Question

Find both exact product and an estimated product.
2 1/5 x 5 1/2

Answer 1

\[\ \ \ \left(\text{2 and } \frac{1}{5}\right)\times \left(\text{5 and } \frac{1}{2} \right) \]\[=\left(2 + \frac{1}{5} \right) \times \left(5 + \frac{1}{2}\right) \]\[\large = \underbrace{\Bigg(2 \times 5\Bigg)}_\text{First} +\underbrace{\left(5 \times \frac{1}{5}\right)}_\text{Inner} +\underbrace{\left(2 \times \frac{1}{2}\right)}_\text{Outer} + \underbrace{\left( \frac{1}{5}\times \frac{1}{2}\right)}_\text{Last} \]\[=10 + 1 + 1 + \frac{1}{10}\]\[ = 12 + \frac{1}{10} \]\[= \text{12 and } \frac{1}{10}\]

Answer 2

can u help me with another one?

Answer 3

Sure

Answer 4

Just to be sure, you are familiar with foiling and the distributive properties I used above yes?

Answer 5

4 5/8 divided by 4 5/6

Answer 6

I'm afraid that the way I'm solving these is not the way your teacher intends you to solve them.

Answer 7

its college i dont think she care as long as we do them bc its all online stuff

Answer 8

Yes, but I'm doing them, so it won't really help you much unless you understand what I'm doing.

Answer 9

i understand the multiplication im not sure about the division tho

Answer 10

\[\ \ \ \ \large\frac{4 + \frac{5}{8}}{4+ \frac{5}{6}}\]\[\large=\frac{4 + \frac{5}{8}}{4+ \frac{5}{6}} \cdot \frac{8\cdot 6}{8 \cdot 6}\]\[=\frac{192 -30 }{192 - 40}\]\[= \frac{162}{152} = \frac{81}{76} = \frac{9}{8}\]

Answer 11

4 and 5/8 = 4+5/8 = 32/8 + 5/8 = 37 / 8
4 and 5/6 = 4+5/6 = 24/6 + 5/6 = 29 / 6

we need to find:
(37/8) divided by (29/6)

This is the same as multiplying by the reciprocal of 29/6 (which is 6/29):
=(37/8)*(6/29)
=(37/4)*(3/29)
=(37*3)/(4*29)
=111/116