Ratios & Proportional Relationships - Common Core: 6th Grade Math

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Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:100\rightarrow \frac{Red}{100}$

Now, we can create a proportion using our two ratios.

$\frac{3}{5}=\frac{Red}{100}$

Cross multiply and solve for .

$5 \times Red=3\times100$

Simplify.

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{300}{5}$

Solve.

There are red cars in the parking lot.

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Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$10:100\rightarrow\frac{10}{100}$

Reduce.

$\frac{10}{100}\rightarrow \frac{1}{10}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:250\rightarrow \frac{Red}{250}$

Now, we can create a proportion using our two ratios.

$\frac{1}{10}=\frac{Red}{250}$

Cross multiply and solve for .

$10 \times Red=1\times 250$

Simplify.

Divide both sides of the equation by .

$\frac{10Red}{10}=\frac{250}{10}$

Solve.

There are red cars in the parking lot.

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Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:136\rightarrow \frac{Red}{136}$

Now, we can create a proportion using our two ratios.

$\frac{1}{4}=\frac{Red}{136}$

Cross multiply and solve for .

$4 \times Red=1\times136$

Simplify.

Divide both sides of the equation by .

$\frac{4Red}{4}=\frac{136}{4}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$25:100\rightarrow\frac{25}{100}$

Reduce.

$\frac{25}{100}\rightarrow \frac{1}{4}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:164\rightarrow \frac{Red}{164}$

Now, we can create a proportion using our two ratios.

$\frac{1}{4}=\frac{Red}{164}$

Cross multiply and solve for .

$4 \times Red=1\times164$

Simplify.

Divide both sides of the equation by .

$\frac{4Red}{4}=\frac{164}{4}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$60:100\rightarrow\frac{60}{100}$

Reduce.

$\frac{60}{100}\rightarrow \frac{6}{10}\rightarrow \frac{3}{5}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:135\rightarrow \frac{Red}{135}$

Now, we can create a proportion using our two ratios.

$\frac{3}{5}=\frac{Red}{135}$

Cross multiply and solve for .

$5 \times Red=3\times135$

Simplify.

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{405}{5}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$40:100\rightarrow\frac{40}{100}$

Reduce.

$\frac{40}{100}\rightarrow \frac{4}{10}\rightarrow \frac{2}{5}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:400\rightarrow \frac{Red}{400}$

Now, we can create a proportion using our two ratios.

$\frac{2}{5}=\frac{Red}{400}$

Cross multiply and solve for .

$5 \times Red=2\times400$

Simplify.

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{800}{5}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$50:100\rightarrow\frac{50}{100}$

Reduce.

$\frac{50}{100}\rightarrow \frac{5}{10}\rightarrow \frac{1}{2}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:200\rightarrow \frac{Red}{200}$

Now, we can create a proportion using our two ratios.

$\frac{1}{2}=\frac{Red}{200}$

Cross multiply and solve for .

$2 \times Red=1\times200$

Simplify.

Divide both sides of the equation by .

$\frac{2Red}{2}=\frac{200}{2}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$30:100\rightarrow\frac{30}{100}$

Reduce.

$\frac{30}{100}\rightarrow \frac{3}{10}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:300\rightarrow \frac{Red}{300}$

Now, we can create a proportion using our two ratios.

$\frac{3}{10}=\frac{Red}{300}$

Cross multiply and solve for .

$10 \times Red=3\times300$

Simplify.

Divide both sides of the equation by .

$\frac{10Red}{10}=\frac{900}{10}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$4:100\rightarrow\frac{4}{100}$

Reduce.

$\frac{4}{100}\rightarrow \frac{2}{50}\rightarrow \frac{1}{25}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:40\rightarrow \frac{Red}{400}$

Now, we can create a proportion using our two ratios.

$\frac{1}{25}=\frac{Red}{400}$

Cross multiply and solve for .

$25 \times Red=1\times400$

Simplify.

Divide both sides of the equation by .

$\frac{25Red}{25}=\frac{400}{25}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$35:100\rightarrow\frac{35}{100}$

Reduce.

$\frac{35}{100}\rightarrow \frac{7}{20}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:200\rightarrow \frac{Red}{200}$

Now, we can create a proportion using our two ratios.

$\frac{7}{20}=\frac{Red}{200}$

Cross multiply and solve for .

$20 \times Red=7\times200$

Simplify.

Divide both sides of the equation by .

$\frac{20Red}{20}=\frac{1400}{20}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$80:100\rightarrow\frac{80}{100}$

Reduce.

$\frac{80}{100}\rightarrow \frac{8}{10}\rightarrow \frac{4}{5}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:800\rightarrow \frac{Red}{800}$

Now, we can create a proportion using our two ratios.

$\frac{4}{5}=\frac{Red}{800}$

Cross multiply and solve for .

$5 \times Red=4\times800$

Simplify.

Divide both sides of the equation by .

$\frac{5Red}{5}=\frac{3200}{5}$

Solve.

There are red cars in the parking lot.

Compare your answer with the correct one above

Question

Red is a very popular car color. A production company manufactures cars and parks them in a lot behind the plant. There are cars in the parking lot and of them are red. How many red cars are in the parking lot?

Answer

We can use ratios and proportions to solve this problem. Percentages can be written as ratios. The word “percent” means for every hundred. In the problem, we are told that of the cars are red. In other words, for every hundred cars of them are red. We can write the following ratio:

$8:100\rightarrow\frac{8}{100}$

Reduce.

$\frac{8}{100}\rightarrow \frac{4}{50}\rightarrow \frac{2}{25}$

We know that there are cars in the parking lot. We can write the following ratio by substituting the variable for the number of red cars:

$Red:3200\rightarrow \frac{Red}{3200}$

Now, we can create a proportion using our two ratios.

$\frac{2}{25}=\frac{Red}{3200}$

Cross multiply and solve for .

$25 \times Red=2\times3200$

Simplify.

Divide both sides of the equation by .

$\frac{25Red}{25}=\frac{6400}{25}$

Solve.

There are red cars in the parking lot.

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $25\ \text{workers}$ .

The factory will need $10\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $5\ \text{workers}$ .

The factory will need $2\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $15\ \text{workers}$ .

The factory will need $6\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $10\ \text{workers}$ .

The factory will need $4\ \text{managers}$ .

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Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $60\ \text{workers}$ .

The factory will need $24\ \text{managers}$ .

Compare your answer with the correct one above

Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $45\ \text{workers}$ .

The factory will need $18\ \text{managers}$ .

Compare your answer with the correct one above

Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $20\ \text{workers}$ .

The factory will need $8\ \text{managers}$ .

Compare your answer with the correct one above

Question

At a local microchip factory, there are managers for every workers. How many managers are needed for workers?

Answer

In order to solve this problem, we will create a table of proportions using the following ratio.

$2\ \text{workers}: 5\ \text{managers}$

If we solve for the table, then we can find the number of managers needed for $50\ \text{workers}$ .

The factory will need $20\ \text{managers}$ .

Compare your answer with the correct one above

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