### Home > CC1MN > Chapter 4 > Lesson 4.1.6 > Problem 4-61

Vu needs to add *“Is there a smaller number that could work as a common denominator?” *he wonders.

Where can you look in the multiplication table to see if

and are each factors of a number less than ? Examine the picture and notice how the square is broken up into

square units. If you created a square unit box and shaded in of the squares, would that be the same as having four of the above shapes placed together to form a box? What about a rectangle with

square units and shaded squares? Can the shape above be rearranged to form 5 rectangles like the one pictured at below? tile

tile

tile

shaded tile

shaded tile

Each of the fractions are equivalent to each other because of the multiplicative identity as noted in the Math Notes box in this lesson. Reminder: Any number divided by itself is equal to

. Consider why using the multiplicative identity changes the numbers of the fractions, but they are all still equivalent.

Use the multiplication table on the Lesson 4.1.6 Resource Page to find other number(s) you could use as a common denominator to add

and . If the equivalent fraction denominator desired is

, then the denominator of must be multiplied by what number? Now, consider the multiplicative identity from part (a).

Now that you have solved for the denominator, what must the numerator be?or the Multiplication Table eTool to find other number(s) you could use as a common denominator to add and .

Vu’s next problem is to add

. Use the multiplication table to find the smallest number you could use as a common denominator. This number is called the lowest common denominator. After you find the lowest common denominator for Vu’s problem, find the sum.