Dividing a Whole Number by a Unit Fraction

Dividing a Whole Number by a Unit Fraction

TEKS 5.3(L)

Imagine This Scenario:

Cameron's dad purchased 4 pizzas for his birthday party. If each of Cameron's friends received 1/4 of a pizza, how many friends got pizza?

What's Happening?

• We started with 4 whole pizzas

• We divided the pizzas into fourths (divided by 1/4)

• We count the number of pieces we have after dividing

• We have 16 pieces

• So... 

   $4\ \div\ \frac{1}{4}\ =\ 16$  

Another Scenario:

Maria is making a fruit tray. She has 5 apples which she divides into eighths. How many apple slices will she add to the fruit tray?

What's Happening?

• We started with 5 whole apples

• We divided the apples into eighths (divided by 1/8)

• We count the number of pieces we have after dividing

• We have 40 pieces

• So... 

   $5\ \div\ \frac{1}{8}\ =\ 40$  

Do you see a pattern???

•  $4\ \div\ \frac{1}{4}\ =\ 16$  

•  $5\ \div\ \frac{1}{8}\ =\ 40$  

Multiple Choice

When we divide a whole number by a fraction...

• We get a smaller fraction.

• We get a larger fraction.

• We get a smaller whole number.

• We get a larger whole number.

Can you solve this problem?

Thomas has 3 yards of fabric. He is making masks for his classmates that each take 1/8 yard of fabric. How many masks will Thomas be able to make?

Multiple Choice

Thomas has 3 yards of fabric. He is making masks for his classmates that each take 1/8 yard of fabric. How many masks will Thomas be able to make?

Which of the following expressions do I need to solve this problem:

• $3\ \div\ \frac{1}{8}$

• $\frac{1}{8}\ \div\ 3$

• $3\ \times\ \frac{1}{8}$

• $3\ -\ \frac{1}{8}$

Multiple Choice

Thomas has 3 yards of fabric. He is making masks for his classmates that each take 1/8 yard of fabric. How many masks will Thomas be able to make?

What do you think the answer will be?

•  $\frac{1}{24}$  
  

• 24

•  $\frac{3}{8}$  
  

•  $2\ \frac{2}{3}$  

Let's take a closer look at the math...

First, it is best to have fractions with fractions. So, we will change the whole number to a fraction by giving it a denominator of 1.

 $5\ =\ \frac{5}{1}$  

Now we have  $\frac{5}{1}\ \div\ \frac{1}{8}$  

Keep --> Change --> Flip

• Keep - Leave the first fraction exactly as it is!

• CHANGE - Change the  $\div$   to   $\times$  .

• FLIP - Flip the second fraction upside down, this is called the reciprocal.

• Now we have  $\frac{5}{1}\ \times\ \frac{8}{1}$  

Now solve!

Multiply the numerators and then the denominators to get your answer!

 $\frac{5}{1}\ \times\ \frac{8}{1}\ =\ \frac{40}{1}\ =\ 40$  

Let's Review...

• Make whole numbers fractions by giving them a denominator of one.

• Keep --> Change--> Flip

• Keep the first fraction

• Change the  $\div$   to  $\times$  

• Flip the second fraction (reciprocal)

• Multiply

Multiple Choice

 $15\ \div\ \frac{1}{4}=$  

•  $\frac{15}{4}$  

•  $\frac{1}{60}$  

• 60

•  $\frac{4}{15}$  

Fill in the Blank

 $10\ \div\ \frac{1}{8}$  

Multiple Choice

Carson has 3 gallons of water. He will fill water bottles which will each hold 1/12 of a gallon. How many bottles can Carson fill?

• $\frac{1}{4}$ because $3\ x\ \frac{1}{12}\ =\ \frac{3}{12}\ =\ \frac{1}{4}\$

• $\frac{1}{36}$ because $\frac{1}{3}\ \div\ 12\ =\ \frac{1}{36}$

• 36 because $3\ \div\ \frac{1}{12}\ =\ 36$

• 4 because $3\ \div\ \frac{1}{12}\ =\ \frac{12}{3}\ =\ 4$