Classifying Rational Numbers

T1/1.5 Test Review

by Matthew Mills

​Classifying Real Numbers

​The Natural numbers are 1, 2, 3... 500, 501, 502... 12,000,000...

• ​they keep going as high as you can count.

​

​The Whole numbers are the Natural numbers and 0.

• ​some square roots are included

​

​The Integers are both positive and negative whole numbers.​

• ​...-2, -1, 0, 1, 2, ...

​All of the above you are able to write without a fraction/decimal.

​Classifying Real Numbers

​​The Rational numbers can be written as a fraction or decimal

• ​Repeating decimals are included since they can be written as fractions

• ​Natural, whole, and integers are included.

Irrational numbers don't stop and don't repeat.

• ​most square roots, pi are included.

Multiple Choice

$$\sqrt[]{13}$$  

• Irrational

• Rational

• Natural

• Integer

Multiple Choice

$$\sqrt[]{100}$$  

• Irrational

• Rational

• Natural

• Integer

Multiple Choice

$$13.5$$  

• Irrational

• Rational

• Natural

• Integer

Multiple Choice

$$\frac{14}{9}$$  

• Irrational

• Rational

• Natural

• Integer

Multiple Choice

$$0$$  

• Whole

• Rational

• Natural

• Integer

Multiple Choice

$$3\pi$$  

• Whole

• Rational

• Irrational

• Integer

​Compare and Order Real Numbers

Can we convert a mixed number into a fraction? A fraction into a decimal?

​

​Can we simplify a fraction?

​

​Can we compare which numbers are smaller/larger?

​

​Can we put numbers in order from smallest to largest?

​

Multiple Choice

Write your answer as a mixed number

$$\frac{13}{4}$$  

• 9

• $$3\ \frac{1}{4}$$  

• 6.5

• $$3\ \frac{1}{2}$$  

Multiple Choice

Write your answer as a decimal

$$\frac{13}{4}$$  

• 3.2

• $$3\ \frac{1}{4}$$  

• 3.5

• 3.25

Multiple Choice

$$3.3333\ \ \ \ \ ?\ \ \ \ \ 3\ \frac{3}{10}$$  

• <

• =

• >

Multiple Choice

$$\frac{9}{7}\ \ \ \ \ \ ?\ \ \ \ \ \ \frac{8}{3}$$  

• <

• =

• >

Multiple Choice

$$\frac{12}{2}\ \ \ \ \ \ ?\ \ \ \ \ \ \sqrt[]{36}$$  

• <

• =

• >

Multiple Choice

Which is the correct order from small to big?

$$\sqrt[]{9},\ \frac{12}{3},\ -4.5,\ \pi$$  

• $$-4.5,\ \sqrt[]{9},\ \pi,\ \frac{12}{3}$$  

• $$\frac{12}{3},\ \pi,\ \sqrt[]{9},\ -4.5$$  

• $$\pi,\ \sqrt[]{9},\ -4.5,\ \frac{12}{3}$$  

​Adding and Subtracting Rational Numbers

​With fractions, we only add/subtract the numerator (top)

​

​With fractions, the denominator (bottom) must be the same number.

​

​Mixed numbers, you can make them into improper fractions first.

Multiple Choice

$$\frac{3}{10}+\frac{4}{10}$$  

• 7

• $$\frac{7}{10}$$  

• $$\frac{7}{20}$$  

• $$13\ +\ 14\$$  

Multiple Choice

$$\frac{12}{20\ }-\frac{4}{20}$$  

• $$\frac{2}{5}$$  

• $$\frac{8}{0}$$  

• $$8-16$$  

• $$\frac{16}{20}$$  

Multiple Choice

$$4\ \frac{2}{3}+1\ \frac{2}{3}$$  

simplify completely

• $$5\ \frac{4}{3}$$  

• $$6\ \frac{1}{3}$$  

• $$5\ \frac{4}{6}$$  

Multiple Choice

$$\frac{1}{3}+\ \frac{2}{5}$$  

• $$\frac{11}{15}$$  

• $$\frac{3}{15}$$  

• $$\frac{3}{8}$$  

Multiple Choice

$$2\ \frac{2}{3}-1\ \frac{1}{6}$$  

• $$1\ \frac{1}{3}$$  

• $$1\ \frac{3}{9}$$  

• $$1\ \frac{1}{2}$$  

​Multiply and Divide Fractions

​When we multiply, it's top times the top and bottom times the bottom

​

​When we divide, KEEP CHANGE FLIP

Multiple Choice

simplify

$$\frac{2}{3}\times\frac{4}{3}$$  

• $$6\ x\ 12\ =\ 72$$  

• $$\frac{8}{9}$$  

• $$\frac{6}{6}=1$$  

• $$\frac{6}{3}=2$$  

Multiple Choice

$$1\ \frac{1}{2}\times\frac{1}{4}$$  

• $$\frac{1}{8}$$  

• $$1\ \frac{2}{6}$$  

• $$1\ \frac{1}{8}$$  

• $$\frac{3}{8}$$  

Multiple Choice

Which is the correct KEEP CHANGE FLIP?

$$\frac{1}{2}\div3$$  

• $$2\times\frac{1}{3}$$  

• $$2\times3$$  

• $$\frac{1}{2}\times\frac{1}{3}$$  

• $$\frac{1}{2}\times3$$  

Multiple Choice

$$4\div\frac{1}{4}$$  

• 1

• 16

• $$\frac{1}{16}$$  

Multiple Choice

$$\frac{1}{5}\div2\ \frac{1}{3}$$  

• $$\frac{3}{35}$$  

• $$\frac{7}{15}$$  

• $$\frac{6}{5}$$