Question

# Alex can do a certain construction task in 3.5 hours. Roger can do the same task in 2.35 hours. _____________is faster by _________hrs.

- Alex by 1.15 hrs
- Roger by 1 hr
- Alex by 1.35 hrs
- Alex by 1.05 hrs

Hint:

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An addition mental math technique is to dissect an addend. This approach might be more effective for some students than left-to-right addition. This method involves dividing up one addend in an equation into more manageable bits. There are certain properties that can be used while calculating which make it easy to add. Here we have given that Alex can do a certain construction task in 3.5 hours. Roger can do the same task in 2.35 hours. We have to find who is faster and how much.

So we will find the difference and then justify it.

An addition mental math technique is to dissect an addend. This approach might be more effective for some students than left-to-right addition. This method involves dividing up one addend in an equation into more manageable bits. There are certain properties that can be used while calculating which make it easy to add. Here we have given that Alex can do a certain construction task in 3.5 hours. Roger can do the same task in 2.35 hours. We have to find who is faster and how much.

So we will find the difference and then justify it.

## The correct answer is: Alex by 1.15 hrs

### Now as we know that here we have to find the step by breaking one number. The fact that there are no steps to memorise is one of the best things about mental math. The "friendly number" addition approach facilitates working with large numbers. This is due to the fact that we are, in essence, decomposing the problem into more manageable components.

Here we will use some properties which are:

- Commutative Property of Addition: if a and b are real numbers, then a+b=b+a
- Associative Property of Addition: if a,b, and c are real numbers, then (a+b)+c=a+(b+c)
- Compensation Property: It is a mental math strategy for multi-digit addition that involves adjusting one of the addends to make the equation easier to solve.

Now we have given 3.50 – 2.35, let's solve this.

3.50 – 2.35

3.50 – 2.40 = 1.10 ( by rounding to the closest tenths place)

1.10 + 0.05 = 1.15 ( compensation)

So, the answer is 1.15.

Here the concept of Break Apart Numbers is used where a number is divided in two parts to make addition easy. The concept of friendly numbers is also used so that it becomes easy for addition or subtraction purpose. Some properties like compensation is also used to solve easily. So, Alex is faster than roger by 1.15 hours.