Multiplication of Fractions
What is a product? What are factors?
Product - the answer to a multiplication problem
Factors - the numbers being multiplied together
Error analysis: Tiffany says that since mixed numbers have fractions, that they must always have a value less than 1.
Is she correct?
No, mixed numbers must have a whole number component, and a fractional component. This means that mixed numbers will always have a value more than 1.
What type of model do you use to multiply mixed numbers with mixed numbers? Why is this type of model helpful?
Use an area model, because you can decompose the mixed number into whole number parts and fractional parts to help you multiply.
Which fraction will result in a product that is greater than 3/4?
3/4 x ____
a. 1/3 b. 1/2 c. 5/8 d. 5/4
d
2/3 x 4/5
8/15
What is the product?
2/3 x 6 1/3
4 2/9 = 4 1/3
Describe the process of using an area model to multiply two mixed numbers
1. Decompose each mixed number into a whole number and fraction.
2. Set them as the side lengths of a rectangle.
3. Multiply through the model to find partial products.
4. Add all of the partial products.
Which fraction will result in a product that is greater than 8/7?
8/7 x ____
a. 5/7 b. 12/6 c. 10/7 d. 8/6
Explain
a.
Because the value of 5/7 is less than one and if we multiply by a number less than one, the number will become less.
Find the product and simplify:
2/3 x 3/5
2/5
What is the product? Simplify.
2/3 x 4 1/3
26/9 = 2 8/9
Find the product:
2 3/5 x 1 1/3
52/15 = 4 7/15
Which expression will have a product that is less than the first factor? Select all that apply.
a. 42 x 1/2
b. 35 x 2/1
c. 78 x 1/5
d. 26 x 4/5
a and c
Without calculating, will the product be greater than each of the factors? How do you know?
6/7 x 9/13?
No, both factors are less than 1, so they product will become smaller.
Fill in the blank:
The product of any number with a mixed number will always be ____________________ than the factor that is not a mixed number.
larger.
The weight of Natalie's backpack is 6 2/3 kg. Her brother's backpack weighs 2 1/4 times that much. How much does Natalie's brother's backpack weigh?
(hint: the answer can be simplified to a whole number)
180/12 = 15 kg
In a cross country race, Duante took 8/9 as long to finish as James. Kofi took 7/8 as long as James to finish. Who took the longest to finish the race?
James.
Josiah ordered 4 pizzas for a pizza party. There was 3/8 of the pizza remaining in the fridge at the end of the party. The next day Josiah at half of the pizza from the fridge. How much pizza is left over? Simplify your answer for full points.
12/16 = 3/4 of a pizza.
There are 3 4/5 kg of apples in the kitchen. Tommy used 3/8 of the apples to make dinner. How many kg of apples did he use?
57/40 = 1 17/40
Find the product and simplify:
5 3/8 x 2 3/4
473/32 = 14 25/32
Jamie is 4/5 as tall as Harriet. Jenny is 1 2/5 as tall as Harriet. Who is the tallest? How do you know?
Jenny is the tallest because Jamie is 4/5 as tall as Harriet, which is less than one whole, so Harriet is taller. And Jenny is more than 1 times taller than Harriet, so Jenny is taller than Harriet. So If Jenny is taller than Harriet; and Harriet is taller than Jamie, then Jenny must be taller than both of them.