6th and 7th grade NS study guide

Addition of Fractions

Addition of Fractions requires you to complete multiple steps in order to solve the problem.

Step 1- Check to see if denominators are the same.

Step 2- If the same- add the top and bottom numbers together

Step 3- Simplify/Reduce to lowest term using GCF

Step 4- If different denominators, you will need to use the Least Common Factor to find a number to make the bottom number or you can keep one of the numbers- as long as it is a factor of both numbers

Step 5- Solve like regular addition of fractions problem

Step 6- Simplify/Reduce to lowest term using GCF.

​Rational Numbers

• ​Rational Numbers can be terminating or repeating decimals.

• ​Rational Numbers can be fractions, where the denominator is not 0.

​Converting Decimals to Fractions

​Use place value to convert from decimal to fraction form.

Every rational number can be expressed as either a terminating or repeating decimal.

• Terminating - decimal that ends and does not repeat

• Repeating - decimal that has one or more digits that repeat

Fractions to Decimals

Examples

Fractions to Percents

Example (strategy #1)

part over whole

Fractions to Percents

Example (strategy #2)

Addition of Fractions-Unlike Denominators

Subtraction of Fractions

Subtraction of Fractions requires you to complete multiple steps in order to solve the problem.

Step 1- Check to see if denominators are the same.

Step 2- If the same- subtract the top numbers

Step 3- Simplify/Reduce to lowest term using GCF

Step 4- If different denominators, you will need to use the Least Common Factor to find a number to make the bottom number or you can keep one of the numbers- as long as it is a factor of both numbers

Step 5- Solve like regular subtraction of fractions problem

Step 6- Simplify/Reduce to lowest term using GCF

Subtraction of Fractions-Unlike Denominators

​Example!

​Copy if you wish...

​Multiplying Mixed Numbers

​

​Please write this down if it will help you to answer the questions on the next few slides, come back to this if you need help!

​

​When multiplying mixed numbers, convert them to an improper fraction first.

Dividing Fractions

Rule#1 for Dividing Fractions: DON'T DIVIDE.

Instead of dividing you do this procedure:

KEEP, CHANGE, FLIP

What are factors?

• Numbers that you multiply together to make a product

• Products are answers to multiplication problems.

• 3 and 5 are factors of 15 because 3 x 5 =15

• 15 is the product of the FACTORS 3 and 5.

Listing Method

• 16 = 1, 2, 4, 8, 16

• 24 = 1, 2, 3, 4, 6, 8, 12, 24

• If we will compare the list of factors of 16 and 24, we can identify the common factors.

• GCF is the highest common factor that appears on the list.

• The GCF of 16 and 24 is 8.

Multiple Select

Select all the true statements about the Additive Inverse.

• 6 is the additive inverse of 6

• -4 is the additive inverse of 4

• 781 is the additive inverse of -781

• -21 is the additive inverse of 22

• 1 is the additive inverse of 0

Multiple Choice

When multiplying 17.98 × 143.5, how many times would you move the decimal?

• 1 time to the left

• 2 times to the left

• 3 times to the left

• 4 times to the left

Multiple Choice

Write 0.14 as a percent.

• 1.4%

• 140%

• 14%

• 0.14%

Multiple Choice

4 x 0.03

• 12

• 0.12

• 120

• 0.012

Multiple Choice

Tue is diving 8 1/2 feet below sea level. He decides to descend 5 1/2 more feet. How many feet below sea level is he?

• 13 2/2

• 14

• -14

• -13 2/2

Multiple Choice

Convert the Mixed Number to an Improper Fraction. 

$$3\ \frac{4}{6}$$  

• $$\frac{12}{6}$$  

• $$\frac{28}{6}$$  

• $$\frac{22}{4}$$  

• $$\frac{22}{6}$$  

Multiple Choice

Evita lives 0.85 mile from her school. Write this distance as a fraction in simplest form.

• 17/20 mi

• 85/100 mi

• 85/1000

• 8 1/2

Multiple Choice

A catepillar is 1 3/8 inches and can have as many as 4,000 muscles, compared to humans, who have about 600. Write the length of the caterpillar as a decimal.

• 1.38

• 1.375

• 1 375/1000

• 1.3

Multiple Choice

Julia spends $5.25 on gas for her lawn mower. She earns $24.00 mowing her neighbor’s yard. What is Julia’s profit?

• 18.75

• -18.75

• 29.75

• .29.75

Multiple Choice

Convert the Mixed Number to an Improper Fraction.  $$7\ \frac{2}{4}$$  

• $$\frac{28}{4}$$  

• $$\frac{30}{7}$$  

• $$\frac{30}{4}$$  

• $$\frac{23}{4}$$  

Multiple Choice

What are all of the factors of 12?

• 1 and 12

• 1, 2, 3, 4, & 6

• 1, 2, 3, 4, 6, & 12

• 1, 2, 3, 4, 6, 10, & 12

• 12, 24, 36, 48, 72 , 84...

Multiple Choice

Which pair of numbers have a GCF of 3?

• 15 and 27

• 20 and 30

• 45 and 15

• 9 and 18

Multiple Choice

Convert the Improper Fraction to a Mixed Number.  $$\frac{21}{5}$$  

• $$6\ \frac{1}{5}$$  

• $$4\ \frac{1}{4}$$  

• $$5\ \frac{1}{20}$$  

• $$4\ \frac{1}{5}$$  

Multiple Choice

Write 1.45% as a decimal.

• 0.145

• 1.45

• 0.0145

• 0.00145

Multiple Choice

Write the decimasl 9.35 as a fraction in simplest form.

• 9 35/100

• 187/20

• 9 7/20

• 0.935

Multiple Select

Select all the true statements about the Additive Identity.

• $$12+1=13$$

• $$21+0=21$$

• $$\left(-7\right)+0=\left(-7\right)$$

• $$15+15=30$$

• $$\left(-12\right)+12=0$$

Multiple Choice

The average length of a conch shell is 9.87 inches. Express as a mixed number in simplest form.

• 9 7/8

• 7 8/9

• 9 87/100

• 9 17/20

Multiple Choice

Multiply and simplify if possible.

• - ¹ / ₉

• ¹ / ₉

• - 9

• 9

Multiple Choice

The temperature of a substance is -16.6 °C. During an experiment, the temperature of the substance decreases 7.5 °C. What is the final temperature?

• 24.1

• -24.1

• 9.1

• -9.1

Multiple Choice

The price of one share of ABC Company declined a total of $65.25 in 5 days. What was the average change of the price of one share per day?

• -13.05

• 13.05

• -326.25

• 326.25

Multiple Choice

Write 0.6 as a percent.

• 6%

• 60%

• 0.6%

• 600%

Multiple Choice

Change this decimal to a percent: 
0.52

• 52%

• .52%

• 5.2%

• .052%

Multiple Choice

Peter hiked for 6 3/4 miles. After resting, Peter hiked back along the same route for 4 1/4 miles. How many more miles does Peter need to hike to return to the place where she started?

• 2 1/2

• -2 1/2

• -11

• 11

Multiple Choice

Find the sum.  Be sure to simplify the answer, if needed. $$3\ \frac{5}{16}+2\ \frac{3}{4}$$  

• $$6\ \frac{5}{6}$$  

• $$5\ \frac{2}{5}$$  

• $$5\ \frac{11}{16}$$  

• $$6\ \frac{1}{16}$$  

Multiple Choice

Your Turn:

$$-30\div-15=$$  

• -2

• 2

• 3

• -3

Multiple Choice

What is the sum of 1.70+4.65?

• 2.95

• 5.35

• 6.35

• a decimal

Multiple Choice

solve 

• - 2/9

• - 5/9 

• 2/9

• no there

Multiple Choice

What is the simplified value of the expression below?

-2.6 + 5.8

• -8.4

• -3.2

• 3.2

• 8.4

Multiple Choice

What is the difference of –96.43 – (–98.67)?

• –195.1

• –2.24

• 2.24

• 195.1

Multiple Choice

7.9 - 3.47=

• 11.37

• 4.43

• 3.32

• 4.37

Multiple Choice

-0.03 - (-0.18) =

• -0.21

• -0.15

• 0.21

• 0.15

Multiple Choice

Anusha brings a $20 bill to the store. She purchases 4 pairs of socks for $2.25 each and a new belt for $7.50. How much change will Anusha receive when she pays for her clothes?

• $3.50

• $7.50

• $9.00

• $16.50

Multiple Choice

Solve the expression:
$19-\left(-0.5\right)$

• $$19.5$$

• $$18.5$$

• $$-19.5$$

• $$-18.5$$

Multiple Choice

Solve the expression: $$\frac{1}{2}\left(0.75\right)$$  

• $$\frac{3}{8}$$  

• $$\frac{0.75}{2}$$  

• $$\frac{4}{6}$$  

Multiple Choice

Solve the expression:
$-9\times2.2$

• $$19.8$$

• $$-198$$

• $$198$$

• $$-19.8$$

Multiple Choice

Solve the expression:
$\frac{-33}{1.1}$

• $$-3$$

• $$30$$

• $$-30$$

• $$3$$

Multiple Choice

Divide these fractions

• $$\frac{8}{2}$$

• $$\frac{54}{4}$$

• $$13\frac{1}{2}$$

• $$13\frac{2}{4}$$

Multiple Choice

$$5\frac{3}{4}\times\frac{1}{4}=?$$  

• $$\frac{23}{16}$$  

• $$1\frac{7}{16}$$  

• $$\frac{15}{16}$$  

Multiple Choice

Sharon wants to make cookies for her class bake sale. She found a recipe that calls for 2/3 cups of flour for each batch of cookies. How many batches can she make using 12 cups of flour?

• 12

• 18

• 6

• 4

Multiple Choice

The price of Quiktrip stock dropped a total of $372.33 over a 7 day period.  The stock dropped the same amount each day.  What amount did they lose each day? (hint : amount should be negative)

• -$53.19

• -$5.32

• $53.19

• -$365.33

Multiple Choice

On Tuesday in Washington D.C. the temperature at 8am was  -8 degrees.  At 1pm, it was 27 degrees.  By how many degrees did the temperature change from morning to evening?

• 21

• -35

• 35

• 19

Multiple Choice

Ella played a math game and had five cards shown. Her score was the sum of the numbers on these five cards. What was Ella's score?

• 3

• 23

• -5

• 10

Multiple Choice

Julie walks 10 dogs a week and gets paid $4.25 for each dog. How much money does she make in one week?

• $42.50

• $442.50

• $425.00

• $3.50

Multiple Choice

If a plant grows 1/4 cm every day for 21 days, what is the total amount of growth?

• 82 cm

• 25 cm

• 17 1/4 cm

• 5 1/4 cm

Multiple Choice

A jug of orange juice contains 40.75 fluid ounces. It is shared equally among 5 people. How many ounces of orange juice does each person receive?

• 81.45 fl. oz.

• 203.75 fl. oz.

• 20.75 fl. oz.

• 8.15 fl. oz.

Multiple Choice

Change the improper fraction to a mixed number.

• 1     1/10

• 2      1/2

• 2     2/5

• 2      1/4

Multiple Choice

Penny and her cousins each have a different bank balance. What is the sum of all the accounts?

• -3

• 7

• -2

• 4

Multiple Choice

Which expression best represents the model?

• -10 x 5

• 5 x -2

• -2 x -5

• -10 x 2

Multiple Choice

A scuba diver is swimming at a depth of -12 feet. She dives down to five times the depth. What is her depth now?

• -7 feet

• -60 feet

• -17 feet

• 60 feet

Multiple Choice

Four equations are listed above. Which is NOT true?

Multiple Choice

What is the rule for adding integers with different signs?

• Negative plus negative = positive

• Add and keep the sign of the bigger number

• Subtract and keep the sign of the number with the greater absolute value

• Positive plus negative = negative

Multiple Choice

What is the rule for subtracting integers?

• Keep the first number the same and add the second number

• Keep the first number the same and add the opposite of the second number

• Keep the first number the same and subtract the opposite of the second number

• Subtracting will always result in a negative answer

Multiple Choice

Which is NOT true when multiplying or dividing integers?

• Two negatives = positive

• Two positives = negative

• A negative and a positive = negative

• Two positives - positive

Multiple Choice

At midnight, the temperature was 30 degrees. By 6:00 a.m, it had dropped 5 degrees, and by noon, it had increased by 11 degrees. What was the temperature at noon? 

• 36 degrees

• 27 degrees

• 39 degrees

• 16 degrees

Multiple Choice

The temperature drops 2°F each hour. What is the total change in temperature after 12 hours?

• -24

• 26

• 24

• -26