fractions: Rida now only has 3/8 of the dolls she had before

[bleuetrose]

Pls help me to understand this math answer.

One day, Fida decided to give half of her dolls to Melika. The day after, she decided to give 3 more dolls to Melika. Fida now only has 3/8 of the dolls she had before. How many dolls did she have originally?

So, I wrote 3 dolls =1/8, because 3/8+1/8= 4/8=1/2, but answer is 24. I don't understand why there is multiplication of 3*8 in answer? Pls may you help me to understand that.

 

[HallsofIvy]

Pls help me to understand this math answer.

One day, Fida decided to give half of her dolls to Melika. The day after, she decided to give 3 more dolls to Melika. Fida now only has 3/8 of the dolls she had before. How many dolls did she have originally?

So, I wrote 3 dolls =1/8,i

"3 dolls= 1/8" makes no sense! 1/8 of what? You probably mean "1/8 of the number of dolls Frida originally had".

because 3/8+1/8= 4/8=1/2, but answer is 24. if 3 is 1/8 of the number of dolls Frida originally have, which means "the number of dolls divided by 8" (multiplying by 1/8 is the same as dividing by 8). To go back to "the number of dolls" we do the opposite of "divide by 8" which is "multiply by 8"

I don't understand why there is multiplication of 3*8 in answer? Pls may you help me to understand that.

 

[JeffM]

Pls help me to understand this math answer.

One day, Fida decided to give half of her dolls to Melika. The day after, she decided to give 3 more dolls to Melika. Fida now only has 3/8 of the dolls she had before. How many dolls did she have originally?

So, I wrote 3 dolls =1/8, because 3/8+1/8= 4/8=1/2, but answer is 24. I don't understand why there is multiplication of 3*8 in answer? Pls may you help me to understand that.

You are studying algebra, so learn how to use it.

First, assign in writing a unique symbol to each potentially relevant number that is unknown.

\(\displaystyle x = \text { original number of dolls Fida had.}\)

\(\displaystyle y = \text { number of dolls Fida had after first gift.}\)

\(\displaystyle z = \text { number of dolls Fida had after second gift.}\)

You have three unknowns so you need three equations.

Fida decided to give half of her dolls to Melika \(\displaystyle \implies y = x - \dfrac{1}{2} * x = \dfrac{1}{2} * x.\)

she gave 3 more dolls to Melika\(\displaystyle \implies z = y - 3 = \dfrac{1}{2} * x - 3.\)

Fida now only has 3/8 of the dolls she had before \(\displaystyle \implies z = \dfrac{3}{8} * x.\)

Now z is certainly equal to itself so

\(\displaystyle z = z \implies \dfrac{1}{2} * x - 3 = \dfrac{3}{8} * x.\)

Fractions are a pain in the neck. Have you ever been taught how to "clear fractions."

You multiply both sides of your equation by the lowest common multiple of the denominators of the fractions in the equation.

What is the lowest common multiple of the denominators of 1/2 and 3/8? 8 of course. So

\(\displaystyle 8 * \left ( \dfrac{1}{2} * x - 3 \right ) = 8 * \left ( \dfrac{3}{8} * x \right ) \implies \\

\dfrac{8}{2} * x - 8 * 3 = \dfrac{8 * 3}{8} * x \implies

4x - 24 = 3x \implies 4x - 24 + 24 = 3x + 24 \implies 4x = 3x + 24 \implies \\

-\ 3x + 4x = -\ 3x + 3x + 24 \implies x = 24 \implies y = \dfrac{1}{2} * x = 12 \implies \\

z = y - 3 = 12 - 3 = 9.\)

Let's check. \(\displaystyle \dfrac{3}{8} * 24 = 3 * \dfrac{24}{8} = 3 * 3 = 9.\)

Is it clear now? Multiplying everything by 8 got rid of those nasty fractions.

 

[Dr.Peterson]

Pls help me to understand this math answer.

One day, Fida decided to give half of her dolls to Melika. The day after, she decided to give 3 more dolls to Melika. Fida now only has 3/8 of the dolls she had before. How many dolls did she have originally?

So, I wrote 3 dolls =1/8, because 3/8+1/8= 4/8=1/2, but answer is 24. I don't understand why there is multiplication of 3*8 in answer? Pls may you help me to understand that.

I'll suppose that, since you submitted this under Beginning Algebra, you aren't yet ready to handle multiple variables, but are able to work with one variable. So let's do that:

x = number of dolls Fida has at first

Now keep track of the number of dolls she has at each step:

One day, Fida decided to give half of her dolls to Melika: Fida has 1/2 x dolls
The day after, she decided to give 3 more dolls to Melika: Fida has 1/2 x - 3 dolls
Fida now only has 3/8 of the dolls she had before: This is 3/8 x

So we have the equation

1/2 x - 3 = 3/8 x

Solve that for x; you can either subtract 1/2 x from both sides, or first clear fractions by multiplying by 8. (If you don't do the latter, you will end up multiplying by 8 later anyway.)

What you did is equivalent to solving this equation; you subtracted 3/8 from 1/2 to get 1/8. This tells you that 1/8 x = 3; multiplying by 8 is the last step, to solve for x.

If you need more help, please tell us whether you have been learning simple algebra, or just fractions. The more you tell us about your own context, the more easily we can give answers suited to your needs.

 

[Denis]

Let dolls F started with = 2u

    F    M
   2u    0
    u    u
   u-3  u+3

u-3 = (3/8)(2u)
8u-24 = 6u
2u = 24