x 20 = 640 square units
Perimeter = l + w + l + w = 32 + 20 + 32 + 20 = 104 units
A scuba diver is 12 feet below sea level, and a helicopter is 18 feet above sea level.
You and your friend are making lemonade. You decide to use a recipe that calls for 2 cup of lemon juice for every 10 cups of water.
How many cups of lemon juice will you need if you pour 40 cups of water?
Create a table to show your reasoning.
4 cups of lemon juice.
Find the quotient: 2/3 divided by 3/4.
1/2
What does absolute value mean? Draw what symbols show absolute value.
Find the absolute value of
a. -7, 7
b. 5
a. 7
b. 5
Find the area of the shape.
1400 u2 or square units
What does the fraction sign represent in 1/4, 3/8, 2/7 ? Write an expression equialvant to the fraction
The fraction sign represents division between the numerator and the denominator.
1 divided by 4.
3 divided by 8
2 divided by 7.
You and your friend are making lemonade. You decide to use a recipe that calls for 2 cup of lemon juice for every 10 cups of water.
What is the unit rate?
1 cup of lemon juice for 5 cups of water, 1:5
Find the quotient using partial products and standard algorithmn:
8,550 divided by 24
356
Write an expression that is equivalant to the following:
- 5(x +4 )
- 9( m - 6 )
5x + 20
9m - 54
.
Describe the difference between area and perimeter.
Area is finding the amount of space an object takes up. Perimeter is the distance around an object.
How do you determine if two numbers are opposite?
They are the same distance from 0 and on different sides of the number line.
For example, 4 is the opposite of -4, and -4 is the opposite of 4. They are both the same distance from 0. One is negative, and the other is positive.
Find 30% of 80.
30 % = 30/100
80 x 30/100 = 24
Write 483.68 in expanded form
(4 x 100) + (8 x 10) + (3 x 1) + (6 x 1/10) + (8 x 1/100)
Describe what the word, 'coefficent' means.
A coefficient is a number that is multiplied by a variable.
Ex: 4x, 4 is the coefficent.
Find the volume of the prism.
V = l x w x h or V = Bh
V = 10 x 5 x 5 = 250 square units
A hiker climbed to an elevation higher than 450 feet above sea level and the temperature stayed below −3∘F.
Write an inequality to represent
- to represent all possible elevations, e, of the hiker.
- to represent all possible temperatures, t, for that day.
t < -3
e > 450
A piece of ribbon is 5 yards long. How many inches long is the ribbon?
Convert yards to feet and then feet to inches. There are 3 feet in a yard and 12 inches in food. This means that there is 36 inches in a yard.
36 x 5 = 180. The ribbon is 180 inches long.
Write a division expression that has the same value as 48.6 / 2.7. Without dividing explain why they have the same quotient.
All possible expressions that are equivlant to this expression multiplied or divided the divisor and dividend by the same power of 10.
Examples include:
- 486 /27
- 4860 / 270
- 4.86 - .27
Identify the independent and dependent variable. Emma's time in hours, t, and distance in miles, d, are related by the equation t=1/4d . She travels 8 miles in 2 hours.
independent = distance (in miles)
dependent = time (in hours)
The distance she travels affects how long she travels, so it is dependent on the distance.
What are the units when finding the area and volume?
Area: units square
Volume: cubic units
Order these rational numbers from least to greatest. Which number is closest to 0?
−3.5, 1/2, -4, 2.25, l -2 l
-4, -3.5, 1/2, l -2l , 2.25