Solving Rational Fractions

​Solving Rational Fractions

Standard

NC.7.NS.2 - Apply and extend previous understandings of multiplication and division.

• A. Understand that a rational number is any number that can be written as a quotient of integers with a non-zero divisor. 

• B. Apply properties of operations as strategies, including the standard algorithms, to multiply and divide rational numbers and describe the product and quotient in real-world contexts. 

• C. Use division and previous understandings of fractions and decimals. 

Learning Targets:

• SWBAT multiply and divide rational numbers

• SWBAT recall how to multiply and divide fractions

Open Ended

Recall: how do we multiply fractions?

Multiple Choice

Solve: $$\frac{7}{9}\ \cdot\ \frac{3}{7}$$ . Your answer should be in simplist form.

• $$\frac{1}{3}$$  

• 7

• $$\frac{3}{9}$$  

• 1

Open Ended

Recall: how do we divide fractions?

Multiple Choice

Divide. 5/3 ÷ 15/7

• 3  4/7

• 7/9

• 7/15

• 2  2/15

~To multiply fractions you do NOT need common denominators.

~Your mixed numbers must be converted to improper fractions before you begin. ~You will want to cross simplify before you multiply.

~Multiply the numerator by the numerator and the denominator by the denominator.

~Follow integer multiplication rules for fractions that contain negatives and positives.

​

​Multiplying rational fractions

​Example 1

Subject | Subject

​Example 2

Subject | Subject

​Example 3

Subject | Subject

Multiple Choice

Example 3: $$-\frac{45}{46}\ \cdot\ \frac{23}{25}$$ (hint: see if you can cross simplify)

• $$-1\ \frac{4}{5}$$

• $$\frac{9}{10}$$

• $$-\frac{9}{10}$$

• $$\frac{68}{71}$$

Fill in the Blanks

Example 4: $-2\ \frac{5}{6}\ \cdot\ \frac{3}{10}$

~To divide fractions you do NOT need common denominators.

~Your mixed numbers must be converted to improper fractions before you begin.

~Keep (the first fraction), change (÷ to •), flip (the second fraction)

~You will want to cross simplify before you multiply.

~Multiply the numerator by the numerator and the denominator by the

denominator.

~Follow integer multiplication rules for fractions that contain negatives and

​

​Dividing Rational Fractions

​Example 1:

Subject | Subject

​Example 2:

Subject | Subject

Multiple Choice

$$1\ \frac{1}{2}\ \div\ \left(-\frac{5}{6}\right)$$

• $$-1\ \frac{4}{5}$$

• $$-1\ \frac{1}{4}$$

• $$-\frac{3}{7}$$

• $$-\frac{5}{9}$$

Fill in the Blanks

$-3\ \frac{1}{5}\ \div\ 1\ \frac{1}{4}$ (Leave answer as improper fraction)

Poll

On a scale from 1 to 4 (with 4 being the best) how do you feel about this topic

• 1

• 2

• 3

• 4

Multiple Choice

Multiply. Write your answer in simplest form.

• 27/40

• -27/40

• 5/6

• -5/6

Multiple Choice

Multiply. Write fractions in simplest form.

$$2\frac{2}{3}\times\left(-4\frac{1}{4}\right)$$   

• $$-11\frac{1}{3}$$   

• $$\frac{34}{3}$$   

• $$-8\frac{3}{12}$$   

• $$-8\frac{1}{4}$$   

Multiple Choice

Evaluate and simplify (reduce): $$3\frac{3}{4}\cdot\frac{1}{2}=$$  

• $$\frac{27}{8}$$  

• $$\frac{15}{8}$$  

• $$\frac{30}{4}$$  

• $$\frac{15}{2}$$  

Multiple Choice

Simplify the expression: $$-15\ \div\ \frac{10}{11}$$  

• $$-16\ \frac{1}{2}$$  

• $$16\ \frac{1}{2}$$  

• $$-13\ \frac{7}{11}$$  

• $$13\ \frac{7}{11}$$  

Multiple Choice

Divide

• 1

• 6/11

• 6/5

• 11/5

Multiple Choice

^-1/₄  ÷  ²/₅

• ^-5/₈

• -2/20

• ^-1/₁₀

• ^-3/₉