represent and find the number of equal - sized parts
1 model with mathematics the visual model represents (3div\frac{1}{6}). write a division equation that represents the visual model.
2 use tools draw a visual model to represent the expression. then find the quotient. (2div\frac{1}{5})
3 (4div\frac{1}{4})
4 stem earth and mars orbit the sun. each time earth makes one complete orbit, mars makes about (\frac{1}{2}) of its orbit. how many orbits does earth make around the sun in the time it takes mars to complete 6 orbits?
5 model with mathematics kat uses (\frac{1}{2}) gallon of water each day on a camping trip. her water jug holds 5 gallons of water. how many days will kat have water to use if she fills her water jug completely before leaving? draw a visual model to solve the problem. write a division equation to model the problem.
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lesson 10.4
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Question

Accepted Answer

### Problem 2: $ 2 \div \frac{1}{5} $
# Explanation:
## Step 1: Recall the rule for dividing by a fraction
Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of $ \frac{1}{5} $ is $ 5 $. So, $ 2 \div \frac{1}{5}=2\times5 $.
## Step 2: Perform the multiplication
$ 2\times5 = 10 $.
# Answer:
$ 10 $

### Problem 3: $ 4 \div \frac{1}{4} $
# Explanation:
## Step 1: Use the division - fraction rule
When dividing by a fraction $ \frac{a}{b} $, we multiply by $ \frac{b}{a} $. For $ 4\div\frac{1}{4} $, the reciprocal of $ \frac{1}{4} $ is $ 4 $, so $ 4\div\frac{1}{4}=4\times4 $.
## Step 2: Calculate the product
$ 4\times4 = 16 $.
# Answer:
$ 16 $

### Problem 4:
# Explanation:
## Step 1: Determine the number of Earth's orbits Mars makes
We know that Mars makes $ \frac{1}{2} $ of an Earth's orbit. Let the number of Earth's orbits Mars makes be $ x $. We want to find $ x $ when the total orbits (in terms of Mars' time) is 6. So we set up the equation $ x\times\frac{1}{2}=6 $ (or we can think of it as dividing 6 by $ \frac{1}{2} $ since we want to find how many $ \frac{1}{2} $ - orbits are in 6 orbits).
## Step 2: Solve for $ x $
Using the rule of dividing by a fraction, $ 6\div\frac{1}{2}=6\times2 $.
## Step 3: Calculate the result
$ 6\times2 = 12 $. So Earth makes 12 orbits in the time Mars makes 6 orbits.
# Answer:
12

### Problem 5:
# Explanation:
## Step 1: Set up the division equation
Kat has 5 gallons of water and uses $ \frac{1}{2} $ gallon per day. To find the number of days $ d $, we divide the total amount of water by the amount used per day. So the equation is $ d = 5\div\frac{1}{2} $.
## Step 2: Use the fraction division rule
Dividing by $ \frac{1}{2} $ is the same as multiplying by 2. So $ 5\div\frac{1}{2}=5\times2 $.
## Step 3: Calculate the number of days
$ 5\times2 = 10 $.
# Answer:
10 (The division equation is $ 5\div\frac{1}{2}=10 $)

### Problem 1:
# Explanation:
## Step 1: Analyze the visual model
The visual model has 3 groups, each representing 1 (or 6 sixths, since each small part is $ \frac{1}{6} $ and there are 6 small parts in each group). We are dividing 3 by $ \frac{1}{6} $.
## Step 2: Write the division equation
From the model, the division equation is $ 3\div\frac{1}{6} $.
## Step 3: Solve the equation (optional, but to check)
Using the rule of dividing by a fraction, $ 3\div\frac{1}{6}=3\times6 = 18 $. The visual model represents this because each of the 3 groups has 6 parts of size $ \frac{1}{6} $, so in total there are $ 3\times6 = 18 $ parts of size $ \frac{1}{6} $, which is equivalent to dividing 3 by $ \frac{1}{6} $.
# Answer:
The division equation is $ 3\div\frac{1}{6} $ (and the quotient is 18)

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QUESTION IMAGE

Question

Explanation:

Problem 2: \( 2 \div \frac{1}{5} \)

Step 1: Recall the rule for dividing by a fraction

Step 2: Perform the multiplication

Step 1: Use the division - fraction rule

Step 2: Calculate the product

Step 1: Determine the number of Earth's orbits Mars makes

Step 2: Solve for \( x \)

Step 3: Calculate the result

Answer:

Problem 3: \( 4 \div \frac{1}{4} \)