Thank you for visiting a Express each ratio in its lowest terms 1 48 seconds to 5 minutes 2 2 mm to 100 cm 3 3600 seconds to missing. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
- Convert 5 minutes to seconds: $5 \text{ minutes} = 300 \text{ seconds}$, then simplify the ratio $48:300$ to $\frac{4}{25}$.
- Convert 100 cm to mm: $100 \text{ cm} = 1000 \text{ mm}$, then simplify the ratio $2:1000$ to $\frac{1}{500}$.
- Solve the proportion $22: 154 = x: 77$ to find $x = 11$.
- Solve the proportion $27: 18 = 3: x$ to find $x = 2$.
- Solve the proportion $8: 2x = 16: 1$ to find $x = \frac{1}{4}$.
- The final answers are: $\frac{4}{25}$, $\frac{1}{500}$, $11$, $2$, $\frac{1}{4}$.
### Explanation
1. Problem Analysis
We are asked to express each ratio in its lowest term and solve for $x$ where applicable. Let's tackle each sub-problem one by one.
2. Ratio of 48 seconds to 5 minutes
(1) We need to express the ratio of 48 seconds to 5 minutes in its lowest terms. First, we convert 5 minutes to seconds: $5 \text{ minutes} = 5 \times 60 = 300 \text{ seconds}$. Now, we express the ratio 48 seconds to 300 seconds as a fraction and simplify:$$\frac{48}{300} = \frac{12 \times 4}{12 \times 25} = \frac{4}{25}.$$
3. Ratio of 2 mm to 100 cm
(2) We need to express the ratio of 2 mm to 100 cm in its lowest terms. First, we convert 100 cm to mm: $100 \text{ cm} = 100 \times 10 = 1000 \text{ mm}$. Now, we express the ratio 2 mm to 1000 mm as a fraction and simplify:$$\frac{2}{1000} = \frac{1}{500}.$$
4. Ratio of 3600 seconds to unknown quantity
(3) The problem is incomplete. We cannot express the ratio without knowing the second quantity.
5. Solving for x in 22:154 = x:77
(4) We need to solve the proportion $22: 154 = x: 77$ for $x$. This can be written as $\frac{22}{154} = \frac{x}{77}$. Simplify the fraction $\frac{22}{154} = \frac{1}{7}$. Then, $\frac{1}{7} = \frac{x}{77}$. Multiply both sides by 77 to solve for $x$:$$x = \frac{77}{7} = 11.$$
6. Solving for x in 27:18 = 3:x
(5) We need to solve the proportion $27: 18 = 3: x$ for $x$. This can be written as $\frac{27}{18} = \frac{3}{x}$. Simplify the fraction $\frac{27}{18} = \frac{3}{2}$. Then, $\frac{3}{2} = \frac{3}{x}$. Cross-multiply to get $3x = 6$, so $x = 2$.
7. Solving for x in 8:2x = 16:1
(6) We need to solve the proportion $8: 2x = 16: 1$ for $x$. This can be written as $\frac{8}{2x} = \frac{16}{1}$. Simplify the fraction $\frac{8}{2x} = \frac{4}{x}$. Then, $\frac{4}{x} = \frac{16}{1}$. Cross-multiply to get $16x = 4$, so $x = \frac{4}{16} = \frac{1}{4}$.
### Examples
Ratios and proportions are fundamental in everyday life. For example, when you're cooking, you often need to adjust ingredient quantities based on a recipe. If a recipe serves 4 people and you want to serve 6, you use proportions to calculate the new amounts. Similarly, when scaling architectural drawings or calculating distances on a map, understanding ratios is crucial for accuracy and efficiency.
- Convert 100 cm to mm: $100 \text{ cm} = 1000 \text{ mm}$, then simplify the ratio $2:1000$ to $\frac{1}{500}$.
- Solve the proportion $22: 154 = x: 77$ to find $x = 11$.
- Solve the proportion $27: 18 = 3: x$ to find $x = 2$.
- Solve the proportion $8: 2x = 16: 1$ to find $x = \frac{1}{4}$.
- The final answers are: $\frac{4}{25}$, $\frac{1}{500}$, $11$, $2$, $\frac{1}{4}$.
### Explanation
1. Problem Analysis
We are asked to express each ratio in its lowest term and solve for $x$ where applicable. Let's tackle each sub-problem one by one.
2. Ratio of 48 seconds to 5 minutes
(1) We need to express the ratio of 48 seconds to 5 minutes in its lowest terms. First, we convert 5 minutes to seconds: $5 \text{ minutes} = 5 \times 60 = 300 \text{ seconds}$. Now, we express the ratio 48 seconds to 300 seconds as a fraction and simplify:$$\frac{48}{300} = \frac{12 \times 4}{12 \times 25} = \frac{4}{25}.$$
3. Ratio of 2 mm to 100 cm
(2) We need to express the ratio of 2 mm to 100 cm in its lowest terms. First, we convert 100 cm to mm: $100 \text{ cm} = 100 \times 10 = 1000 \text{ mm}$. Now, we express the ratio 2 mm to 1000 mm as a fraction and simplify:$$\frac{2}{1000} = \frac{1}{500}.$$
4. Ratio of 3600 seconds to unknown quantity
(3) The problem is incomplete. We cannot express the ratio without knowing the second quantity.
5. Solving for x in 22:154 = x:77
(4) We need to solve the proportion $22: 154 = x: 77$ for $x$. This can be written as $\frac{22}{154} = \frac{x}{77}$. Simplify the fraction $\frac{22}{154} = \frac{1}{7}$. Then, $\frac{1}{7} = \frac{x}{77}$. Multiply both sides by 77 to solve for $x$:$$x = \frac{77}{7} = 11.$$
6. Solving for x in 27:18 = 3:x
(5) We need to solve the proportion $27: 18 = 3: x$ for $x$. This can be written as $\frac{27}{18} = \frac{3}{x}$. Simplify the fraction $\frac{27}{18} = \frac{3}{2}$. Then, $\frac{3}{2} = \frac{3}{x}$. Cross-multiply to get $3x = 6$, so $x = 2$.
7. Solving for x in 8:2x = 16:1
(6) We need to solve the proportion $8: 2x = 16: 1$ for $x$. This can be written as $\frac{8}{2x} = \frac{16}{1}$. Simplify the fraction $\frac{8}{2x} = \frac{4}{x}$. Then, $\frac{4}{x} = \frac{16}{1}$. Cross-multiply to get $16x = 4$, so $x = \frac{4}{16} = \frac{1}{4}$.
### Examples
Ratios and proportions are fundamental in everyday life. For example, when you're cooking, you often need to adjust ingredient quantities based on a recipe. If a recipe serves 4 people and you want to serve 6, you use proportions to calculate the new amounts. Similarly, when scaling architectural drawings or calculating distances on a map, understanding ratios is crucial for accuracy and efficiency.
Thank you for reading the article a Express each ratio in its lowest terms 1 48 seconds to 5 minutes 2 2 mm to 100 cm 3 3600 seconds to missing. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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