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**Inverse Proportion What is it?**

Inverse Proportion is when one quantity increases and the other decreases at the same rate. The two quantities are said to be INVERSELY Proportional or (INDIRECTLY Proportional) to each other.

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Examples: Light and distance The further away we are from a light, the less bright it is: As distance increases, brightness decreases And as distance goes down, brightness goes

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Speed and travel time Speed and travel time are Inversely Proportional because the faster we go the shorter the time. As speed goes up, travel time goes down And as speed goes down, travel time goes up

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**Some examples… A) 4 people can paint a fence in 3 hours.**

How long will it take 6 people to paint it? It is an Inverse Proportion: Why? - Because as the number of people goes up, the painting time goes down. As the number of people goes down, the painting time goes up.

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**How can you solve it? Use these 3 steps:**

4 people can paint a fence in 3 hours. How long will it take 6 people to paint it? Identify the variables and write them (people and hours) People Hours

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**4x3 6 4 people can paint a fence in 3 hours.**

How long will it take 6 people to paint it? 2) Identify the numbers mentioned and place them in the correct position. (4, 3 and 6) 3) Multiply and divide As you can see, when you multiply and divide , it is like making a triangle. People Hours 4 3 6 ? (X) 4x3 6

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**What are the differences between direct and inverse proportion**

What are the differences between direct and inverse proportion? Quantities can increase or decrease. The order for solving the problems is different. Can you give some examples???

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**Solve the following problems**

1. 3 workers build a wall in 12 hours. How long would it have taken for 6 equally productive workers? In this example, the number of workers and the time are inversely proportional, because when the quantity of people decreases, the total time increases and when the quantity of people increases, the total time decreases.

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2. It takes 14 hours for a faucet with a flow of 18 liters per minute to fill a reservoir with water. How long will it take if its flow is reduced to 7 liters per minute?

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**3. If there are 6 builders, it takes 80 days to complete the house**

3. If there are 6 builders, it takes 80 days to complete the house. How many builders must be employed to build the house in just 16 days?

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**5. If it takes 3 men 8 hours to build a wall.**

4. It takes one person 8 days to complete a job. How many days will it take 4 people? 5. If it takes 3 men 8 hours to build a wall. How long will it take 4 men.

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**6. 12 men can dig a pond in 8 days. How many men can dig it in 6 days**

6. 12 men can dig a pond in 8 days. How many men can dig it in 6 days? 7. It takes 10 men 12 months to build a house. How long should it take 15 men.

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**8. At 8 m/s a journey takes 32 minutes. **

How long should it take at 4 m/s. 9. If a school kitchen has enough food for 150 students for 24 days, how long will the same food last 12 students ?

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**10. A fort had provisions for 300 men for 90 days**

10. A fort had provisions for 300 men for 90 days. If there are 30 less men. For how many days the food will last?

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