Jessica L.
asked • 02/21/1411\5 time 18 1\3 simplify your answer type a whole number fraction or mixed number
1 1\5 time 18 1\3 simplify your answer type a whole number fraction or mixed number
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2 Answers By Expert Tutors
Steve S. answered • 02/21/14
Tutor
5
(3)
Tutoring in Precalculus, Trig, and Differential Calculus
11/5 * (18 + 1/3)
= 11/5 * (18*3/3 + 1/3)
= 11/5 * (54/3 + 1/3)
= 11/5 * (55/3)
= 11*55/(5*3)
= 11*11/3
= 121/3
= (120 + 1)/3
= 120/3 + 1/3
= 40 + 1/3
=====
Or:
11/5 * (18 + 1/3)
= (10 + 1)/5 * (18 + 1/3)
= (2 + 1/5) * (18 + 1/3)
= 2*18 + 2*1/3 + 18*1/5 + (1/5)*1/3
= 36 + 2/3 + (15+3)/5 + 1/15
= 36 + 2/3 + 3 + 3*3/(5*3) + 1/15
= 36 + 2/3 + 3 + (9 + 1)/15
= 39 + 2/3 + 2/3
= 39 + 4/3
= 39 + (3 + 1)/3
= 39 + 1 + 1/3
= 40 + 1/3
=====
Or if the question was:
(1 + 1/5) * (18 + 1/3)
= 1 (18 + 1/3) + (1/5) (18 + 1/3)
= 18 + 1/3 + (18/5) + (1/5)(1/3)
= 18 + 1/3 + (15 + 3)/5 + 1/15
= 18 + 1/3 + 3 + 3/5 + 1/15
= 21 + 1*5/(3*5) + 3*3/(5*3) + 1/15
= 21 + (5 + 9 + 1)/15
= 21 + 15/15
= 22
Vivian L.
Steve;
In the heading, this is 11/5. However, in the question there is an extra space between the 1 and 1/5. I think this is 1 1/5, 1 & 1/5.
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02/21/14
Steve S.
Thanks, Vivian.
Report
02/21/14
Parviz F.
Students should notice that 2nd method is use of distributive law of addition.
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02/21/14
Vivian L. answered • 02/21/14
Tutor
3
(1)
Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH
Hi Jessica;
(1 1/5)(18 1/3)
Let's convert 1 1/5 from a whole number and a fraction into a fraction.
The denominator of 5 will remain unchanged.
Let's multiply the whole number 1 times the denominator 5 and add this to the numerator 1...
[(1)(5)]+1=6
(6/5)(18 1/3)
Let's convert 18 1/3 from a whole number and a fraction into a fraction.
The denominator of 3 will remain unchanged.
Let's multiply the whole number 18 times the denominator 3 and add this to the numerator 1...
[(18)(3)]+1=55
(6/5)(55/3)
For the multiplication, we will multiply the numerators together...
(6)(55)
We will multiply the denominators together...
(5)(3)
Let's first switch the numerators...
(55/5)(6/3)
While each fraction now has a different value, after multiplication, this will not matter.
55/5=11 because (11)(5)=55
6/3=2 because (2)(3)=6
(11)(2)=22
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Steve S.
Forward slash, /, denotes Normal Division.
Backward slash, \, denotes Integer Division where the remainder is discarded.
E.g., 10/3 = 3 + 1/3; BUT 10\3 = 3.
[see http://mathworld.wolfram.com/IntegerDivision.html]
The point is, Math is a language with grammar and syntax that is a large part of its value. You should learn how to write it correctly so you are not misunderstood.
02/22/14