Operations with Fractions
The product of 1/2 and 6
3
If a rectangle has side lengths 1 and 1/2 unit, what is its area?
1/2 unit2
Sarah ate 1/3 of a cake. She then gave 1/2 of what she ate to a friend. What fraction of the whole cake did the friend get?
1/6
True or False: Multiplying a number by a fraction less than 1 gives a smaller number. Explain and give an example.
True. Multiplying by a fraction gives a smaller number because you are taking only part of the original amount. 6 x 2/5 = 12/5 = 2 2/5. 2 2/5 < 6
Write 6/9 in simplest form. Then multiply the simplified fraction by 3.
2/3
2/3 x 3 = 2
6
A rectangle is 3 units by 2/3 units. What is its area?
2 sq. units
A ribbon is 4 meters long. You need 2/3 of that length for a project. How many meters is that?
2 2/3
Without calculating exactly, is the product larger or smaller: 8 x 4/3? Explain your reasoning.
Larger because 4/3 > 1
The product is 32/3 = 10 2/3
Compute and simplify:
8/12 x 3/2
8/12 x 3/2 = 24/24 = 1
Find 2/3 x 3/5
2/5
Draw or describe a visual model showing 2/5 x 3/4 and state the product. Show on your white board.
A recipe calls for 3/4 cup of oil. If you make 2/3 of the recipe, how much oil do you need?
1/2 cup
3/4 x 12 means taking 3 of the 4 equal parts of 12. 3/4 x 12 = 9
Convert the product to a mixed number: 5/3 x 4/5
Remember to simplify
5/3 x 4/5 = 20/15 = 1 5/15 = 1 1/3
Multiply and simplify
4/7 x 14
8
A rectangle has side lengths 3/2 and 4/3. What is the area? Show how multiplying the side lengths gives the same area as tiling.
Area = 3/2 x 4/3 = 12/6 = 2 sq. units
Show image of tiling.
A garden bed is 5/6 meter wide and 2 meters long. How much area does the bed cover?
1 1/3 meter2
Describe how multiplying by 5/2 compared to multiplying by 2 changes a number. Give an example with 6.
Multiplying by 5/2 is the same as multiplying by 2.5 which is larger than 2. So, multiplying by 5/2 yields a greater answer than multiplying by 2.
6 X 5/2 = 30/2 = 15
6 x 2 = 12
9/14 x 7/3
63/42 = 9/6 = 1 3/6 = 1 1/2
OR Simplify before multiplying
9x7/14x3 = 9x1/2x3 = 3x1/2x1
Multiply and simplify
5/6 x 12/15
2/3
Explain why multiplying 2/3 x 3/2 gives 1 using a rectangular area model.
2/3 x 3/2 = 6/6 = 1
Area model: a 2/3 by 3/2 rectangle covers exactly one whole square when tiled appropriately.
A poster is 7/4 feet wide and 3/2 feet tall. What is its area in square feet? Show your work with a diagram, equation, and solve.
7/4 x 3/2 = 21/8 = 2 5/8 sq. ft.
A model shows a whole divided into 5 equal parts; you take 2 of those partes, then take 3/4 of that amount. Write an expression for this situation and find the final fraction of the whole.
2/5 x 3/4
2/5 x 3/4 = 6/20 = 3/10 of the whole
Multiply and express in simplest form:
11/6 x 9/10
11/6 x 9/10 = 99/60 = 33/20 = 1 13/20