5th grade module 4 review

Division as fractions

100

Write the following as a fraction, and then change it to a mixed number 5 ÷ 3

The fraction for 5÷3 5/3. 

The mixed number is 1 and 2/3.

200

Write the following as a fraction, and then change it to a mixed number 12 ÷ 5

The fraction for 12÷5 is 12/5.

The mixed number is 2 and 2/5.

300

Write the following as a fraction, and then change it to a mixed number 30 ÷ 5

The fraction for 30÷5 is 30/5.

The mixed number is 6.

400

Write the following as a fraction, and then change it to a mixed number 15 ÷ 4

The fraction for 15÷4 is 15/4.

The mixed number is 3 and 3/4.

500

Write the following as a fraction, and then change it to a mixed number 27 ÷ 7

The fraction for 27÷7 is 27/7.

The mixed number is 3 and 6/7.

Multiplying whole numbers by fractions

100

4 of 1/2

4 times 1/2 can be written as:

4/1×1/2=4/2=2

The answer is 2.

200

14 x 1/3

14/1×1/3=14/3

As a mixed number this is 4 and 2/3.

Answer: 14/3 or 4 and 2/3. 

300

Solve 3/6 of 12

3/6×12 = 3×12/6 = 36/6 =6

The result is 6. 

400

Solve 14 x 2/6

14×2/6=28/6=4 and 2/3

500

Solve 1/5 of 27

1/5×27=27/5=5 and 2/5

Multiplying Fractions by Fractions using models

100

Solve using a model 1/2 of 2/3

1. First Tape (Representing 2/3):

   • Draw a rectangle (tape) and divide it into three equal segments.
   • Shade two of the three segments to represent 2/3.

2. Second Tape (Representing 1/2 of the First Tape):

   • Now, consider taking half of the colored portion representing 2/3.
   • Divide each of the shaded segments into two equal parts.
   • Select one out of the two parts in each shaded segment.

3. Calculate the Result:

   • The original tape had three segments, with two shaded.
   • Since you took half of the shaded segments, you now have two parts (from the first tape) that each have been split into two, resulting in a total of six smaller segments.
   • If you took one part out of every two in the shaded area, the total number of shaded sections becomes 2 out of 6, which can be simplified to 1/3.

200

Solve using a model 1/3 of 1/3

1. Initial Tape (Representing 1/3):

   • Draw a rectangle (tape) and divide it into three equal parts.
   • Shade one of these parts to represent 1/3.

2. Taking 1/3 of the Shaded Part:

   • Now, divide the shaded part into three equal sections.
   • Shade one of these new smaller sections to represent 1/3 of 1/3.

3. Calculate the Result:

   • Given the original tape had three parts, the division of each segment into three parts gives a total of nine smaller sections.
   • Since one section out of the nine is shaded, the fraction that represents this area is 1/9.

300

Solve using a model 1/2 of 1/3

1. First Tape (Representing 1/3):

   • Draw a rectangle (the tape) and divide it into 3 equal sections.
   • Color one of the three sections to represent 1/3.

2. Second Tape (Representing 1/2 of the First Tape):

   • Now, take the colored section (representing 1/3) and divide it into 2 equal parts.
   • Color one of these two parts to represent 1/2.

3. Calculate the Result:

   • Since your original tape had 3 equal parts, and you took half of one of those parts, you have effectively taken 1 out of 6 equal parts (because each of the original 3 sections has now been divided into 2, making a total of 6 smaller sections).
   • So, 1/2 of 1/3 is equivalent to 1/6
     
     The result is 1/6. 

400

Solve using a model 2/4 x 1/5

1. First Tape (Representing 1/5):

   • Draw a rectangle (tape) and divide it into 5 equal sections.
   • Color one of the five sections to represent 1/5.

2. Second Tape (Representing 2/4):

   • Draw another rectangle and divide it into 4 equal sections.
   • Color two of the four sections to represent 2/4. This is equivalent to 1/2.

3. Combining the Tapes:

   • Now, consider that the problem asks for 2/4 of 1/5. You need to take half of the colored section representing 1/5.
   • Divide the colored section (representing 1/5) into two equal parts.
   • Color one of these halves. This represents taking 2/4 of 1/5.

4. Result:

   • With the original tape divided into 5 sections, and then each section divided into 2, you now have a total of 10 sections.
   • The colored portion represents 1/10, indicating that 2/4 of 1/5 is equivalent to 1/10.

500

Solve using a model 2/3 of 4/5

1. First Tape (Representing 4/5):

   • Draw a rectangle (tape) and divide it into 5 equal parts.
   • Shade 4 out of 5 segments to represent 4/5.

2. Second Tape (Representing 2/3):

   • Draw a rectangle (another tape) and divide it into 3 equal parts.
   • Shade 2 out of 3 segments to represent 2/3.

3. Combining the Tapes to Get the Result:

   • You now need to consider 2/3 of 4/5. To do this, let's take the first tape representing 4/5 and divide each of the 5 parts into 3 sections, so you have 15 smaller sections in total.
   • Because the question requires 2/3, you need to consider 2 out of every 3 sections. From the first tape (which has 15 sections), shade every group of 2 out of 3 sections to represent 2/3.

4. Finding the Result:

   • Since the first tape was divided into 15 segments, the original shading covered 12 out of 15 segments (representing 4/5).
   • After dividing into smaller parts, you should shade only 2 out of every 3 sections, indicating 2/3.
   • Now, out of 15 sections, you should shade a total of 8, indicating that 2/3 of 4/5 results in 8/15.

Division of fractions

100

2 ÷ 1/2

What is 4

200

5 ÷ 1/4

What is 20

300

1/2 ÷ 6

1/12

400

5 ÷ 1/8

What is 40

500

1/5 ÷ 12

1/60

Word Problems

100

Steve had 1/2 of a lasagna left over. Three friends came over. Him AND HIS FRIENDS shared it. How much did they each get?

What is 1/8 of the lasagna

200

Three fifths of the students in a class were girls. Of the boys, 1/2 had glasses. What fraction of the class were boys with glasses?

What is 2/10

300

The race was 6 miles long. If there were water stops every 1/2 of a mile, how many water stops were there?

What is 12 water stops

400

Mr. Nevitt's plant grew 1 and 1/2 inches. Shayla's plant grew 1/2 as much as his. How much did Shayla's plant grow?

What is 3/4 of an inch

500

Steve and George share a 16 ounce box of cereal. By the end of the week, Steve has eaten 3/8 of the box, and George has eaten 1/4 of the box. How much cereal is left?

What is 6 ounces of cereal