Search 74,228 tutors
0 0

# 11\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

Jessica,

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.

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

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.
Thanks, Vivian.
Students should notice that 2nd method is use of distributive law of addition.

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