I broke the 27 into 25 + 2. Seeing the 25 made me think of money.

8 X 25 = 8 quarters = $2.00
8 X 2 = 16 pennies = $0.16

$2.00 + $0.16 = $2.16

8 x 27 = 216

I can see that. Being able to do a trick requires skill and understanding (in both magic and skateboarding). I can see kids liking that they know a math trick that will help make a problem easier to solve - or a way that works that is less conventional.

David, I wonder if calling them Strategies rather than Tricks would clear up the issue. When I hear the word trick - I think of magic, where I don't understand how it's done. With a strategy, it is more of a plan of action that could work. I think of sports - different strategies can win a game.

Flip the problem - What is 50% of 30?

Half of a number is easier for me. Half of 30 is 15.

I used the model on the right, but then double checked with the original one on the left.

2 ways.

1st - I was born in 1974, so they are 2 years younger than me. I'm 51, they are or will be 49.

2nd - On a number line. 2025 - 50 is 1975. I subtracted 1 too many. Add the -1 back and I also get 49.

(number line not to scale)

Good seeing you again!

I added all the tens first to get 40. I was left with 3+5+7+9.

3+7= 10 (add that to my 10's group to now have 50)
5+9= 14 (another ten to get 60)

60 + 4 = 64

First thought - it is just less than 20 if I didn't need to be exact.

Second thought - reverse the numbers - 40% of 45.
10% of 45 is 4.5. I need four of those.

4.5 + 4.5 + 4.5 + 4.5 = 18.
(Solved this as 9 + 9 or (4x4) + 2)

I made all the numbers 20. 20 x 5 = 100

Then, subtracted 4, 3, 2, and 1.

100 - 10 = 90

A second way (not my preferred, but a different way to solve it.)

First way I saw it was --

6+9 = 15
7+8 = 15

15+15 = 30

I subtracted 50 instead of 45. I knew I subtracted too much, so I added 5 back.

112-45 = 112-50+5

67

Knowing 7.5% x 250 is the same as 250% of 7.5, I am going to find double and half of 7.5. I know 100% of 7.5 = 7.5.

Double - 200% of 7.5 = 15

Half - 50% of 7.5 = 3.75

Using those numbers to find 250% -

15+ 3.75 = 18.75

Three 7's is 21
Two 5's are 10

21 + 10 = 31

Start by rearranging the problem into 3 smaller problems.

2x5=10
2x5=10
3x3=9

Use those products again
10x10= 100
10x9=900

I divided the entire problem by 2 to get 500 ÷ 4.

I saw it as $5.00 ÷ 4. Each area gets 1 dollar, then each area gets 0.25¢.

1000 ÷ 8 = 125

If 20 = $36, then 10 = $18

If 10 = $18, then I know 5 = $9 and 1 = $1.80

Knowing all that, I can use those numbers to find the cost of 6.

$9.00 + $1.80 = $10.80

625 - 75 = 550 (thinking about money and subtracting quarters helped.)

I know I subtracted 3 more than I needed to, so I can add that back.

550 + 3 = 553

If 6 stickers cost $4.50, how much do 2 stickers cost?

$4.50 ÷ 3 = $1.50

2 stickers cost $1.50, and we need 10 times that amount.

2 X 10 = 20
$1.50 X 10 = $15.00

14/40 = 7/20
7/20 = 3.5/10
3.5/10 = 35/100
35/100 = 35%

Like your subtraction post the other day. Change the numbers to make them easier.

89 + 17 becomes 90 + 16

90 + 10 = 100
100 + 6 = 106

89 + 17 = 106

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Losses in service jobs sparked the first negative job growth in two years.

Change the problem to 75% of 60.

60 ÷ 4 = 15

60 - 15 = 45

Change the problem to 20 x 8. 20 x 8 = 160

I know I have 2 groups of 8 more than I need. 2 x 8 = 16

Subtract the extra. 160 - 16 = 144

I multiplied 9 x 40 to get 360. Then I moved the decimal to what makes the most sense. I could have chosen:

.360
3.60
36.0
360.0

Knowing that 10% of 40 is 4, the only option that makes sense is 3.6.

Like finding the amount of a 20% tip, I found 10% and doubled it.

10% = $2.40
20% = $4.80

Instead of adding (like a tip), I subtracted for the sale price.

I had to write all the number out. When I did, I saw I could make groups of 30. (0+30, 3+27, 6+24, 9+21, 12+18) with 15 remaining.

5 groups of 30 is 150.

150 + 15 = 165

If 45 = 30%, I can figure out that 15 = 10% by dividing both by 3.

45 + 45 + 45 + 15 = 150
30% + 30% + 30% + 10% = 100%

45 is 30% of 150

I saw that 89 was 11 away from 100 and I could subtract 11 from 88 easily.

I took 11 from the 88 making it 77. I then added the 11 to 89 making it 100.

My new problem is 77 + 100 = 177

Both fractions are close to 1, so I compared what was missing.

1/8 is smaller than 2/12. (I changed 1/8 to 2/16 in my head).

Since 1/8 is the smaller of the pieces, it must be closer to 1. That makes 7/8 the larger fraction.