Using Multiples to Find a Common Denominator

Scene #

Description

Narration

1

A CHEF IS IN A KITCHEN MAKING SALSA. THE EQUATION 1/3 CUP PLUS ¼ CUP IS ON THE SCREEN.

THIS CHEF IS MAKING SALSA FOR 20 PEOPLE. HE THOUGHT HE HAD JUST ENOUGH TO SERVE EACH PERSON 1/3 OF A CUP WITH THEIR DINNERS. BUT HE ACTUALLY HAS ENOUGH TO GIVE EACH PERSON 1/4 CUP MORE.

SO, IF HE GIVES EACH PERSON 1/3 CUP PLUS 1/4 CUP, HOW MUCH SALSA IS HE GIVING EACH PERSON? THESE FRACTIONS HAVE DIFFERENT DENOMINATORS. TO ADD THEM, WE HAVE TO MAKE THE DENOMINATORS THE SAME, SO WE'RE ADDING THE SAME-SIZED PORTIONS TO ONE ANOTHER.

2

THE CHEF IS SCOOPING SALSA INTO BOWLS. THE MULTIPLES OF 3 AND 4 ARE ON THE SCREEN. 12 IS BLINKING IN RED AMONG BOTH LISTS OF MULTIPLES.

TO FIND A COMMON DENOMINATOR FOR 1/3 AND 1/4, WE NEED TO FIND A NUMBER THAT IS A MULTIPLE BOTH OF 3 AND 4 -- A COMMON MULTIPLE. LET'S LOOK AT THE MULTIPLES OF 3 AND 4. NOTICE THAT 12 IS A COMMON MULTIPLE. WE CAN USE THAT AS A COMMON DENOMINATOR. SO IS 24, BUT WE DON'T NEED TO USE IT WHEN WE HAVE A LESSER ONE.

3

3 X 4 IS ON THE SCREEN. THE NUMBERS CHANGE TO 1/3 AND ¼ AND ?/12.

NOTICE THAT 12 IS ALSO 3 TIMES 4. THE PRODUCT OF TWO NUMBERS IS ALWAYS A COMMON MULTIPLE BECAUSE WE GOT IT BY MULTIPLYING THE TWO OF THEM. SO, HOW DO WE CONVERT THIRDS AND FOURTHS TO TWELFTHS?

4

AS THE NARRATOR DESCRIBES THE PROBLEM THE STEPS TO ADDING THE FRACTIONS APPEAR ON THE SCREEN.

FOR EACH FRACTION, MULTIPLY BOTH THE NUMERATOR AND DENOMINATOR BY A NUMBER THAT RESULTS IN 12, THE COMMON MULTIPLE, IN THE DENOMINATOR. FOR THIRDS, IT'S 4 -1 TIMES 4 IS 4. 3 TIMES 4 IS 12. FOR FOURTHS, IT'S 3. 1 TIMES 3 IS 3, AND 4 TIMES 3 IS 12. 3/12 PLUS 4/12 IS 7/12. SO EACH PERSON RECEIVES 7/12 CUP OF SALSA.