Math Cross Products 7th grade
Isabella worked 50 hours over the past two weeks, and she gets paid by the hour. During the first week of the two-week span, she worked 30 hours and got paid $285.00. How much did she get paid during the second week of the two-week span?
$190.00
Caroline works in Shelley's store. She earns $36 for a 4-hour shift. If she works for 7 hours, how much can Caroline expect to earn?
$63
One of the dog treats in Shelley's shop is 8 inches long and 3.2 inches wide. She wants to make a miniature version that has proportional dimensions. If the miniature treat will be 3 inches long, how wide should it be?
1.2 inches
In a photograph, a house is 4 inches wide and 6 inches tall. The photograph is enlarged while keeping proportional dimensions, and the width of the house in the enlarged photograph is 9 inches. What is the height of the house in the enlarged photograph?
13.5 inches
Shelley's pet food store sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20. Write a proportion that compares the sales of these two items, and find the cross products. The cross products are both equal to
21
Which is a valid proportion?
3/4=21/8
Which of the paired items from the pet store can be used to create a proportion?
4 cans of salmon for $9 and 6 cans of chicken for $13.50
Which equation could you use to solve for x in the proportion StartFraction 4 over 5 EndFraction = StartFraction 9 over x EndFraction?
4x=45
Shelley sells 5 bone-shaped treats for $3.50. How much should she charge for a package of 12 treats? Which proportion is needed to solve the problem?
5/3.5=12/x
Javed downloaded from the Internet two files that had a combined size of 696 megabytes. The size of the first file was 290 megabytes, and it took 5 minutes to download. Assuming that the files downloaded at a constant speed, how long did it take for the second file to download?Javed downloaded from the Internet two files that had a combined size of 696 megabytes. The size of the first file was 290 megabytes, and it took 5 minutes to download. Assuming that the files downloaded at a constant speed, how long did it take for the second file to download?
7 minutes
If 2/3= x=12 what is the value of x?
8
How can you check to see if two ratios form a proportion? Explain the method you used to find the answer to the previous problem.
In problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. To find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.
Claire correctly solved the proportion StartFraction x over 4 EndFraction = StartFraction 36 over 16 EndFraction for x by using cross products to get the equation 16 x = 144 and then dividing both sides by 16 to get x = 9. She showed that she can use cross products to solve the proportion because she gets the same answer if the solves it as shown.
Multiplication property of equality
Bone-shaped treats are 5 for $3.50 at Shelley's store and Sarah wants to buy 12. She set up and solved this proportion to find how much they would cost. Describe her error and find the correct solution.
Sarah multiplied the denominator by the denominator and the numerator by the numerator instead of finding the cross products. The equation should be 5x = 42, so the cost should be $8.40.
Joanie believes that you cannot use cross products to solve the proportion StartFraction 50 over 3 EndFraction = StartFraction 75 over x EndFraction for x. She says that if you multiply both sides of the equation by x, you get StartFraction 50 x over 3 EndFraction = 75. Then, if you multiply both sides of the equation by 3, you get 50 x = 75, which is a different equation than you would get if you cross multiplied. What mistake did Joanie make in her reasoning?
She assumed that 50x=75 is the equation that you get if you multiply both sides of the equation 50x/3=75 by 3
Think about the proportion and the cross products for this problem: Shelley sold one customer 5 peanut butter biscuits for $3. She sold another customer 7 beef treats for $4.20. Because the cross products are equal, which statements are true? Select all that apply.
The ratios are equivalent and The ratios are proportional
Why can you use cross products to solve the proportion StartFraction 18 over 5 EndFraction = StartFraction x over 100 EndFraction for x?
because 18 times 100 is equal to 5 times x, which means that x is equal to 360
Why are the solutions to the proportions StartFraction 40 over 8 EndFraction = StartFraction x over 10 EndFraction and StartFraction x over 40 EndFraction = StartFraction 10 over 8 EndFraction the sam
because both result in the equation 8 x = 400, which simplifies to x = 50
What is the solution to the proportion? Round the answer to the nearest tenth if necessary. 52/x=9.5/3.25
x=17.8
The following three proportions can all be used to solve the problem about Caroline's salary. Explain why the solutions to each proportion are the same.
Each proportion is written so the units are in the corresponding positions. The cross products of all the proportions result in the equation 4x = 252, which results in x = 63.
