BE A MATH WIZARD

The topics here are intended for Grade 3 levels and above...

Consecutive numbers means successive numbers in a particular sequence without a break. Example:  2 and 3 are two consecutive numbers; 4 and 6 are two consecutive even numbers; 5, 7, and 9 are three consecutive odd numbers.

Now can you answer this question: What two consecutive numbers give a sum of 15?
Since 7 + 8  =  15, therefore the answer is 7 and 8.

What two consecutive even numbers give an average of 23?
Solution: We place the average 23 in between the two even numbers.
Obviously, the answer is: 22 and 24.
Checking the answer by solving for the average:  (22 + 24) / 2  =  23

The average of five consecutive odd numbers is 45. What is the highest number of these five consecutive odd numbers?
Solution: Again we place the given average number at the middle of the sequence numbers. Thus we have the following five consecutive odd numbers as 41, 43, 45, 47, and 49. So the answers is 49.

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From 1 to 10, it's easy to say that there are 10 numbers in all.
But, what if I ask "How many numbers are there from  10 to 20?" How do we solve this kind of problem?... we have the simple solution: (Last Number - First Number) + 1  =  (20 - 10) + 1  =  11.

Now, try this one: How many numbers are there from 23 to 72?

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Give the standard form of 83 ones.
Solution: It's like being asked if how many ones are there in 83. Therefore, just multiply the given number by 1.  83 x 1  =  83  In short, using the identity property of multiplying any number by 1, whatever is the given number is the answer itself.

What is the standard form of 47 tens?
Solution:  47 x 10  =  470.  Or just simply annex one "zero" to the given number since there is one "zero" in the number 10.

Write 365 hundreds in standard form.
Solution:  365 x 100  =  36,500.  Or just simply annex two "zeroes" to the given number since there are two "zeroes" in the number 100.

Now, try this one:  90 tens is what number in standard form?

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Midway or Halfway means the value at half the distance or the number at the middle which is equally distant from the extremes.
Example: What number is midway between 11 and 21?
There are two ways to solve this problem.
1st Solution:  Using the Listing Method -  11,  12,  13,  14,  15,  16,  17,  18,  19,  20,  21.
Now looking at the middle number between 11 and 21 we can easily see that the answer is 16.
For longer list of numbers, we may use common difference like 11,  13,  15,  17,  19,  21 then identify the middle number/numbers (in this case, the number between 15 and 17 is 16)
2nd Solution:  Add the two numbers,  11 + 21  =  32.  Then divide the sum by 2,   32 / 2   =  16.

Now, try this one:   Find the number halfway between 148  and 526.

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Adding or Subtracting Fractions is easy when the given fractions have the same denominators.  In Dissimilar Fractions, one needs to change it first to similar fractions in order to solve it.
Example:  What is 2/3  +  1/4 equal to?
1st Solution:  Multiply 2/3 by 4/4  and 1/4 by 3/3 in order to make a similar denominator. Just add the numerators together then copy the similar denominator. Therefore the given fractions become 8/12  +  3/12 and the sum is 11/12.
2nd Solution:  Cross-multiply the numerator of the first fraction by the denominator of the second fraction to have a new numerator. Do the same process for the second fraction. Then multiply both the denominators for a new overall denominator.  2 x 4  =  8   and  1 x 3  =  3,  Adding the two sums give us the new overall numerator which is 11. Multiplying the first denominator from the first fraction by the denominator of the second fraction,  3 x 4  =  12, and this becomes the new overall denominator. Thus, the final answer is 11/12.
3rd Solution is by finding the Least Common Denominator (or LCD) which is almost the same as the same 2nd Solution. The LCD for the given fractions here is 12 and it is the new overall denominator. Divide the LCD by the denominator of the first fraction then multiply the quotient with its numerator to give a new numerator then do the same process for the second fraction. At this point, the solution is now the same as that of the 2nd Solution. Adding together the new numerators yield 11. Therefore, the answer is 11/12.

Now, try this one:   Add  2(3/5)  and 1/2.   [Hint  -  Change first the mixed number to improper fraction.]

You may post solutions and answers at the comment box below.  Thanks