Unit 2 · Standard 6.NS.1
Divide Fractions
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
In 3/4 ÷ 1/2, the dividend is 3/4 — the total amount being split
Dividend
The number you are splitting up in a division problem.
In 3/4 ÷ 1/2, the divisor is 1/2 — the size of each group
Divisor
The number you split by in a division problem.
The reciprocal of 2/3 is 3/2. To divide by 2/3, multiply by 3/2.
Reciprocal
A fraction turned upside down.
In 3/4 ÷ 1/4 = 3, the quotient is 3 — three 1/4-size pieces fit into 3/4
Quotient
The answer when you divide.
8/12 → GCF is 4 → 8÷4 / 12÷4 = 2/3
Simplify
To make a fraction smaller using the same parts, like 2/4 = 1/2.
Key Ideas & Notes
- Agent Rivera is dividing a 3/4-pound evidence bag into portions that each weigh 1/8 pound.
- She needs to know exactly how many portions she can make for testing.
- Can you solve the case?
- Use the bar model to see how many 1/8-pound portions fit into 3/4 pound.
Think About It
- What is the total weight being divided?
- What is the size of each portion?
- Will the answer be more or less than 1?
My Notes
Guided Examples
Example 1
What is the reciprocal of 3/5?
Solution: To find the reciprocal, flip the fraction. The reciprocal of 3/5 is 5/3.
Answer: A. 5/3
Example 2
What is 1/2 ÷ 1/4?
Solution: 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. Two 1/4-size pieces fit into 1/2.
Answer: A. 2
Example 3
What is 3/4 ÷ 1/8?
Solution: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6. Six 1/8-size pieces fit into 3/4.
Answer: A. 6
Write About the Math The Writing Revolution
I can explain my steps using the words dividend, divisor, reciprocal, quotient, and simplify.
1. Kernel Sentence subject + verb
Model: Simplify is to make a fraction smaller using the same parts, like 2/4 = 1/2.Simplificar es hacer una fracción más pequeña con las mismas partes, como 2/4 = 1/2.
Write a kernel sentence about simplify. Use a subject and a verb.Escribe una oración base sobre simplificar. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Simplify matters in mathSimplificar importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Simplify matters in math because ___.Simplificar importa en matemáticas porque ___.
Simplify matters in math, but ___.Simplificar importa en matemáticas, pero ___.
Simplify matters in math, so ___.Simplificar importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about simplify.Di un hecho verdadero sobre simplify.
Simplify ___.
Ask a question about simplify.Haz una pregunta sobre simplify.
How does ___ ?¿Cómo ___ ?
Show excitement about simplify.Muestra entusiasmo sobre simplify.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with simplify.Dile a un compañero qué hacer con simplify.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I flipped the fraction because ___.Volteé la fracción porque ___.
The answer is ___.La respuesta es ___.
This helps when ___.Esto ayuda cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. What is 2/3 ÷ 1/3?
- 2
- 2/9
- 1/2
- 6
2. A recipe needs 2/3 cup of sugar. You only have a 1/6-cup scoop. How many scoops do you need?
- 4 scoops
- 3 scoops
- 6 scoops
- 2 scoops
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
Is 3/4 ÷ 1/2 the same as 1/2 ÷ 3/4? Solve both and explain why or why not. What does this tell you about the order in division?
Sentence starter: 3/4 ÷ 1/2 = ___ and 1/2 ÷ 3/4 = ___. These are ___ because ___. This shows that division is ___.
Reflect — Exit Ticket
What is 4/5 ÷ 2/5?
- 2
- 8/25
- 2/5
- 10/5
Answer Key & Teacher Guide
- Try It 1: A. 2 — 2/3 ÷ 1/3 = 2/3 × 3/1 = 6/3 = 2. Two 1/3-size pieces fit into 2/3.
- Try It 2: A. 4 scoops — 2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4 scoops.
- Exit Ticket: A. 2 — 4/5 ÷ 2/5 = 4/5 × 5/2 = 20/10 = 2. Two groups of 2/5 fit into 4/5.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Simplify is to make a fraction smaller using the same parts, like 2/4 = 1/2.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).