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Math 101 Exam 1

1. (2 pts) Write the number “ Two thousand three hundred fifty two” in Egyptian.

2. (2 + 2 = 4 pts) The ____property and ____property are special cases
of the Any-order property of addition .

3. (5 pts) Define algorithm.

4. (2+2 = 4 pts) In the subtraction problem , 17−8 = 9, the number 17 is called the____
and the number 9 is called the____ .

5. (4 pts) ( Circle all that apply .) The long division algorithm is a prerequisite for learning:

Successive Approximation  Measurement Division Number bonds
Distributive Property  Mental Math Converting fractions to decimals


6. (5 pts) Fill in the blank:

(a) The most useful model for teaching the commutative property is____ .

(b) The most important arithmetic property learned in teaching the multiplication algorithm is

(c) After estimating the quotient and calculating the remainder in long division,
it is necessary to check that 0 ≤· remainder < ____.

(d) When 176 ÷ 8 is presented as finding the number of segments of size 8 that fit in a segment of
of size 176, one is using the____ interpretation of division.

(e) The most complicated case in learning the subtraction algorithm is____ .

7. (6 pts) Compute 478 × 86 using the Lattice method.

8. (12 pts) Use mental math to compute the following. Write down your answer in a way that clearly
shows the steps involved in solving the problem mentally.

9. (3 + 3 = 6 pts) Find estimations for the following using the technique specified.

(a) Simple Estimation : 6246 ÷ 74

(b) Over Estimate: 2523 − 437

10. (7 + 7 + 7 = 21 pts) For the following word problems, give a full teacher’s solution which does not use

(a) A shop sold 178 cakes on Monday. It sold 326 cakes total for Monday and Tuesday. How many
more cakes did it sell on Monday than on Tuesday?

(b) Jill has four times as many stamps as David. How many stamps must Jill give to David so that
they each have 90 stamps?

(c) Peter has twice as many stickers as Ali. Ali has 40 less stickers than Lihua. They have 300 stickers
altogether. How many stickers does Peter have?

11. (4 + 2 + 4 = 10 pts) Write a word problem using partitive division for 92 ÷ 4 by following these steps:

(a) Draw the Singapore bar diagram which corresponds to partitive division for 92÷4 and use mental
math to solve the problem .

(b) Write the interpretive question which corresponds to partitive division for 92 ÷ 4.

(c) Make up an interesting, short, realistic , one-step word problem using the partitive interpretation
which corresponds to 92 ÷ 4.

12. (6 pts) Explain why 0 ÷ 0 is undefined.

13. (7 pts) Find 4370 ÷ 47 by long division. Show your estimates and use of place value to obtain the
quotient of each step.

14. (4+2+2 = 8 pts) (a) Explain the place value process in detail. (b) Using 2- digit numbers , give an example
of an addition problem which does not use Step (ii). (c) Using 2-digit numbers, give an example
of an addition which does use Step (ii).

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