Representing Ratios w/Equations
Write the ratio 4:7 as an equation.
4/7
A recipe calls for 2 cups of flour to make 12 cookies.
How many cups of flour are needed to make 24 cookies?
4 cups of flour
To find the number of cups of flour needed to make 24 cookies, we can set up a proportion using the given information.
2 cups of flour makes 12 cookies
Let x represent the number of cups of flour needed to make 24 cookies.
The proportion can be set up as:
2/12 = x/24
To solve for x, we can cross-multiply:
2 * 24 = 12 * x
48 = 12x
Divide both sides by 12 to solve for x:
48/12 = x
x = 4
Therefore, 4 cups of flour are needed to make 24 cookies.
Plot the point (2, 4) on the coordinate plane.
To plot the point (2, 4) on the coordinate plane, we can use the x-coordinate (2) to determine the horizontal position and the y-coordinate (4) to determine the vertical position.
Start by drawing the x-axis (horizontal line) and the y-axis (vertical line) that intersect at the origin (0, 0).
Then, locate the point (2, 4) by moving 2 units to the right along the x-axis and 4 units up along the y-axis from the origin.
Mark this point with a dot or a small circle to represent the coordinates (2, 4).
The resulting plot should have a point at (2, 4) on the coordinate plane.
What is the missing value in the equivalent ratio 3:6 = ?:12?
6
Complete the missing values in the ratio table:
Ratio: 4:6
8:12
(multiply the ratio by same number to get an equivalent ratio on the table)
The sum of two numbers is 45.
If the ratio of the two numbers is 3:5, find the larger number.
To find the larger number out of two numbers with a given ratio and a sum, we can use algebraic equations.
Let's assume the two numbers in the ratio are 3x and 5x, where x is a constant.
According to the given information, the sum of the two numbers is 45:
3x + 5x = 45
Combining like terms:
8x = 45
Divide both sides by 8 to solve for x:
x = 45/8
x ≈ 5.625
Now, we can find the larger number by substituting the value of x back into the ratio:
5x = 5 * 5.625 ≈ 28.125
Therefore, the larger number is approximately 28.125.
A map scale indicates that 1 inch represents 10 miles.
How far is it between two cities if they are 2.5 inches apart on the map?
25 miles apart
1 inch to every 10 miles unit rate x10
2.5 x10
According to the scale, 1 inch represents 10 miles. Therefore, we can set up a proportion to find the actual distance.
Let x represent the actual distance between the two cities in miles.
The proportion can be set up as:
1 inch / 10 miles = 2.5 inches / x miles
To solve for x, we can cross-multiply:
1 inch * x miles = 10 miles * 2.5 inches
x miles = 25 miles
Therefore, when the two cities are 2.5 inches apart on the map, the actual distance between them is 25 miles.
Plot the points (3, 6), (4, 8), and (5, 10) on the coordinate plane.
0,0
3,6
4,8
5,10
Simplify the ratio 12:18.
2:3 (6)
Ratio: 5:8, Number of oranges: 24.
How many apples are there?
15 apples
Ratio: 5:8
Number of oranges: 24
Let x represent the number of apples.
The proportion can be set up as:
5/8 = x/24
To solve for x, we can cross-multiply:
5 * 24 = 8 * x
120 = 8x
Divide both sides by 8 to solve for x:
120/8 = x
x = 15
Therefore, there are 15 apples in the given ratio table.
Write the ratio equation for the relationship: The number of boys to girls is 7:9.
So, the ratio equation for this relationship is:
x:y = 7:9
7:9
If 15 people can paint a house in 6 hours, how many people would it take to paint the house in 3 hours?
7.5 people in 3 hours
15/6 x/3
divide 6 by 2 to get to 3 hours
same to top 15 divided by 2 is 7.5
Let x represent the number of people needed to paint the house in 3 hours.
The proportion can be set up as:
15 people / 6 hours = x people / 3 hours
To solve for x, we can cross-multiply:
15 people * 3 hours = 6 hours * x people
45 people-hours = 6x people-hours
Divide both sides by 6 to solve for x:
45 people-hours / 6 = x
x = 7.5
Determine the coordinates of the point that represents the ratio 2:3 on the coordinate plane.
2:3
you can't determine anything more without any other information given
Find the missing number in the ratio 2:4 = 6:?.
12 (3)
Ratio Table:
Apples:Oranges = 9:12
Write the ratio for the number of oranges to the number of apples.
12:9
Find the smaller number of a ratio if the larger number is 16 and the ratio is 3:5.
9.6 : 16
According to the given information, the larger number is 16 and the ratio is 3:5.
We can set up a proportion using these values:
3/5 = x/16
To solve for x, we can cross-multiply:
3 * 16 = 5 * x
48 = 5x
Divide both sides by 5 to solve for x:
48/5 = x
x = 9.6
Therefore, the smaller number in the ratio 3:5, when the larger number is 16, is approximately 9.6.
The price of 5 oranges is $2.50.
What is the cost of 12 oranges?
5/2.50 12/x
5 to 12 we multiply by 2.4
2.50 multiplied by 2.4 is $6
Which point represents the ratio 4:7 on the coordinate plane: A(8, 14) or B(12, 21)?
A and B
4:7 is equivalent to 8:14
4:7 is equivalent to 12:21
Determine if the ratios 3:4 and 6:8 are equivalent.
yes , (2)
Ratio Table:
Cats: Dogs = 6:10
What is the ratio of dogs to cats?
10:6
Write the ratio equation for the relationship: The number of boys to the total number of students is 3:8.
3:8
3 x is representing boys to 8 y is total of students means that there is 5 girls
A bicycle travels 10 miles in 30 minutes.
How many miles will it travel in 1 hour?
10/30 x/60 (1 hour)
multiply 30 by 2
multiply 10 by 2
20 miles to 1 hour
Plot the points (0, 0), (3, 6), and (6, 12) on the coordinate plane.
0,0
3,6
6,12
Simplify the ratio 20:25.
4:5 (5)
Ratio: 2:3
Number of triangles: 12.
How many squares are there?
8 squares
2/3 and x/12
3 to 12 we multiply by 4
2 x 4 is 8
or cross multiply
Let x represent the number of squares.
The proportion can be set up as:
2/3 = x/12
To solve for x, we can cross-multiply:
2 * 12 = 3 * x
24 = 3x
Divide both sides by 3 to solve for x:
24/3 = x
x = 8