Theory
Dividing by Repeated Subtractions
The result of division is to separate a group of objects
into several equal smaller groups. The starting group is called the dividend.
The number of groups that are separated out is called the divisor. The number of
objects in each smaller group is called the quotient.
The results of division can be obtained by repeated
subtraction. If we are separating 24 objects into 6 equal groups of four, we
would take (or subtract) four objects at a time from the large group and place
them in 6 equal groups. In mathematical terms this would be: 24 – 4 – 4 –
4 – 4 – 4 - 4.
Solutions from the Previous Issue:
Find a:
1.
(a - 2) ∙ 6 + 2∙ (7 – 5) ∙6 - 30 = 0
Solution:
(a - 2) ∙ 6 + 2 ∙ (7
– 5) ∙6 - 30 = 0
(a - 2) ∙ 6 + 2 ∙ 2
∙ 6 - 30 = 0
(a - 2) ∙ 6 + 24 - 30 = 0
(a - 2) ∙ 6
- 6 = 0
(a - 2) ∙ 6
= 6
a - 2 = 1
a = 3
2.
[(a + 1880 : 2) ∙ 4 + 4} ∙ 2 = 4 ∙ 1990
Solution:
[(a + 1880 : 2) ∙ 4 +
4}∙ 2 = 4 ∙ 1990|:2
(a + 1880 : 2) ∙ 4 + 4 = 2
∙ 1990
(a + 1880 : 2) ∙ 4 + 4 =
3980| - 4
(a + 1880 : 2) ∙ 4 =
3976|:4
a + 1880 : 2 = 994
a + 940 = 994| -940
a = 54
3.
Solution:
a =7
4.
[40 ∙ (a : 8 - 32) ∙ 450 : 15 –1990]:2 = 3805
Solution:
[40 ∙ (a : 8 - 32) ∙
450 : 15 –1990]:2 = 3805| ∙2
40 ∙ (a : 8 - 32) ∙
450 : 15 –1990 = 7610|+1990
40 ∙ (a : 8 - 32) ∙
450 : 15 = 9600
40 ∙ (a : 8 - 32) ∙
30 = 9600|:30
40 ∙ (a : 8 - 32) = 320|:40
a : 8 - 32 = 8
a : 8 = 40
a = 5
5.
30 + 3∙[85 –(78 –65) ∙ a + 80] = 330
Solution:
30 + 3∙[85 –(78 –65)
∙ a + 80] = 330
3∙[85 –(78 –65) ∙
a + 80] = 300
85 –(78 –65) ∙ a + 80 =
100
85 – (78 –65) ∙ a = 20
85 – 13 ∙ a = 20| -20 +
13 ∙ a
85 – 20 = 13 ∙ a
65
= 13 ∙ a
a = 5
Proposed
Problems:
1.
Grace and her family are going to the beach during spring break. It is a
long drive across the state to the beach and her father is trying to figure out
how much the gas will cost. Gas costs $1.97 per gallon. It is four hundred
twenty-two miles to the beach from Grace's house. Their car can go twenty-six
miles on one gallon of gas. How much will gas for the trip cost? Don't forget
that they have to come back home, too!
2.
Hannah's recipe for Daffodil Cake calls for three and two-thirds cups of
flour. Hannah wanted to make the cake to take to her class party. She measured
all the ingredients and had only one and one-fourth cups of flour. How much more
flour does she need to bake the cake?
3.
Joshua is helping his grandfather plan a garden. His grandfather said he
needed at least two hundred thirty-one square feet of space for the garden.
Joshua found a corner of his grandfather's property that is large enough. If the
corner is fifteen feet wide what is its minimum length in feet?
4.
Herman Hedgehog was ecstatic. It was spring and he could scurry through
the weeds and sniff and snuffle until he found some really juicy bugs to eat! He
was so tired of winter. In the first hour of snuffling, Herman found twenty-two
ladybugs (yuck!), two little grasshoppers, five crickets, and eleven delicious
ants (yum!). At that rate, how many bugs will Herman find in 2 hours and 28
minutes hours?
5.
Mrs. Teague's class took a survey of the students at their school. The
survey question was, "What is your favorite season?" The class members
asked three hundred people to answer the question. 14% said winter was their
favorite, 21% liked fall best, and 45% named summer their favorite season. How
many people chose spring as their favorite season?
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