5th Grade Winter Break Tutorials Fractions and Operations Review

Adding and Subtracting Fractions

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When adding or subtracting fractions with LIKE denominators you...

• Simply add the numerators together

• DO NOT add the denominators

Notice

• The top numbers were added

• The bottom number stayed the same

• If it starts the same, it will end the same (bottom number that is)

Multiple Choice

 $\frac{1}{8}+\frac{4}{8}$  

•  $\frac{5}{16}$  

•  $\frac{4}{64}$  

•  $\frac{5}{8}$  

•  $\frac{3}{8}$  

Multiple Choice

 $\frac{2}{5}+\frac{3}{5}$  

•  $\frac{5}{10}$  

•  $\frac{1}{5}$  

•  $\frac{5}{5}$  

Subtraction Works the same way

Multiple Choice

 $\frac{4}{5}-\frac{2}{5}$  

•  $\frac{6}{5}$  

•  $\frac{2}{0}$  

•  $\frac{2}{5}$  

•  $\frac{2}{10}$  

Multiple Choice

 $\frac{9}{10}-\frac{2}{10}$  

•  $\frac{7}{10}$  

•  $\frac{11}{10}$  

•  $\frac{11}{20}$  

•  $\frac{7}{0}$  

What about fractions that don't have the same denominator?

• We have to find the least common multiple (lcm)

• Or we can use the butterfly method

Finding the lcm of two numbers

• First - List the multiples of each number

• Find the lowest (least) number in common

• That number will become your new denominator

Next Steps

• Multiply each fraction by a factor that will make the denominator the lcm

• Make sure you multiply both the top and bottom by the same value!

Multiple Choice

What is the lcm of 3 and 5?

• 3

• 5

• 15

• 9

Multiple Choice

What is the lcm of 2 and 7

• 2

• 7

• 14

• 9

Multiple Choice

Rewrite this problem with common denominators

 $\frac{1}{3}+\frac{2}{5}$  

•  $\frac{1}{3}+\frac{2}{5}$  

•  $\frac{1}{3}+\frac{2}{3}$  

•  $\frac{1}{5}+\frac{2}{5}$  

•  $\frac{5}{15}+\frac{6}{15}$  

•  $\frac{1}{15}+\frac{2}{15}$  

Multiple Choice

Answer the last problem $\frac{1}{3}+\frac{2}{5}$  

•  $\frac{3}{3}$  

•  $\frac{3}{5}$  

•  $\frac{11}{15}$  

•  $\frac{3}{8}$  

Multiple Choice

 $\frac{3}{4}-\frac{2}{3}$  

•  $\frac{1}{1}$  

•  $\frac{1}{7}$  

•  $\frac{1}{12}$  

•  $\frac{1}{4}$  

•  $\frac{1}{3}$  

The butterfly method

• Multiply the denominators together

• Multiply the denominator with the numerator from the other fraction

• Add the multiplied numbers together

Multiple Choice

Use the butterfly method to answer $\frac{1}{5}+\frac{2}{4}$  

•  $\frac{14}{20}$  

•  $\frac{3}{9}$  

•  $\frac{3}{20}$  

Multiple Choice

 $\frac{6}{7}-\frac{2}{5}$  

Use the butterfly method to answer

•  $\frac{4}{2}$  

•  $\frac{16}{35}$  

•  $\frac{44}{35}$  

•  $\frac{4}{35}$  

Adding and Subtracting Fractions Word Problems

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Multiple Choice

In preparation for a picnic, Samaj made a salad with 1/4 of a bag of iceberg lettuce and 5/8 of a bag of romaine lettuce. How many bags of lettuce did Samaj use in all?

What operation is this question asking you to do?

• Add

• Subtract

Multiple Choice

In preparation for a picnic, Samaj made a salad with 1/4 of a bag of iceberg lettuce and 5/8 of a bag of romaine lettuce. How many bags of lettuce did Samaj use in all?

• 3/8 bag

• 4/8 bag

• 6/8 bag

• 7/8 bag

Multiple Choice

Paula made cookies. She used 3/4 of a cup of flour and 5/8 of a cup of sugar. How much more flour than sugar did Paula use?

What operation should we use to solve this problem?

• Addition

• Subtraction

Multiple Choice

Solve:

Paula made cookies. She used 3/4 of a cup of flour and 5/8 of a cup of sugar. How much more flour than sugar did Paula use?

• 6/8 cup

• 3/8 cup

• 2/8 cup

• 1/8 cup

Multiple Choice

Colton and Hayley made a stir-fry for dinner. They used 1/6 of a pound of bell peppers, 1/3 of a pound of mushrooms, and 1/6 of a pound of snow peas. How many pounds of vegetables did they use in the stir-fry? Answer MUST be written in simplest form.

• 2/3 pound

• 5/6 pound

• 1/3 pound

• 4/6 pound

Multiple Choice

During a canned food drive, items were sorted into bins. The drive resulted in 1/4 of a bin of soup, 5/12 of a bin of vegetables, and 1/4 of a bin of pasta. Altogether, how many bins would the canned food take up?

• 1 whole bin

• 8/12 bin

• 6/12 bin

• 11/12 bin

Multiple Choice

Leslie and Greg own neighboring cornfields. Leslie harvested 1/2 acre of corn on Monday and Greg harvested 1/6 of an acre. How many more acres did Leslie harvest than Greg? Answer must be in simplest form.

• 4/6 acre

• 2/3 acre

• 1/3 acre

• 4/6 acre

Multiple Choice

In Brooke's history class, 1/8 of the students are making videos for their final project and 3/4 are making dioramas. What fraction of the students are making either a video or diorama?

• 5/8 of the students

• 6/8 of the students

• 7/8 of the students

• 8/8 of the students

Multiple Choice

During P.E. class, students were instructed to travel around the track in various ways. They did 1/4 of a lap skipping, 7/12 of a lap running, and 1/12 of a lap walking backwards. In total, how many laps did the students have to make?

• 11/12 laps

• 10/12 laps

• 4/12 laps

• 8/12 laps

Multiple Choice

Over the weekend, Josie drank 1/2 bottle of soda and Kang drank 3/10 of a bottle. How much more soda did Josie drink than Kang? Answer MUST be in simplest form.

• 2/10 bottle

• 1/5 bottle

• 2/8 bottle

• 2/5 bottle

Multiple Choice

At the farmers' market, Jasmine bought 9/10 of a pound of string beans and 3/5 of a pound of lima beans. How many more pounds of string beans did Jasmine purchase?

• 2/10 pound

• 3/10 pound

• 6/5 pound

• 12/15 pound

Multiple Choice

Javon made an apple pie. He used 3/5 of a tablespoon of cinnamon and 1/10 of a tablespoon of nutmeg. How much more cinnamon than nutmeg did Javon use? Answer MUST be in simplest form.

• 1/2 tablespoon

• 5/10 tablespoon

• 7/10 tablespoon

• 4/15 tablespoon

Adding and Subtracting Fractions with Models

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What fraction is being represented?

Write your answer in the chat.

What fraction is being taken away?

Write your answer in the chat.

Multiple Choice

What operation was being represented?

• Addition

• Subtraction

• Multiplication

• Division

Let's break down a STARR question.

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Multiple Choice

Is 

 $\frac{11}{15}$  - $\frac{1}{6}$  
a possible answer? Is 1/6 equivalent to 6/15?

• Yes

• No

Multiple Choice

Is 

 $\frac{11}{12}$  - $\frac{6}{12}$  
a possible answer? 

• Yes

• No

Multiple Choice

Is 

 $\frac{6}{15}$  - $\frac{4}{15}$  
a possible answer? 

• Yes

• No

Multiple Choice

Is 

 $\frac{11}{15}$  - $\frac{2}{5}$  
a possible answer? Is 2/5 equivalent to 6/15?

• Yes

• No

Let's break down a STARR question.

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How many twelths do I have in red?

What is the sum of the two fractions put together?

Let's break down a STARR question.

Let's go to a website you can use on your own to help us out!! (Link is in Blend)

Go go to Blend and complete your check for understanding. Your fraction tool is linked below to help!

Adding and Subtracting Mixed Numbers

with Mrs. LaCross

Adding Fractions with Like Denominators

• Add the numerators

• Keep the denominators the same

Model

When the denominator is the same you will add the numerators. All of your pieces are the same size when you have like denominators.

Model

You will use the same process with subtraction. Keep your denominators the same and subtract the numerators.

Examples

• Keep the denominator the same

• Add the numerators

Multiple Choice

  $\frac{1}{5}+\frac{3}{5}\ =\$  

•  $\frac{4}{5}$  

•  $\frac{4}{10}$  

•  $\frac{2}{5}$  

•  $\frac{3}{5}$  

Multiple Choice

 $\frac{7}{15}\ -\ \frac{5}{15}\ =$  

•  $\frac{12}{15}$  

•  $\frac{2}{30}$  

•  $\frac{2}{15}$  

•  $\frac{12}{30}$  

Mixed Numbers

• Have a whole

• Have a part (fraction)

Adding Mixed Numbers

Step 1: Add whole numbers

Step 2: Add numerators

Step 3: Same denominators

Multiple Select

 $2\ \frac{3}{5}\ +\ 1\ \frac{3}{5\ }\ =$  

•  $1\ \frac{0}{5}$  

•  $4\ \frac{1}{5}$  

•  $\frac{36}{5}$  

•  $3\ \frac{6}{5}$  

Multiple Choice

 $5\ \frac{3}{7}\ +\ 3\ \frac{2}{7}\ =$  

•  $8\ \frac{5}{14}$  

•  $2\ \frac{1}{7}$  

•  $8\ \frac{5}{7}$  

•  $\frac{85}{7}$  

Multiple Choice

 $6\ \frac{4}{5}\ -\ 3\ \frac{3}{5}\ =$  

•  $9\ \frac{7}{5}$  

•  $9\ \frac{7}{10}$  

•  $3\ \frac{7}{5}$  

•  $3\ \frac{1}{5}$  

Poll

Are you understanding adding and subtracting mixed numbers?

• Yes, I am understanding well!

• I think I get it, but need a little more practice.

• It is beginning to make sense, but I need more examples.

• Can we schedule a google meet for more explanation?

Multiple Choice

3/12 + 4/12

• 7/12

• 6/12

• 12/12

• 1/12

Multiple Choice

1/4 + 3/4

• 4/4

• 1/4

• 1/8

• 3/8

Multiple Choice

• 5/14
• 3/7
• 5/7
• 5/14

Multiple Choice

Add these Fractions

• 2/4
• 3/4
• 4/8
• 1

Multiple Choice

2/6 -1/6

• 1/6

• 3/6

• 6/6

Multiple Choice

8/8-3/8

• 5

• 7/8

• 5/8

• 4/8

Multiple Choice

9/12 - 4/12

• 2/12

• 5/12

• 24

• 7/12

Multiple Choice

When adding mixed numbers, which do you add first?

• The whole number

• The fractions

• It doesn't matter

Multiple Choice

To simplify an answer, which operation do you use?

• Addition

• Subtraction

• Multiplication

• Division

Multiple Choice

Solve

• 11 3/4

• 11 3/8

• 11

• 3/4

Multiple Choice

11/5 - 6/5

• 1 1/5
• 1 7/5
• 1
• 5/5

Multiple Choice

Raoul collects sports cards. He has six baseball cards, three football cards, four hockey cards, and three basketball cards. What fraction of his sports cards are either hockey cards OR baseball cards? Make sure you reduce the fraction to its lowest terms.

• 1/2
• 2/3
• 9/16
• 5/8

Multiple Choice

3 3/10 + 5 2/10

• 8 6/20

• 15 6/20

• 7 6/10

• 8 5/10

Multiple Choice

4 3/8 + 5 6/8

• 10 1/8

• 9 9/8

• 10

• 9 9/16

Multiple Choice

4 1/5 - 2 4/5

• 3 3/5

• 7

• 6 5/5

• 1 2/5

Multiple Choice

 $5\ \frac{3}{6}\ -\ 2\ \frac{4}{6}=$  

•  $5$  

•  $2\ \frac{5}{6}$  

•  $4\ \frac{4}{6}$  

•  $3\ \frac{5}{6}$  

Multiple Choice

 $12\ \frac{3}{8}\ -\ 9\ \frac{2}{8}\ =$  

•  $3\ \frac{1}{8}$  

•  $4\ \frac{2}{8}$  

•  $20$  

•  $2\ \frac{2}{8}$  

Multiple Choice

 $13\ \frac{7}{9}\ -\ 10\ \frac{8}{9}\ =$  

•  $12\ \frac{2}{9}$  

•  $23$  

•  $2\ \frac{1}{9}$  

•  $2\ \frac{8}{9}$  

Multiple Choice

 $5\ \frac{1}{4}\ -\ 1\ \frac{2}{4}=$  

•  $3\ \frac{1}{8}$  

•  $3\ \frac{3}{4}$  

•  $2\ \frac{3}{4}$  

•  $2$  

Multiple Choice

 $7\ \frac{1}{3}\ -\ 4\ \frac{2}{3}=$  

•  $\frac{2}{3}$  

•  $3\ \frac{2}{3}$  

•  $2\ \frac{2}{3}$  

•  $2$  

Multiple Choice

Which equation represents the fraction of beads that are green or yellow?

• 1/2 + 1/4 = 3/4

• 1/4 + 1/8 = 3/8

• 1/2 + 1/8 = 5/8

• 3/4 + 2/8 = 1

Multiple Choice

Jason is making a fruit salad. He mixes in 3 1/4 cups of orange melon and 2 2/3 cups of green melon. How many cups of melon does Jason put in the fruit salad?

• 5 1/4 cups

• 5 1/3 cups

• 5 7/12 cups

• 5 11/12 cups

Multiple Choice

Harry filled a watering can with 3/4 gallon of water. After watering a plant, he sees that 1/8 gallon is left. How much water did Harry use to water the plant?

• 4/8

• 7/8

• 4/12

• 1/12

Multiple Choice

Which shows how to use objects to model 1/2 – 1/4?

Multiple Choice

Jose ran 3 3/10 miles and Syd ran 6 1/2 miles. How many more miles did Syd run than Jose?

• 3 1/4 miles

• 3 1/2 miles

• 3 1/5 miles

• 3 1/3 miles

Multiple Choice

Which shows how to use objects to model 1/5 + 1/2?

Multiple Choice

Anton is making a fruit salad. He uses 2/3 cup of grapes and 1/2 cup of strawberries. What is the total amount of fruit Anton uses?

• 1 cub

• 2/6 cup

• 4/6 cup

• 1 1/6 cups

Multiple Choice

Neil swam 4 2/3 lengths of the pool. Mia swam 6 1/2 lengths of the pool. How many more lengths of the pool did Mia swim than Neil?

• 2 1/6

• 1 1/6

• 1 5/6

• 2 1/2

Multiple Choice

How much longer is Oksana’s chain than Gabrielle’s chain?

• 4 1/12 feet

• 14 1/12 feet

• 4 1/2 feet

• 15 7/12 feet

Multiple Choice

Mia hiked 2 1/2 miles farther than Jacob. Which could be the two distances each person hiked?

• Mia: 2 1/2 miles; Jacob: 1 1/4 miles

• Mia: 2 1/2 miles; Jacob: 7 1/2 miles

• Mia: 3 2/5 miles; Jacob: 5 9/10 miles

• Mia: 5 9/10 miles; Jacob: 3 2/5 miles

Multiple Choice

What multiplication problem does this array show?

• 4 x 5
• 2 x 10
• 5 x 5
• 1 x 20

Multiple Choice

Does this picture show 7 x 3?

• YES!
• NO!

Multiple Choice

What equation does this picture represent?

• 3 + 7 = ?
• 6 + 6 + 6 = ?
• 3 x 7 = ?
• 3 + 3 + 3 + 3 + 3 + 3 + 3 = ?

Multiple Choice

True or False. You can add 7 + 7 to find the total number of stars. 

• TRUE
• FALSE

Multiple Choice

TRUE or FALSE. You can add 2 + 7 to find the total number of stars.

• TRUE
• FALSE

Multiple Choice

Which division equation is shown by the picture?

• 4 ÷ 3 = 1
• 3 + 3 + 3 + 3 = 12
• 12 ÷ 4 = 3 

Multiple Choice

What division equation is shown by the picture?

• 5 + 5 = 10
• 10 ÷ 5 = 2
• 5 ÷ 5 = 1

Multiple Choice

Which equation would be used to represent the following story:
Chloe has 8 shells in each box. She has 2 boxes of shells. How many shells does Chloe have?

• 8 - 2  = ∎
• 8 x 2 = ∎
• 8 ÷ 2 = ∎

Multiple Choice

Which equation would be used to represent the story below?
Miles has 10 books. He puts the same number of books in 5 bags. How many books are in each bag?

• 10 ÷ 5 = ∎
• 10 x 5 = ∎
• 10 ÷ 2 = ∎

Multiple Choice

Christopher practiced for both baseball AND gymnastics. He practiced for baseball for 5 weeks for 2 hours each week. He practiced for gymnastics for 10 weeks for 3 hours each week. Choose the TRUE statement below. 

• Christopher practiced more for baseball than gymnastics.
• Christopher practiced gymnastics for 30 hours.
• Christopher practiced baseball for 7 hours.
• Christopher practiced 50 hours for both gymnastics and baseball. 

Multiple Choice

What fact is shown by the model?

• 3 / 8 = 18

• 18 / 3 = 6

• 3 x 8 = 16

• 18 - 8 = 3

Multiple Select

Select all of the facts that equal 4.

• 4 / 4

• 4 / 1

• 0 / 4

• 16 / 4

• 8 / 4

Multiple Choice

Which equation is shown?

• 5 x 4 = 20

• 20 / 5 = 4

• 5 + 4 = 9

• 20 - 5 = 15

Multiple Choice

What number sentence matches the picture?

• 4 * 4 = 16

• 8 / 2 = 4

• 8 / 2 = 16

• 8 x 2 = 16

Multiple Choice

Which fact is shown on the number line?

• 12 / 3

• 8 + 4

• 3 x 4

• 3 + 4

Multiple Choice

What fact is shown by the model?

• 4 + 5 = 9

• 4 x 5 = 25

• 4 * 5 = 20

• 20 - 5 = 4

Multiple Select

Select all of the facts that equal 12.

• 12 x 1

• 12 x 0

• 4 x 3

• 6 x 2

• 10 x 2

Multiple Choice

• 24 / 4

• 24 - 6

• 24 - 4

• 6 x 4

Multiple Choice

Which equation matches the picture?

• 3 / 2 = 6

• 6 / 3 = 2

• 3 x 6 = 18

• 2 x 6 = 12

Multiple Choice

• F

• G

• H

• I

Multiple Choice

Which is represented by the number line?

• 7 / 3

• 21 / 3

• 21 - 3

• 7 x 21

Multiple Choice

Mrs. Ivey was making muffins. She made a total of 28 muffins. If she shared them on 4 plates, how many would be on each plate?

• 7

• 6

• 5

• 8

Multiple Choice

Frisco ran 4 laps in the backyard.

Jack ran twice as far as Frisco.

How far did Jack run?

• 6

• 8

• 4

• 2

Multiple Choice

There were 28 bouncy balls in the bucket.

If they were shared among 7 friends, how many would each friend get?

• 4

• 5

• 3

• 2

Multiple Choice

Two loaves of pumpkin bread cost a total of 12 dollars. How much did each loaf cost?

• 3 dollars

• 4 dollars

• 5 dollars

• 6 dollars

Multiple Choice

Joey had 18 pieces of candy to eat. If he was going to eat the same amount each day for three days, how much would he eat in one day?

• 12

• 6

• 8

• 10

Multiple Choice

Brittany bought three cups of coffee. Each cup cost 4 dollars. How much did she spend on coffee?

• 10 dollars

• 7 dollars

• 12 dollars

• 8 dollars

Multiple Choice

The Halloween party had 3 boxes of prizes to choose from.

Each box had 9 prizes.

How many prizes were there in all?

• 12 prizes

• 27 prizes

• 6 prizes

• 4 prizes

Multiple Choice

Oak Grove raised $20 a day for 7 days for Run for the Gold.

How much money did Oak Grove raise?

• $27

• $13

• $140

• $120

Multiple Choice

NCG sold 80 tickets to Despicable me on Friday, Saturday, and Sunday. How many tickets were sold in all?

• 83 tickers

• 200 tickets

• 240 tickets

• 175 tickets

Multiple Choice

Ms. Kahley bought 4 bags of candy.

Each bag had 80 pieces.

How many pieces of candy are there in all?

• 300 pieces

• 84 pieces

• 320 pieces

• 300 pieces