Answers to
Review Exercises for Test 2
1. Use break apart again: 11 x 20 + 11 x 5 = 220 + 55 = 275
2. a) 12 x (40 x5) = 12 x 200 = 2400 compatible numbers 40 x 5 or 5 x 12
b) (7 + 3)14 = 10 x14 = 140 use distributive to get compatible of 10
c) 30 + 488 use count on: 488  498, 508, 518
3. Yes, this is correct because 2 too many was subtracted, so 2 must be
added back to the first result.
4. 400 + 200 = 600
5. Greatest whole number is 20,499 and the least whole number is
19,500.
6. 800 – 150 or 800 – 140 gives 650/660
7. All the numbers are about 125 x 6 months = 750. This is quantity and
the technique is clustering.
8. 376 + 495 a) Standard  start on the right adding ones, then tens,
then hundreds carrying as necessary b) start on the left adding by
place values
9. a) sometimes b) always c)sometimes d) always e) always
10.
425 – 200 = 225 87 can’t be subtracted from 25, so sub
compatible number 100 for 87. 225 – 100 = 125 then add back extra
13 subtracted.
11.
Using F for flat, R for rod, S for single I would have the following:
Factors
R
R
R
R
S
S
R
F
F
F
F
R
R
R
F
F
F
F
R
R
S
R
R
R
R
S
S
S
R
R
R
R
S
S
S
R
R
R
R
S
S
800 + 160 + 6 = 966
12.
omit
13.
Caleb is using an alternative expanded form where he subtracts
away groups/multiples of 15 to make the dividend smaller faster. He
counts the number of groups and the remainder for the answer.
14.
a) 1, 2, 3, 6, 9, 18 b) 0, 18, 36, 54, 72, 90, 108 c) 1 + 2 + 3 + 6 + 9
=21 or abundant since sum of proper factors > 18
15.
3 x 5 x 23
16.
The geometric representations for 16 are rectangles with
dimensions of the pairs of factors: 1 x 16, 2 x 8, 4 x 4 Primes only
have two distinct factors, one and itself.
17.
Both are natural numbers with factors of one and itself. A prime
has only two distinct factors while a composite has more than two
distinct factors.
18.
Fundamental Theorem of Arithmetic says that any natural
number has only one prime factorization. This is important because
the properties of numbers are consistent.
19.
We look at what factors are common to both lists to determine
the GCF.
20.
Factor Test Theorem says to take the square root of the
number. We only have to test from 1 to the whole part of the number
to find all factors of the original number. This does not mean that the
square root will be a factor, only that we test to that number.
Example: the sqrt(18) = 4.24 (approx.) So, we test 1, 2, 3, 4 to get all
factors and 4 is not one of them.
21.
GCF – LCM Product Theorem says the product of two numbers
equal the product of the GCF and LCM of the two numbers.
22.
GCF(28, 42) = 14 LCM(28, 42) = 84
7 x 84 = 1176 and 28 x 42 = 1176
23.
by 5: ends in 5 sum of digits = 9  by 3 and by 9 b/c 3 divides 9
and 9 divides 9
24.
78,488 must be divisible by both 4 and 3. 4 divides the number
but 3 does not.
25.
When a number is divisible by another, there is no remainder.
26.
345 + 789 = 1000 + 120 + 14 = 1,134
1246 – 896  1200 – 800 = 400300 + 140 – 90 = 300 + 50 + 6 –
6=350
47 x 28 = 800 + 320 + 140 + 56 = 1316
225 – 150 = 75 10
75 – 60 = 15  4
15 – 15 =0  1
So, the quotient is 15 or 225/15 = 15.