Question

5 2/5 ÷ 2 1/4 =

Answer 1

2 2/5

Answer 2

\[5 \frac{2}{5} \div 2 \frac{1}{4}\]
\[=\frac{27}{5} \div \frac{9}{4}\]
\[=\frac{27}{5} \times \frac{4}{9}\]
\[=\frac{3}{5} \times \frac{4}{1}\]
\[=\frac{12}{5} = \frac{10 + 2}{5} = \frac{10}{5} + \frac{2}{5} = 2 + \frac{2}{5}\]

Answer 3

For fraction division, invert the fractions then multiply.
5 (2/5) / 2 (1/4) equals
(27/5) * (4 / 9) equals
108 / 45
= 2 (18/45)
= 2 (2 / 5)

Answer 4

Actually just invert one fraction.
(a/b) ÷ (c/d) equals
(a/b) × (d/c)

Answer 5

If I did that would I use 27/5 and 9/4 still?

Answer 6

There's more than one way to solve this

Answer 7

\[\left(5 + \frac{2}{5}\right) \times \frac{4}{9}\]
\[=\left(5 \times \frac{4}{9}\right) + \left(\frac{2}{5} \times \frac{4}{9}\right)\]
\[=\left(\frac{20}{9}\right) + \left(\frac{8}{45}\right)\]
\[=\frac{100}{45} + \frac{8}{45}\]
\[=\frac{108}{45}\]
\[=\frac{90}{45} + \frac{18}{45}\]
\[=2+ \frac{2}{5}\]

Answer 8

How does it go from 20 to 100?

Answer 9

If you multiply 20/9 by 5/5 then you get 100/45.

You learned in basic math that in order to add fractions the denominator must be the same.

We needed to add 20/9 + 8/45

Answer 10

Yes.

Answer 11

I understand now

Answer 12

Thanks!

Answer 13

Personally, I like the second method better. The reason is because I don't like improper fractions.

Answer 14

I was taught with improper fractions so the second one is new to me.

Answer 15

The second method is new to everyone. I sort of invented it.

Answer 16

How do you get the 90/45 and the 18/45? I know if you add them together you get 108 but how do you decide how to do that?

Answer 17

Well, there are two reasons and it beginning with a rule of fractions:

\[\frac{c}{d} = \frac{a + b}{d} = \frac{a}{d} + \frac{b}{d}\]

In other words, if you had

\[\frac{21}{5}\] you can rewrite it as \[\frac{20 + 1}{5}\] Then further re-write it as \[\frac{20}{5} + \frac{1}{5}\] and ultimately \[4 + \frac{1}{5}\] or simply \[4 \frac{1}{5}\]

You simplify in this manner to avoid doing side work and show all the steps you did to reduce the problem. I try to produce steps in a manner that shows every step. I don't like using scratch paper to do side work

So if I want to reduce 21/5 , I present it in the following manner:

\[\frac{21}{5} = \frac{20 + 1}{5} = \frac{20}{5} + \frac{1}{5} = 4 + \frac{1}{5} = 4 \frac{1}{5}\]

Answer 18

Hero - that is an interesting alternative method.

Answer 19

The interesting methods are just the ones that haven't been taught in a classroom. Many students here post alternative methods.

Answer 20

I'm still not understanding where the 90 and 18 come from. Sorry.

Answer 21

It results from thinking ahead. Basically, we know that 108/45 is an improper fraction, so we know it can be reduced to a whole number plus a fraction. 90/45 = 2 because 45 + 45 = 90 and 90 is a multiple of 45, 90 represents the portion of 108 that is divisible by the denominator 45. 18 is what remains since 90 + 18 = 108

Remember we used the addition rule for fractions to rewrite it.

Answer 22

ok

Answer 23

You have to practice it with smaller numbers first in order to understand. Try to reduce \[\frac{13}{3}\] using the same method.

Hint:
\[\frac{12}{3} = 4\]

Answer 24

so 4 1/3?

Answer 25

Exactly

Answer 26

Because

\[\frac{13}{3} = \frac{12 + 1}{3} + \frac{12}{3} + \frac{1}{3} = 4 + \frac{1}{3}\]

Answer 27

Now you can just practice on your own until you get good at it.

Answer 28

Thanks