Unit 3 Lesson 3

Adding and Subtracting Mixed Numbers

​Fraction

1 +

​Whole Number and a

What is a mixed number?

Adding mixed numbers with like denominators

- To add mixed numbers with the same denominator, follow these steps:
1. add fractions
2. add whole numbers
3. regroup if needed
4. add partial sums if needed

- You need to regroup when your numerator is equal to or bigger than your denominator after adding

1. divide numerator by denominator
2. the answer will be a whole number or mixed number
3. add that to the original whole number, and you will have your answer

​

​What does it mean to regroup in addition?

Multiple Choice

Which is the first step in adding mixed numbers?

• Add the fractions

• Regroup and simplify, if needed

• Add the whole numbers

Multiple Choice

Which is the 2nd step in adding mixed numbers?

• Add the fractions.

• Regroup and simplify, if needed.

• Add the whole numbers.

Multiple Choice

Which is the 3rd step in adding whole numbers?

• Add partial sums

• Add the fractions.

• Add the whole numbers.

• regroup if needed

Multiple Choice

Which is the 4th step in adding mixed numbers?

• Nothing, you're done!

• Regroup and simplify if needed

• Add whole numbers to fractions

• Add partial sums if needed

Subtracting mixed numbers with like denominators

- To subtract mixed numbers with the same denominator, follow these steps:
1. subtract the fractions
2. regroup from the whole number if needed
3. subtract whole numbers
4. simplify if needed

Subtracting mixed numbers can be trickier if you have to regroup!!

• Just remember, 1 whole is any fraction with the same numerator and denominator!!

Multiple Choice

Which of these fractions equals 1?

• $$\frac{1}{4}$$  

• $$\frac{2}{4}$$  

• $$\frac{3}{4}$$

• $$\frac{4}{4}$$

Multiple Choice

Which of these fractions equals 1?

• $$\frac{1}{6}$$  

• $$\frac{3}{6}$$  

• $$\frac{6}{6}$$

• $$\frac{7}{6}$$

- To regroup fractions, follow these steps:
1. borrow from the whole number
2. add the denominator to the numerator
3. write the new numerator
4. keep the denominator the same

​

​So, how do you regroup fractions with subtraction??

​Follow the regrouping steps

1. borrow from the whole number
2. add the denominator to the numerator
3. write the new numerator
4. keep the denominator the same

​

Multiple Choice

$$3\ \frac{1}{3}-1\ \frac{2}{3}=$$  

• $$2\ \frac{1}{3}$$  

• $$2\ \frac{2}{3}$$  

• $$1\ \frac{2}{3}$$  

Simplifying Fractions

Simplifying Fractions

Simplify your MATH LIFE!

These words also mean to simplify

​Reduce
Simplest Form
Lowest Form

Simplifying Fractions

We use simplification to find a fraction that is easier or friendlier to use. We try to find familiar fractions that we have worked with before.

For example, if we have the fraction, 36/40, we could simplify to 9/10.

Where to Start

• Look at the numerator and denominator

• Look for any patterns or fact families

• LIST OUT THE FACTORS OF BOTH THE NUMERATOR AND DENOMINATOR

This means you write out the numbers that multiply together to give the answer 2

​

​List the factors of 2

This means you write out the numbers that multiply together to give the answer 2

​

​List the factors of 6

​6

​2

Compare each numbers factors

Congrats! You have found, what is called, the Greatest Common Factor, or GCF!

​
-Now, divide the numerator and denominator by the GCF

​Find the biggest factor BOTH numbers share

This means you write out the numbers that multiply together to give the answer 8

​

​List the factors of 8

This means you write out the numbers that multiply together to give the answer 24

​

​List the factors of 24

​24

​8

Compare each numbers factors

Congrats! You have found, what is called, the Greatest Common Factor, or GCF!

​
-Now, divide the numerator and denominator by the GCF

​Find the biggest factor BOTH numbers share

Look for the GREATEST COMMON FACTOR.

You need to find the GCF so that you can begin division to reduce the fraction down to simplest form.

Oh no! What if I forget all the factors for a number?

This happens often! Don't panic. Do what you know and reduce, reduce, reduce! Until you can't anymore! 

Select the GCF you've listed. For example, let's say our fraction is 8/24 and you choose 4 (instead of 8) as your GCF. Divide both the numerator and denominator by 4. You will get 2/6. Start the process over. List factors of 2 and 6. Divide by the GCF. You will get 1/3. 

Multiple Choice

Simplify

$$\frac{6}{12}$$  

• $$\frac{1}{3}$$  

• $$\frac{1}{2}$$  

• $$\frac{5}{10}$$  

• $$\frac{2}{3}$$  

Multiple Choice

Reduce

$$\frac{6}{36}$$  

• $$\frac{2}{12}$$  

• $$\frac{3}{18}$$  

• $$\frac{1}{6}$$  

• 6

Multiple Choice

Put

$$\frac{24}{36}$$  

into simplest form

• $$\frac{2}{3}$$  

• $$\frac{4}{6}$$  

• $$\frac{4}{5}$$  

• $$\frac{3}{12}$$  

Multiple Choice

Simplify

$$\frac{15}{25}$$  

• $$\frac{1}{5}$$  

• $$\frac{4}{5}$$  

• $$\frac{5}{6}$$  

• $$\frac{3}{5}$$  

Multiple Choice

Reduce

$$\frac{16}{32}$$  

• $$\frac{2}{4}$$  

• $$\frac{1}{2}$$  

• $$\frac{8}{16}$$  

• $$\frac{4}{8}$$  

​Simplify your answer using GCF

​Remember the steps for adding/subtracting mixed numbers

Now let's put it all together!

Multiple Choice

$$3\frac{1}{4}\ +\ 5\frac{2}{4}\ =$$  

• $$\frac{3}{4}$$  

• $$8$$  

• $$8\ \frac{2}{4}$$  

• $$8\ \frac{3}{4}$$  

Multiple Choice

$$4\ \frac{4}{5}\ +3\ \frac{2}{5}$$  

• $$7\ \frac{1}{5}$$  

• $$7\ \frac{4}{5}$$  

• $$8\ \frac{1}{5}$$  

• $$8$$  

Multiple Choice

$$5\ \frac{3}{8}\ -2\ \frac{1}{8}$$  

• $$7\ \frac{1}{2}$$  

• $$3\ \frac{1}{4}$$  

• $$3$$  

• $$3\ \frac{1}{2}$$  

Multiple Choice

$$7\frac{3}{5}+9\frac{2}{5}$$

• 17
• 17 5/10
• 16 5/5
• 18

Multiple Choice

$$\frac{6}{9}+\frac{5}{9}=$$  

• $$\frac{1}{9}$$  

• $$\frac{10}{9}$$  

• $$1\ \frac{2}{9}$$  

• $$\frac{11}{18}$$  

Multiple Choice

$$6\frac{2}{6}+1\frac{2}{6}$$

• 7 
• 7  4/12
• 7  2/3
• 8  4/6

Multiple Choice

$$3\ \frac{1}{4\ }\ +\ 2\ \frac{1}{4}$$

• $$5\ \frac{2}{8}$$  

• $$5\ \frac{1}{2}$$  

• $$3\ \frac{1}{4}$$  

• $$5\ \frac{2}{8}$$  

Multiple Choice

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

• $$9\ \frac{2}{3}$$  

• $$8\ \frac{4}{6}$$  

• $$8\ \frac{1}{3}$$  

• $$9\ \frac{1}{3}$$  

Multiple Choice

   $$2\ \frac{3}{8}$$  -  $$\frac{5}{8}$$  

• 2  $$\frac{2}{8}$$  

• 3

• 1  $$\frac{3}{4}$$  

• 2  $$\frac{1}{4}$$  

Multiple Choice

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

• 1  2/4
• 2  1/2
• 1  3/4
• 6  3/4

Multiple Choice

$$5\frac{1}{7}-2\frac{4}{7}$$

• 3  4/7
• 3  3/7
• 2  4/7
• 7  5/7

Multiple Choice

$$7\frac{4}{7}-5\frac{2}{7}$$

• 2  2/7
• 2  6/7
• 12  6/7
• 2  1/7

Changing mixed numbers to improper fractions

1. Multiply by denominator

2. Add result to numerator

3. Denominator is the same

Multiple Choice

Convert this mixed number to an improper fraction.

• 1/6
• 21/6
• 13/6
• 12/6

Multiple Choice

Convert this mixed number to an improper fraction.

• 3/2
• 1/2
• 2/3
• 11/2

​1. Set up a division problem
2. Divide like normal
3. Any remainder goes over the denominator
4. Simplify fraction if needed

Multiple Choice

If I have $$\frac{5}{4}$$ of a candy bar, how many candy bars do I have?

• $$1\frac{5}{4}$$

• $$1\frac{1}{4}$$

• 1

Multiple Choice

Convert $$\frac{22}{5}$$ to a mixed number.

• $$\frac{5}{22}$$

• $$4\frac{2}{5}$$

• $$2\frac{1}{5}$$

• $$4\frac{3}{22}$$

Multiple Choice

Convert into an improper fraction.

• $$\frac{5}{4}$$

• $$\frac{4}{5}$$

• $$\frac{11}{4}$$

• $$\frac{4}{11}$$

Multiple Choice

Convert into an improper fraction.

• $$\frac{15}{2}$$

• $$\frac{10}{5}$$

• $$\frac{17}{5}$$

• $$\frac{11}{2}$$

Multiple Choice

Write $$\frac{22}{3}$$ as a mixed number.

• 
  $$7\frac{1}{3}$$

• $$7\frac{1}{2}$$

• $$7\frac{1}{4}$$

• $$7\frac{1}{9}$$

Multiple Choice

Convert $$1\frac{3}{5}$$ to an improper fraction.

• $$\frac{8}{5}$$

• $$\frac{13}{5}$$

• $$\frac{9}{5}$$

• $$\frac{18}{5}$$

Multiple Choice

Convert $$\frac{25}{3}$$ to a mixed number.

• $$8\frac{1}{3}$$

• $$8\frac{3}{25}$$

• $$7\frac{5}{7}$$

• $$2\frac{5}{8}$$

Multiple Choice

Convert $$\frac{14}{6}$$ to a mixed number. Simplify if needed.

• $$1\frac{6}{8}$$

• $$2\frac{1}{3}$$

• $$2\frac{2}{6}$$

• $$1\frac{4}{6}$$

• how many fewer

• less than

• difference

• decreased

• how many more

​Subtraction

• in all

• sum

• total

• altogether

• increased by

​Addition

Word problem clue words

Multiple Choice

There were $$3\ \frac{1}{6}$$ pies on the shelf. The server took away $$1\ \frac{5}{6}$$ pies from the shelf. How many pies remain on the shelf? Simplify if needed.

• $$3\ \frac{1}{6}$$ pies

• $$2\ \frac{1}{6}$$ pies

• $$1\ \frac{2}{6}$$ pies

• 2 pies

Multiple Choice

Leland used $$1\ \frac{3}{4}$$ cups of flour and then used an additional $$1\ \frac{3}{4}$$ cups of flour again. How much flour did he use altogether? Simplify if needed.

• $$2\ \frac{6}{8}$$ cups

• $$\frac{6}{4}$$ cups

• $$2\ \frac{2}{4}$$ cups

• $$3\ \frac{2}{4}$$ cups

Multiple Choice

Lelan has $$6\frac{3}{8}$$ pizzas.  His family ate some.  He has $$2\frac{5}{8}$$ pizza left.  How much did his family eat? Simplify if needed.

• $$3\frac{3}{4}$$

• $$4\frac{2}{8}$$

• 9 pizzas
• $$3\frac{3}{8}$$

Multiple Choice

Teresa ran one lap around the park in $$1\frac{2}{4}$$ minutes. Her second lap took $$1\frac{3}{4}$$ minutes. How many minutes did it take her to complete two laps? Simplify if needed.

• 2 and 1/4 minutes

• 3 and 1/4 minutes

• 3 and 4/5 minutes

• 1 and 1/4 minutes

Multiple Choice

Mrs. Vasquez bought $$2\frac{1}{3}$$ pounds of grapes and $$1\frac{2}{3}$$ pounds of bananas. How many total pounds of fruit did she buy? Simplify if needed.

• 5 pounds

• 4 pounds

• $$2\frac{1}{3}$$ pounds

• $$1\frac{2}{3}$$ pounds

Multiple Choice

Monica rides her bike 3 $$\frac{1}{4}$$   days on Monday. She rides 2 $$\frac{2}{4}$$   days on Tuesday. How much farther does Monica ride her bike on Monday than on Tuesday? Simplify if needed.

• $$\frac{3}{4}$$  miles

• 1 $$\frac{3}{4}$$  miles

• 1 $$\frac{2}{4}$$  miles

• 1 $$\frac{1}{4}$$  miles

Multiple Choice

Jose has $$8\frac{3}{4}$$ pounds of bananas at his fruit stand. If he sells $$2\frac{1}{4}$$ pounds of bananas, how many pounds does he have remaining? Simplify if needed.

• $$6\frac{2}{4}$$ pounds

• 11 pounds

• $$9\frac{1}{2}$$ pounds

• $$6\frac{1}{2}$$ pounds

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