7.NS.A.3 Operations with Rational Numbers

Operations with Rational Numbers

7th Grade Math

Let's Remember our Rules

Operations with Rational Numbers

DECIMALS​

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​ADDING AND SUBTRACTING DECIMALS

• ​LINE UP YOUR DECIMALS

First you line up the decimals then add.​

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​Some text here about the topic of discussion.

Adding Decimals​

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You line up the decimals and subtract.​

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​Some text here about the topic of discussion.

Subtracting Decimals​

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Add (+) or Subtract (-) with Decimal

• Find the decimal

• Line up the decimals

• Fill in the empty spots with zero

• Add or Subtract

• Bring down the decimal in your answer

Multiplying ( × ) with Decimals

• The number with the most digits goes on top

• Decimals do not line up

• Multiply like normal

• Count how many places in the first number (top) the decimal is moved over

• Count how many places in the 2nd number (bottom) the decimal is moved over

• The total number of places moved in the 1st and 2nd number is how many places you move the decimal in your answer

Multiple Choice

When you multiply two decimal numbers, you line up the digits not the decimal points.

• True

• False

Dividing (÷) with Decimals

• Divisor cannot have a decimal

• Move the divisor decimal so it is a whole number

• Move the same amount of places in the dividend

• Place a decimal straight up where you write your answer 

• Divide like normal

• **When the divisor has no decimal but the dividend does, just move the decimal up and divide normally.

Multiple Choice

When you add two decimal numbers, you do not need to line up the decimal points.

• True

• False

Multiple Choice

When you divide two decimal numbers, the divisor cannot have a decimal.

• True

• False

​MUTLIPLYING DECIMALS

• ​IGNORE THE DECIMALS

• ​THEN, COUNT THE DECIMALS TO THE RIGHT OF EACH FACTOR

Multiple Choice

7.32 + (-180.6)

• -183.32

• 173.28

• -173.28

• -187.92

Multiple Choice

4.65 - (-32.5)

• -37.15

• 27.85

• 37.15

• -27.85

Multiple Choice

$$-4.6\times\left(-2.73\right)$$  

• 12.558

• -12.558

• -12.5580

• 12.5580

​DIVIDING DECIMALS

• YOUR DIVISOR CANNOT BE A DECIMMAL​

• ​IF YOU MOVE THE DECIMAL IN THE DIVISOR, YOU MUST MOVE THE DECIMAL IN THE DIVIDEND THE SAME NUMBER OF PLACES

Match

Match the following fraction with the reciprocal

• 1/6

• 3/4

• 2/7

• 9/10

• 3/8

6

4/3

7/2

10/9

8/3

• 6

• 4/3

• 7/2

• 10/9

• 8/3

Multiple Choice

$$37.5\div2.5$$  

• 0.15

• 1.5

• 15

• 150

​FRACTIONS

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​ADDING AND SUBTRACTING FRACTIONS

• YOU MUST HAVE THE SAME DENOMINATOR​

Multiple Choice

$$-\frac{5}{6}+\left(-\frac{4}{9}\right)$$  

• $$-1\frac{5}{18}$$  

• $$1\frac{5}{18}$$  

• $$-\frac{23}{18}$$  

• $$-\frac{9}{15}$$  

Multiple Choice

$$-\frac{3}{7}-\left(-\frac{5}{14}\right)$$  

• $$\frac{11}{14}$$  

• $$-\frac{11}{14}$$  

• $$\frac{1}{14}$$  

• $$-\frac{1}{14}$$  

​MULTIPLYING FRACTIONS

• ​JUST MULTIPLY ACROSS

• ​YOU DO NOT NEED TO HAVE COMMON DENOMINATORS

Multiple Choice

Solve:

$$\frac{2}{5}\cdot\frac{5}{4}$$  

• $$\frac{10}{20}$$  

• $$\frac{7}{9}$$  

• $$\frac{1}{2}$$  

What if there is a whole number?

• A whole number can be written as a fraction by putting it over 1

• Remember, anything divided by 1 is itself!

Multiple Choice

Solve:

$$5\ \cdot\frac{2}{3}$$  

• $$\frac{10}{3}$$  

• $$\frac{15}{2}$$  

• $$5\ \frac{2}{3}$$  

What if there is a mixed number?

• Big C

• Multiple the denominator by the integer (whole number), then add the numerator

• Denominator stays the same

• Draw it out!

Multiple Choice

Which fraction is equal to

$$7\ \frac{3}{5}$$  

• $$\frac{21}{35}$$  

• $$\frac{21}{5}$$  

• $$\frac{38}{5}$$  

What if I need to simplify?

Multiple Choice

Which fraction is equal to

$$7\ \frac{3}{5}$$  

• $$\frac{21}{35}$$  

• $$\frac{21}{5}$$  

• $$\frac{38}{5}$$  

Multiple Choice

$$-\frac{3}{5}\times\left(-\frac{7}{6}\right)$$  

• $$\frac{21}{30}$$  

• $$-\frac{7}{10}$$  

• $$\frac{7}{10}$$  

• $$-\frac{21}{30}$$  

Multiple Choice

$$-1\frac{3}{5}\times3\frac{2}{6}$$  

• $$-5\frac{1}{3}$$  

• $$5\frac{1}{3}$$  

• $$-5\frac{5}{15}$$  

• $$5\frac{5}{15}$$  

​DIVIDING FRACTIONS

• ​KCF (KEEP, CHANGE, FLIP)

• ​CHANGE DIVISION TO MULTIPLICATION

• ​FLIP THE SECOND FRACTION TO ITS RECIPROCAL

Multiple Choice

5/6 $$\div$$  3/4 =

Divide the fractions. Simplify the answer.

• 15/24

• 20/18

• 10/9

• 18/24

Multiple Choice

6/7 $$\div$$  1/4

Divide the answer. Simplify the fraction.

• 24/7

• 6/28

• 3/14

• 7/24

Multiple Choice

8/3 $$\div$$  5/4

Divide the answer. Simplify the fraction.

• 15/32

• 32/15

• 3/14

• 7/24

Match

Match the following improper fractions to mixed numbers.

• 15/3

• 7/2

• 14/3

• 25/6

• 45/10

5

3 1/2

4 2/3

4 1/6

4 5/10

• 5

• 3 1/2

• 4 2/3

• 4 1/6

• 4 5/10