Add Similar Terms
Algebra Help: Section 2.2
Have help adding similar terms with algebra.
Apply positive and negative operators. Replace named objects with literals.
Case 1
To Add Similar Terms
1. A cooper made 7 barrels on Monday, 9 barrels on Tuesday, and 6 barrels on Wednesday. How many barrels did the cooper make?
ARITHMETICALLY
7 barrels 9 barrels 6 barrels ____________ 22 barrels
Answer: 22 barrels.
ALGEBRAICALLY
7b9b6b____________22b
Answer: 22b
ANALYSIS - We represent 1 barrel by the letter b;
then 7b will represent 7 barrels,
9b will represent 9 barrels,
6b will represent 6 barrels.
Since 7 barrels, 9 barrels, plus 6 barrels are 22 barrels,
7b, 9b with 6b are 22b.
2. A mass of iron and wood is submerged in water by its own gravity.
Let the literal l represent weight of mass.
The iron tends to sink with a force of 20l,
and the wood bouys upward with a force of 16l.
What will the whole mass weigh while under water?
+20l-16l____________ +4l
ANALYSIS - We indicate actual weight by the plus sign,
and the opposite force, or bouyancy, by the minus sign.
Since the tendency to sink is greater by 4l
than the tendency to rise, the mass has a weight of 4l;
hence, + 20l and - 16l united are + 4l.
NOTE - The answer, + 4l, in the above example,
is called, the algebraic sum of the two forces,
+ 20l and -16l, because it
shows their unified effect.
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Help with Algebra Homework
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New Elementary Algebra
containing the rudiments of the science for schools and academies.
By Horation N Robinison, LL. D. Ivison, Blakeman & Company, Publishers, New York and Chicago.
