nderstanding Multiplying Fractions, Mixed Numbers, and Simplifying Fractions

	Rewrite	Compare with $\frac{1}{2},$ or $\frac{6}{1 2}$
$\frac{1 0}{1 2}$	$\frac{1 0}{1 2}$	$\frac{1 0}{1 2} > \frac{6}{1 2}$
$\frac{2}{3}$	$\frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{1 2}$	$\frac{8}{1 2} > \frac{6}{1 2}$

Rewrite

Compare with

\frac{1}{2},

\frac{6}{1 2}

\frac{1 0}{1 2}

\frac{1 0}{1 2}

\frac{1 0}{1 2} > \frac{6}{1 2}

\frac{2}{3}

\frac{2 \cdot 4}{3 \cdot 4} = \frac{8}{1 2}

\frac{8}{1 2} > \frac{6}{1 2}

	Estimate for $\frac{1 0}{1 2} \times \frac{2}{3}$
Round $\frac{1 0}{1 2}$ to $1$	$1 \times \frac{2}{3} = \frac{2}{3}$
Round $\frac{2}{3}$ to $1$	$\frac{1 0}{1 2} \times 1 = \frac{1 0}{1 2}$

Estimate for

\frac{1 0}{1 2} \times \frac{2}{3}

Round

\frac{1 0}{1 2}

1

1 \times \frac{2}{3} = \frac{2}{3}

Round

\frac{2}{3}

1

\frac{1 0}{1 2} \times 1 = \frac{1 0}{1 2}

Activity	Fraction
Warm-up	$\frac{1}{5}$
Instruction	$\frac{1}{2}$
Playing a game	$\frac{1}{1 0}$
Cool-down	$\frac{1}{5}$

Activity

Fraction

Warm-up

\frac{1}{5}

Instruction

\frac{1}{2}

Playing a game

\frac{1}{1 0}

Cool-down

\frac{1}{5}

Part of $1 \frac{5}{1 2}$ -hour Class
Activity	Fraction
$Warm - up$	$\frac{1}{5}$
Instruction	$\frac{1}{2}$
Playing game	$\frac{1}{1 0}$
$Cool - down$	$\frac{1}{5}$

Part of

1 \frac{5}{1 2}

-hour Class

Activity

Fraction

Warm - up

\frac{1}{5}

Instruction

\frac{1}{2}

Playing game

\frac{1}{1 0}

Cool - down

\frac{1}{5}

Part of $1 \frac{5}{1 2}$ -hour Class
Activity	Fraction
$Warm - up$	$\frac{1}{5}$
$Instruction$	$\frac{1}{2}$
Playing game	$\frac{1}{1 0}$
$Cool - down$	$\frac{1}{5}$

Part of

1 \frac{5}{1 2}

-hour Class

Activity

Fraction

Warm - up

\frac{1}{5}

Instruction

\frac{1}{2}

Playing game

\frac{1}{1 0}

Cool - down

\frac{1}{5}

The diagram shows how Zain multiplies two mixed numbers.

Is Zain correct?

Let's examine the steps Zain followed when multiplying 3 14 and 6 25. We want to figure out if their work is correct.

As we can see, Zain directly multiplies the integer and fraction parts of both mixed numbers with each other. They then add these two products. However, this is an incorrect procedure. We calculate the product of two mixed numbers by rewriting the mixed numbers so that they are improper fractions.

We need to remember that the product of two fractions is equal to the product of the numerators divided by the product of the denominators. Let's find the product!

Finally, let's rewrite the answer as a mixed number and see if our friend was correct.

The result of the product is different from what Zain found. Therefore, Zain is not correct. The answer is C.

We can also calculate the product by using the Distributive Property. Remember, a mixed number a bc is the same as a + bc. Let's rewrite the given expression as follows. 3 14 * 6 25 = (3+1/4) * (6 + 2/5 ) If we apply the Distributive Property here, we get a different expression than the one that Zain found.

There are two missing terms in the Zain's work, 65 and 32. This means that Zain is not correct. Let's continue and find the correct answer.

As we can see, we ended with the same result as before. Therefore, Zain is not correct.

Ali spends $\frac{3}{1 2}$ of the day at an amusement park. He spends $\frac{4}{9}$ of that time driving a go-kart.

How many hours does he spend driving the go-kart? Write the answer as a mixed number.

We know that Ali spent 312 of his day at an amusement park and 49 of that time driving a go-kart. The product of these two fractions will give us what fraction of the day Ali spent driving the go-kart. Let's find it! 3/12 * 4/9 Notice that we can simplify the first fraction to 14 because 12 is 4 times 3. 3/3* 4 * 4/9 = 1/4* 4/9 We can also simplify across the two fractions. There is a common factor between the numerator of 49 and the denominator of 14. 1/4* 4/9 = 1/1 * 1/9 ⇒ 1/9 Since 1 is the identity element of multiplication, the product is 19. This means that Ali spent 19 of his day driving the go-kart. We can calculate how many hours this ride took by multiplying 19 by the 24 hours in a day.

Ali spent 2 23 hours driving the go-kart.

Jordan's family owns a paint shop. They have

42

gallon of paint in storage,

\frac{5}{9}

of which are for outdoor use. The rest of the paint is for indoor use. If each gallon costs

$ 18,

what is the total cost of the indoor paint in storage?

We want to find the total cost of the indoor paint in storage. There are 42 gallons of paint in storage. We know that 59 of that paint is for outdoor use and the rest is for indoor use. Since the total amount of paint is 1 when represented as a fraction, we can determine the fraction of the indoor paint by subtracting 59 from 1.

We found that four-ninths of 42 gallons of paint is for indoor use. 42Liters of Paint ↙ 1.5cm ↘ Outdoor Use Indoor Use 5/9 2cm 4/9 Now we can find the number of gallons of paint for indoor use. To do so, we need to multiply 42 by 49. The result will represent 49 of the 42 gallons of paint in storage. 42 * 4/9 To calculate this product, we will move the whole number to the numerator of the fraction as a factor. Let's do it!

We found that there are 563 gallons of paint for indoor use in storage. Finally, we can find the total cost of the indoor paint in storage. There are 563 gallons paint and each one costs $18. To find the total cost, we need to multiply the fraction and the whole number like we did before.

The total cost of the indoor paint in storage is $336.

Without calculating the product, complete the statement with

<,

>,

= .

\frac{1 0}{1 2} \times \frac{3 2}{2 0} ∣ \frac{1 0}{1 2}

We want to compare the quantities on each side of the box and complete the statement. 10/12 * 32/20 10/12 Notice that the expression on the left-hand side is 1012 multiplied by a fraction. When we multiply a number by a fraction, the product can be greater than, less than, or equal to the multiplicand, or the original number. If the multiplier fraction is less than 1, the result will be less than the multiplicand. Let's see an example! 1/2 * 1/2 = 1/4 ⇒ 1/4 < 1/2 If the fraction is equal to 1, the result will be equal to the multiplicand. 1/2 * 2/2 = 1/2 ⇒ 1/2 = 1/2 Finally, if the fraction is greater than 1, the result will be greater than the multiplicand. 1/2 * 4/2 = 2 ⇒ 2 > 1/2 Let's focus on the given statement. The fraction 1012 is multiplied by 3220. Since the numerator 32 is greater than the denominator 20, the fraction 3220 is greater than 1. Therefore, the product of 1012 and 3220 is greater than 1012. With this in mind, we can complete the statement. 10/12 * 32/20 > 10/12

Multiply Fractions

Catch-Up and Review

Running Time

Multiplying Fractions

Finding What Fraction of the Water in a Bottle Is Drunk

Hint

Solution

Extra

Finding the Product of Fractions

Multiplying Fractions by Whole Numbers and By Mixed Numbers

Multiplying Fractions By Whole Numbers

Multiplying Fractions By Mixed Numbers

Finding Times Allocated For Activities

Hint

Solution

Finding the Area of a Printed Photograph

Hint

Solution

Finding the Product of Mixed Numbers

Finding Time Paulina Runs

Hint

Solution

Multiply Fractions

Recommended exercises

	10 Theory slides
	10 Exercises - Grade E - A
	Each lesson is meant to take 1-2 classroom sessions