We are learning to use number sense to estimate the product of fractions (including whole and mixed numbers ). Example 1: Multiplying a whole number by a fraction. When you multiply a whole number by a fraction, the product becomes smaller than the whole number. 5 x 14 = 1 14 Example 2: Multiplying two proper fractions. When you multiply two proper fractions, the product will be less than one and less than both factors. 1
3
x 15 = 151 Example 3: Multiplying two mixed numbers (or numbers greater than 1) When you multiply two mixed numbers, the product will be greater than both factors: 2 12 x 3 12 =8 34 Complete the chart below: We are learning to multiply a fraction by a whole number. When you multiply a fraction by a whole number, turn the whole number into a fraction and then multiply across. 5 x 14 = 5
1
5
1
x =
=1
1
4
4
4 ****​
Remember to change any improper fractions you may get for an answer to a mixed number. 8 x 13 = 81 x 13 = 83 =2 23 Solve: 1
4 x 6 7 x 25 1
3
We are learning to use models and procedures to multiply two fractions. 2
x 25 = 15
Solve using an area model: 1 3
3x5 2 1
3x2 We are learning to multiply mixed numbers with an area model. We are learning to multiply mixed numbers. We are learning about the relationship
between fractions and division.
A fraction can be written as a division problem. A division problem can be written as
a fraction.
2 ÷ 3= 23
Write the following fractions as division expressions:
3
10
4
9 3 5
Write the following division expressions as fractions:
5 ÷ 6 8 ÷ 10 3 ÷ 4 1
1÷ 4 = 4 15
20 25 ÷ 6 Karen had 12 cookies to share equally among 5 people. How many cookies will each
person get?
Marcus had a rope that was 7 feet long. He wants to cut the rope into 4 equal pieces.
How long will each piece of rope be?
We are learning to divide a whole
number by a unit fraction.
Use Models to help! The dividend tells you what to draw.
1
4÷ 3 Think: How many thirds can fit into 4 wholes? 12!
1
2÷ 9 Think: How many ninths can fit into 2 wholes? 18!
Solve, use models to help!
1
5÷ 3 3 ÷ 12 1
8÷ 4 We are learning to divide a unit
fraction by a whole number.
Use models to help! The dividend tells you what to draw.
1
3
÷ 4
Now that you have shown ⅓, divide each section by 4.
How many total pieces are there? 12
Out of those that are shaded, how many could each person get? 1
So, the answer is
1
12 .
Solve, use models to help:
1 ÷ 5 5 1 ÷ 4 3 1 ÷ 6 2 Bridget, Beth and Becca shared ½ of a casserole. What fraction of the original
casserole did each friend get?
We are learning to solve problems
involving unit fractions.
Think about what is being divided! Mary wants to make tarts. To make tarts, she needs 14 of a cup of flour per batch of tarts. If Mary has 5 cups of flour, then how many batches of tarts can Mary make? Mary is dividing up the 5 cups of flour for each batch. Mary can make 20 batches of tarts with her 5 cups of flour. 1. One track coach wants his athletes to race 3 miles around a track to measure how fast each person can run. If the track is 14 of a mile around, then how many laps around the track will the athletes have to run to complete the race? 2. Sharon has ½ of a gallon of milk to share equally between 3 people. How much milk, in gallons, will each person get? 3. John made 9 pints of hot chocolate for his friends. If each of John's mugs holds 1
2 of a pint of liquid, then how many friends will get hot chocolate?