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Exercise 1:

**It is known that a certain open faucet can fill eight ten-liter buckets in two minutes.** *That’s 80 liters for two minutes.*

**How long does it take to fill a four hundred liter tank?** (Note in the three tables below the **time **is in **seconds**)

Answer: First, let’s find out how long it takes to fill 1 liter. This is called**“the transition to unity**“.

We have 80 liters in 120 seconds or 1 liter in (1*120)/80 seconds according to the cross product rule.

This gives us the following table:

Now I apply the “multiplication by the unit”.

To answer the question:

and 400×1.5=600 seconds or 10 minutes.

**Still with this same tap, how much water flows in one hour?** (Note: In the following table the time is in seconds)

Let’s go back to the table and look at the proportionality coefficient between the top and bottom line, it is 1.5. Just multiply in one direction by 1.5 and divide in the other direction by 1.5 to find your way.

It is known that for every 1.5 seconds elapsed, 1 liter of water has flowed.

For 1 hour, or 3600 seconds, the water will have flowed according to the following proportionality table:

So in one hour 3600/1,5 = 2400 liters!

All this remains true if and only if *the water flow remains constant* and no one has turned off the tap.

Exercise 2:

To make my concrete, I mixed 2 bags of cement with 12 buckets of fine sand and 30 L of water.

How much sand and water would I need if I put 6 bags of cement in the mixer?

Let’s look at the table below and see the proportions noted, and the proportionality coefficients deduced:

The green arrow indicates that to pass from the first line to the second line I have a coefficient equal to 6 and to pass from the first line to the third I have a coefficient equal to 15.

So for 6 bags of cement I need 6 x 6 buckets of fine sand, that is 36 buckets of fine sand. And you need 6×15 liters of water, that is 90 liters.

*It is also possible to look at the proportionality coefficient between the first and second columns of the table. This coefficient is 3, because to go from 2 to 6 I have to multiply by 3. We then find that we need 3×12 buckets of fine sand and 3×30 liters of water.*

Exercise 3:

Let’s start by transferring these values into a proportionality table: We know that January has 31 days and that February most of the time has only 28 days.

a) **Verify over the first two months that his monthly salary is proportional to the**

**number of days in the month.**

Let’s see if 1937.5/31 is equal to 1750/28, and to do so let’s calculate these expressions separately.

1937,5/31 = 62,5€/day

1750/28 = 62,5€/day

so this table is well proportional and we can pass to the unit

and replace in this case, in the table, the question mark by 62.5€.

b) **Deduct his annual salary**.

A year such as February has 28 days instead of 29 and consists of 365 days.

Therefore, it is sufficient to multiply 365 by the daily wage which is 62.5€.

365×62,5 =22 812,50€ per year.

Jean’s annual salary will be 22812,50€(and probably no 13th month ).

Exercise 4:

A motorcycle always running at the same speed takes 6 minutes to cover 9km.

**1. What is the distance covered in 30 minutes?**

in 30 min=5x6min

He will travel 5×9=45 km

**2. What is the time taken to travel 54 km?**

9×6=54 km

6×6=36 min

It will take 36 minutes to travel 54 km.

## The answers to the exercises on proportionality in 6th grade.

After consulting **the answers to these exercises on proportionality in 6th** grade, you can return to the **exercises in 6th grade**.

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