# Mental Subtraction Strategies

This mental math lesson explains 6 different strategies you can use for mentally subtracting 2-digit numbers, meant for 2nd or 3rd grade. It contains the instruction, examples, lots of exercises, and word problems for students to complete.

Strategy 1:    Subtract in two parts
 53 − 8 = 53 − 3 − 5 =      50 − 5 = 45
 72 − 6 = 72 − 2 − 4 =      70 − 4 = 66

Subtract 8 in two parts: first 3, then 5.

Subtract 6 in two parts: first 2, then 4.

In other words, first subtract to the previous whole ten, then the rest.

1. Subtract the elevated number in parts first subtract to the previous whole ten; then the rest.

 − 5 /         \ a.  51 − 1   −  4 = ______
 − 7 /          \ b.   62 − ____  − ____ = ______
 − 4 /          \ c.   33 − ____  − ____ = ______
 − 5 /          \ d.   92 − ____  − ____ = ______
 − 6 /          \ e.   75 − ____  − ____ = ______
 − 7 /          \ f.   63 − ____  − ____ = ______
 − 7 /          \ g.   35 − ____  − ____ = ______
 − 5 /          \ h.   74 − ____  − ____ = ______

2. First subtract the balls that are not in the ten-groups.

 a.      51 − 7 = _______ 51 − 5 = _______ 51 − 3 = _______ 51 − 6 = _______
 b.     42 − 4 = _______ 42 − 5 = _______42 − 3 = _______ 42 − 6 = _______

 Strategy 2:    Use known subtraction facts Since 14 − 6 = 8, we know that the answer to 74 − 6 will end in 8, but it will be in the sixties sixty-something. So it is 68. Since 15 − 8 = 7, we know that the answer to 55 − 8 will end in 7, but it will be in the forties forty-something. So it is 47.

3. Subtract. The first problem in each box is a “helping problem” for the others.

 a.  14 − 9 = _______     24 − 9 = _______     44 − 9 = _______ b.  17 − 8 = _______     27 − 8 = _______     37 − 8 = _______ c.  12 − 9 = _______     52 − 9 = _______     32 − 9 = _______ d.  15 − 9 = _______     65 − 9 = _______     45 − 9 = _______ e.  13 − 8 = _______     33 − 8 = _______     93 − 8 = _______ f.  16 − 8 = _______     86 − 8 = _______     36 − 8 = _______

4. a. Amy has \$32. She bought a comic book for \$7.
How much does she have now?

b. Peter had \$29. A toy train he wants costs \$39.
Mom paid him \$5 for working. How much more
does Peter now need to buy the train?

c. A flower shop has 55 roses. Eight of them are white,
and the rest are red. How many are red?

Strategy 3:  Subtract in parts: tens and ones
Break the number being subtracted into its tens and ones. Subtract in parts.
 75 − 21 = 75 − 20 − 1 =      55 − 1 = 54

First subtract 20, then 1.

 87 − 46 = 87 − 40 − 6 =      47 − 6 = 41

First subtract 40, then 6.

5. Subtract in parts: Break the second number into its tens and ones.

 a.  89 − 26 89 − 20 − 6

= __________

 b.  56 − 35 56 − −

= __________

 c.  75 − 51 75 − −

= __________

d.   69 −   19

e.  67 −   36

f.  64 −  33

 Strategy 4:    Add. You can “add backwards”. This works well if the two numbers are close to each other. Instead of subtracting, think how much you need to add to the number being subtracted (the subtrahend) in order to get the number you are subtracting from (the minuend). 71 − 67 = ??Think: 67 + ____ = 71 558 − 556 = ??Think: 556 + ____ = 558

6. Subtract.

 a.  78 − 75 = _______     61 − 58 = _______ b.  112 − 108 = _______     692 − 688 = _______ c.  505 − 499 = _______     1000 − 994 = _______

7. You had \$50. You purchased two bouquets of roses for \$13 each.
How much do you have left after the purchase?

8. What if you bought three bouquets of roses for \$13 each with your \$50?
How much would you have left after the purchase?

9. Fifteen children were playing on the playground. Seven of them left.
Then, ten more children came. How many are playing on the playground now?

10. A lion chased an antelope for 400 feet, then another 200 feet, and
lastly 200 feet more. Then the lion pounced on the antelope.
What was the total number of feet that the lion chased the antelope?

Strategy 5:    Add up to find the difference.

To find the difference, start at the smaller number, and add up until you get to the bigger number. You can first complete the next ten, then add whole tens, then add ones again.

84 − 37 = ?

 37 + 3 = 40 40 + 40 = 80 80 + 4 = 84

I added 3, 40, and 4 or a total of 47.
84 − 37 = 47.

92 − 35 = ?

 35 + 5 = 40 40 + 50 = 90 90 + 2 = 92

I added a total of 57.
92 − 35 = 57.

11. Add up to find the differences, or use some other strategy such as subtracting in parts.

a.

65 − 26

= _____

 + + + 26

30

60

65
b.

83 − 35

= _____

 + + + 35

40

80

83
 c. 56 − 28  = _______ 55 − 24  = _______ d. 72 − 18  = _______ 82 − 46  = _______ e. 54 − 37  = _______ 91 − 57  = _______ f. 74 − 55  = _______ 63 − 34  = _______

 Strategy 6: Subtract an easy number that is close, and then correct the answer. 74 − 39 = ? First subtract 74 − 40 = 34, since 40 is close to 39 and an easy number to subtract. But, you subtracted one too many. Therefore, add 1 to the answer:   34 + 1 = 35. 81 − 57 = ? First subtract 81 − 60 = 21, since 60 isclose to 57 and an easy number to subtract. But, you subtracted three too many. Therefore, add 3 to the answer:  21 + 3 = 24.

12. Subtract mentally.

 a. 34 − 18 = ______ 42 − 29 = ______ b. 65 − 27 = ______ 55 − 38 = ______ c.97 − 49 = ______ 62 − 19 = ______ d.65 − 29 = ______ 83 − 38 = ______

13. A subtraction challenge!

 a.  101 − _____ = 92 b.  ________ −  60 = 7 c.  ________ −  132 = 40

14. Another challenge! − 30 − 4 − 5 − 20 − 9 − 10  100

______ _____ _____ _____ _____ _____ Solve the mystery numbers and !
Hint: guess and check. Then improve your guess.

 a. + = 30 − = 14 = _______ = _______ b.  99 − − − = 36 = _______ c. − 7 =  − − = 4 = _______ = _______

This lesson is taken from Maria Miller's book Math Mammoth Add & Subtract 3, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.

#### Math Mammoth Add & Subtract 3

A self-teaching worktext for 2nd-3rd grade that covers mental addition & subtraction with three-digit numbers, regrouping with three-digit numbers (carrying and borrowing), rounding, estimating, and word problems.