Primer: Fraction Operations (V2 Interactive Version)

🎯 Goal

Stop passive reading.

Hunt for the mathematical clues hidden throughout the guide to complete each task.

All answers are hidden at the very end of the guide so you can check your work later.

Flipping Flashcards First

Click Here to Open Quizlet

Flip through your flashcard set before starting and again after finishing your primer.

🔍 HUNTING ZONE A — Adding & Subtracting

The Matching Law & Vertical Rule

1. Simple Fractions (The Common Denominator Rule)

You cannot add or subtract fractions unless the denominators match.

If they don't match, multiply the numerator and denominator of each fraction to create a common denominator.

Example:

\frac12+\frac13 \rightarrow \frac{1\times3}{2\times3} + \frac{1\times2}{3\times2} \rightarrow \frac36+\frac26 = \frac56

🧗 Reese Scavenger Task 1 — Simple Match

Look at the problem

\frac25+\frac14

Question 1A

Do these denominators match?

👉 Answer: [ A ] (this connects back to your answer key at the bottom)

Action 1B

Write the common denominator your brain must create before solving.

👉 Target Denominator: [ B ]

2. Mixed Numbers (The Vertical Borrowing Rule)

When subtracting mixed numbers:

🚫 Never work sideways.

Always stack the numbers vertically.

If the top numerator is too small, borrow 1 whole from the whole number.

That one whole becomes a matching fraction such as

\frac44,\quad \frac55,\quad \frac77

depending on the denominator.

🧗 Reese Scavenger Task 2 — The Mixed Borrow

Study the regrouping below.

4\frac15 \rightarrow 3+\frac55+\frac15 \rightarrow 3\frac65

Question 2A

Where did the extra $\frac55$ come from? 👉 Answer [C]

Action 2B

Fill in the missing numerator.

\begin{array}{rcl} 6\frac27 &\rightarrow& 5\frac{[\ D\ ]}{7}\\\\ -2\frac57&&-2\frac57 \end{array}\\---- \space \space\space----

🔍 HUNTING ZONE B — Multiplication

Straight Across & Cross-Simplifying

1. Simple Fractions (The Direct Line Rule)

Multiplication is the easiest fraction operation because you do not need common denominators.

Simply multiply:

top × top
bottom × bottom

Example

\frac23\times\frac57 = \frac{2\times5}{3\times7} = \frac{10}{21}

Before multiplying, always check diagonally to see whether you can cross-simplify.

Keeping numbers small makes the problem much easier.

🧗 Reese Scavenger Task 3 — Direct Line Check

Look at

\frac34\times\frac52

Question 3A

Do you need a common denominator?

👉 Answer: [ E ]

Action 3B

Multiply straight across.

What is the numerator before simplifying?

👉 Top Numerator: [ F ]

2. Mixed Numbers (The Improper Mandate)

🚫 Critical Law

You may never multiply or divide while numbers are still mixed numbers.

Always convert them into improper fractions first.

Use the Circle Method:

Bottom × Whole + Top

🧗 Reese Scavenger Task 4 — The Circle Hack

Study the example

\frac94\times\frac23

Question 4A

Look diagonally at 9 and 3.

What number can both divide by?

👉 Answer: [ G ]

Action 4B

Use the Circle Method.

Fill in the missing numerator.

2\frac34 = \frac{[\ H\ ]}{4}

🔍 HUNTING ZONE C — Division

The Reciprocal Override

You never actually divide fractions.

Instead, use Keep • Change • Flip (KCF)

Keep the first fraction.
Change division into multiplication.
Flip the second fraction into its reciprocal.

🧗 Reese Scavenger Task 5 — The Override Run

Study the division problem

\frac52\div\frac34

Question 5A

True or False:

You should first find a common denominator.

👉 Answer: [ I ]

Question 5B

According to Keep • Change • Flip,

what happens to

\frac34

👉 Answer

It flips into its reciprocal:

[ J ]

Action 5C

Rewrite the division problem as multiplication.

\frac52 \div \frac34 \rightarrow \frac52 \times \frac{[\ K\ ]}{[\ L\ ]}

🚀 STEP 2 — WATCH & WRITE 3 SENTENCE SUMMARY OF EACH

🎯 STEP 3 — INDEPENDENT CLEARANCE CHECK

Show all of your work in the spaces provided.

Do not check the Answer Vault until you have finished every question.

1. Find a Common Denominator and Solve

\frac13+\frac25 = \underline{\qquad\qquad\qquad}

2. Stack and Subtract

Show the borrow step.

5\frac14-2\frac34

\begin{array}{r} [\quad]\frac{[\quad]}{4}\\ -2\frac34\\ \hline \end{array}

Final Value

\underline{\qquad\qquad\qquad}

3. Multiply Straight Across

Cross-simplify first!

\frac43\times\frac92 = \underline{\qquad\qquad\qquad}

4. Convert to an Improper Fraction

4\frac23 = \frac{[\quad]}3

5. Execute Keep • Change • Flip

\frac75\div\frac{14}{10} = \underline{\qquad\qquad\qquad}

🕵️‍♂️ THE ANSWER VAULT

(Student Self-Check Only — Don't Peek Early!)

🔑 Scavenger Hunt Clue Key

Clue	Answer
A	No
B	20
C	4
D	9 (because one whole becomes $\frac77$ , then $\frac77+\frac27=\frac97$ )
E	No
F	15
G	3
H	11 (because $4\times2+3=11$ )
I	False
J	$\frac43$
K / L	$\frac43$

✅ Step 3 Clearance Check Key

1.

\frac{5}{15}+\frac{6}{15} = \boxed{\frac{11}{15}}

2.

4\frac54-2\frac34 = \boxed{2\frac24} = \boxed{2\frac12}

3.

Cross-simplify first.

$4$ and $2$ simplify to $2$ and $1$
$9$ and $3$ simplify to $3$ and $1$

Then multiply:

\frac21\times\frac31 = \boxed6

4.

4\frac23 = \boxed{\frac{14}{3}}

5.

\frac75 \div \frac{14}{10} = \frac75 \times \frac{10}{14}

Cross-simplify diagonally.

\frac11\times\frac22 = \boxed1