Question

Can someone help me please? justify your answer also plz!​

Answer 1

Answer:

a. True

b. False

c. True

Step-by-step explanation:

a.

12 ÷$\frac{36}{7}$ is equal to $\frac{7}{3}$

Personally, I hate fractions so I make these into decimals by dividing the numerator by the denominator, but I'll do both to show you.

Decimal:

$\frac{36}{7}$

In your calculator, type 12

Then the division sign.

Then make parenthesis

in the parenthesis you will have (36/7)

End parenthesis

Press the equal sign and you should get a grand total of 2.333 repeating

To see if its equal to $\frac{7}{3}$, you put 7 divided by 3 in your calculator next

If you do, you should get 2.333 repeating.

This shows they are equal.

Fraction:

Keep, switch, flip

The first step will be to make your whole number into a fraction.

$\frac{12}{1}$÷$\frac{36}{7}$

The first thing we use is keep

The first number in this equation is that $\frac{12}{1}$

We're going to leave it as it is.

Next we have to use switch. To do this we make the ÷ into a ×

So your problem should look as so:

$\frac{12}{1} * \frac{36}{7}$

Lastly, we have flip.

The last number in our equation is $\frac{36}{7}$

We are going to use the reciprocal of it which would be $\frac{7}{36}$

So your problem should now look like this:

$\frac{12}{1} * \frac{7}{36}$

At this point, we can now cross multiply

So from the numerator 12 to the denominator 36, if we divided 36 by 12 its 3.

But the denominator 1 and the numerator 7 are already divided as much as they can be.

So now your expression should be: $\frac{1}{1} * \frac{7}{3}$

This is because of that cross multiplication we did.

12 goes into 36, 3 times so 3 would substitute 36 while 1 would substitute 12

So now its just basic multiplication

$\frac{1*7}{1*3} = \frac{7}{3}$

So we can conclude that $12 * \frac{36}{7}$ does in fact equal $\frac{7}{3}$

b.

Multiplying a number by $\frac{1}{2}$ is the same as dividing by 2

This is false

When you multiply by 2, you are doubling the original number

When you multiply by $\frac{1}{2}$, you are cutting the number in half

Ex:

18 * 2 = 36

18 * $\frac{1}{2}$ = 9

If it was dividing instead of multiplying, this would be true but since $\frac{1}{2}$ halves the number whether you multiply or divide it would not be true.

c.

$\frac{3}{2}$ of a number is less than this number

Basically, what this is saying is if you divide by $\frac{3}{2}$, would it give you less than the original number.

The answer would be true

It would be division first of all because your looking for $\frac{3}{2}$ of a number.

Secondly, if you divide by a fraction or decimal, the number tends to be smaller than the number you started with.

Ex:

6 ÷ $\frac{3}{2}$ = 4 or 6 ÷ 1.5 = 4

Ex2:

682 ÷ $\frac{3}{2}$ = 454.6 repeating or 682 ÷ 1.5 = 454.6 repeating

I hope this helps! Don't be afraid to reach out with any further questions!