6th grade common core weekly math homework

Question

The ratio of boys to girls in Ms. Smith's class is 3 to 4 if there are 12 boys how many girls are there???

Answer 1

The RATIO of BOYS TO GIRLS is 3 to 4.

Some texts use 3:4.

It's a fraction. That's what a RATIO is! A FRACTION!

BOYS 3

--------- = -----

GIRLS 4

So, we start with the fraction 3

---

4

We are told there are 12 BOYS, and we are to

determine how many girls.

Let G = the number of girls

12

---------

G

Now, we know the two fractions or ratios are equal

to each other.

3 12

------ = -------

4 G

Method 1: Logic

12 is three-fourths of 16. So 16 GIRLS.

Method 2: CROSS MULTIPLY (I teach this.)

Multiply the denominator of the first ratio, 4, times

the numerator of the second ratio, 12. And,

multiply the numerator of the first ratio, 3, times the denominator of the second ratio, G.

DO YOU SEE HOW THE TWO MULTIPLICATIONS CROSS EACH OTHER?

4 * 12 = 3 * G . (By CROSS MULTIPLICATION)

48 = 3 * G

48/3 = 3 * G/3 (Divide both sides by 3)

16 = 3 * G/3

16 = G (The 3's cancel each other out)

ANSWER: 16 GIRLS

CHECKING:

DOES 3 12

----- = ------

4 16

Yes it does. When you reduce the fraction 12/16

by dividing the numerator and denominator by 4,

you get 3/4.

Hope this helps Jerry.