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3 years ago

What does it mean to multiply and divide fractions

Mathematics

2 answers:

Otrada [13]3 years ago

5 0

Answer:

Step-by-step explanation:

o multiply fractions, all you have to do is multiply the numerators and denominators and simplify the result. To divide fractions, you simply have to flip the numerator and denominator of one of the fractions, multiply the result by the other fraction, and simplify.

Airida [17]3 years ago

4 0

As you have not asked for any particular question so I am writing some examples to make you understand your question.

Example 1

1/5 X 3 = 3/5

Example 2

9X 2/3=6. here 9 and 3 both can be simplified by 3 tables to left with 3x2= 6

Example 3.

3 3/4 X 3/4X1 7/9

in this case where some numbers are given as a mixed number so we first change all mixed numbers into top-heavy fractions also called improper fractions.

= 15/4X 3/4 X16/9

=5.

Here we simplify the numerator and denominator numbers by the same number.

Now for division

Example 1

2/5 divided by 3

the division sign is changed to a Multiplication sign and the number after the division sign will be upside down ie numerator will become denominator and denominator will become numerator

= 2/5X 1/3 as here none of the numbers can be reduce to a simpler form we simply take the product of numerator and denominator

= 2/15 Answer

Example 2.

3 1/2 divided by 3/4

= 7/2 divided by 3/4

= 7/2X 4/3

= 14/3= 4 2/3 mixed number answer

Example 3.

42/15X16/21 division sign 48/20 in this question first step to change division sign to multiplication sign and the fraction after division only that will be upside down

so the question becomes

=42/15 X 16X 21 X 20/48

=2/3 Ans

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Answer:

y = x + 3 is the Green Line

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3 years ago

A school janitor has my 1/3 of the classroom in five minutes at what rate is he mopping

hjlf

Answer:

1/15 per min

Step-by-step explanation:

3 times 5 equals 15 and so 1/15.

Try making a visual picture to see yourself.

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3 years ago

Suppose that a large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved. Another br

aliya0001 [1]

Answer:

$A=1500-1450e^{-\dfrac{t}{250}}$

Step-by-step explanation:

The large mixing tank initially holds 500 gallons of water in which 50 pounds of salt have been dissolved.

Volume = 500 gallons

Initial Amount of Salt, A(0)=50 pounds

Brine solution with concentration of 2 lb/gal is pumped into the tank at a rate of 3 gal/min

$R_{in}$ =(concentration of salt in inflow)(input rate of brine)

$=(2\frac{lbs}{gal})( 3\frac{gal}{min})\\R_{in}=6\frac{lbs}{min}$

When the solution is well stirred, it is then pumped out at a slower rate of 2 gal/min.

Concentration c(t) of the salt in the tank at time t

Concentration, $C(t)=\dfrac{Amount}{Volume}=\dfrac{A(t)}{500}$

$R_{out}$ =(concentration of salt in outflow)(output rate of brine)

$=(\frac{A(t)}{500})( 2\frac{gal}{min})\\R_{out}=\dfrac{A}{250}$

Now, the rate of change of the amount of salt in the tank

$\dfrac{dA}{dt}=R_{in}-R_{out}$

$\dfrac{dA}{dt}=6-\dfrac{A}{250}$

We solve the resulting differential equation by separation of variables.

$\dfrac{dA}{dt}+\dfrac{A}{250}=6\\$The integrating factor: e^{\int \frac{1}{250}dt} =e^{\frac{t}{250}}\\$Multiplying by the integrating factor all through\\\dfrac{dA}{dt}e^{\frac{t}{250}}+\dfrac{A}{250}e^{\frac{t}{250}}=6e^{\frac{t}{250}}\\(Ae^{\frac{t}{250}})'=6e^{\frac{t}{250}}$

Taking the integral of both sides

$\int(Ae^{\frac{t}{250}})'=\int 6e^{\frac{t}{250}} dt\\Ae^{\frac{t}{250}}=6*250e^{\frac{t}{250}}+C, $(C a constant of integration)\\Ae^{\frac{t}{250}}=1500e^{\frac{t}{250}}+C\\$Divide all through by e^{\frac{t}{250}}\\A(t)=1500+Ce^{-\frac{t}{250}}$