Math / Numbers & Operations

QuestionCopy and complete the workings below to calculate $\frac{1}{10} \div 6 \frac{1}{3}$
Give your answer as a fraction in its simplest form. $\begin{aligned} \frac{1}{10} \div 6 \frac{1}{3} & =\frac{1}{10} \div \frac{19}{3} \\ & =\frac{1}{10} \times \frac{\square}{\square} \\ & =\frac{1 \times \square}{10 \times \square} \\ & =\frac{\square}{\square} \end{aligned}$

Studdy Solution

STEP 1

What is this asking? We need to divide one tenth by six and one-third, and give the answer as a simplified fraction. Watch out! Remember to flip the second fraction when dividing and always simplify your final answer!

STEP 2

1. Convert the mixed number to an improper fraction.
2. Divide the fractions.
3. Simplify the result.

STEP 3

Alright, let's rewrite that mixed number $6\frac{1}{3}$ as an improper fraction.
Remember, a mixed number is a whole number plus a fraction.
To convert it, we multiply the whole number ( $6$ ) by the denominator of the fraction ( $3$ ), and then add the numerator ( $1$ ).
This gives us $6 \cdot 3 + 1 = 18 + 1 = \textbf{19}$ .
This becomes our new numerator, and we keep the same denominator ( $3$ ).
So, $6\frac{1}{3}$ is the same as $\frac{\textbf{19}}{3}$ !

STEP 4

Now, we're dividing $\frac{1}{10}$ by $\frac{19}{3}$ .
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of a fraction is just flipping it upside down!
So, the reciprocal of $\frac{19}{3}$ is $\frac{3}{19}$ .

STEP 5

Let's rewrite our division problem as a multiplication problem: $\frac{1}{10} \div \frac{19}{3} = \frac{1}{10} \cdot \frac{3}{19}$

STEP 6

Now, we multiply the numerators together and the denominators together: $\frac{1}{10} \cdot \frac{3}{19} = \frac{1 \cdot 3}{10 \cdot 19} = \frac{3}{190}$

STEP 7

Let's see if we can simplify $\frac{3}{190}$ .
Since $3$ is a prime number and doesn't divide $190$ , this fraction is already in its simplest form!
Awesome!

STEP 8

Our final answer is $\frac{3}{190}$ .

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Studdy Solution

STEP 1

What is this asking? We need to divide one tenth by six and one-third, and give the answer as a simplified fraction. Watch out! Remember to flip the second fraction when dividing and always simplify your final answer!

STEP 2

1. Convert the mixed number to an improper fraction.
2. Divide the fractions.
3. Simplify the result.

STEP 3

STEP 4

Now, we're dividing $\frac{1}{10}$ by $\frac{19}{3}$ .
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of a fraction is just flipping it upside down!
So, the reciprocal of $\frac{19}{3}$ is $\frac{3}{19}$ .

STEP 5

Let's rewrite our division problem as a multiplication problem: $\frac{1}{10} \div \frac{19}{3} = \frac{1}{10} \cdot \frac{3}{19}$

STEP 6

Now, we multiply the numerators together and the denominators together: $\frac{1}{10} \cdot \frac{3}{19} = \frac{1 \cdot 3}{10 \cdot 19} = \frac{3}{190}$

STEP 7

Let's see if we can simplify $\frac{3}{190}$ .
Since $3$ is a prime number and doesn't divide $190$ , this fraction is already in its simplest form!
Awesome!

STEP 8

Our final answer is $\frac{3}{190}$ .

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Studdy Solution

STEP 1

What is this asking? We need to divide one tenth by six and one-third, and give the answer as a simplified fraction. Watch out! Remember to flip the second fraction when dividing and always simplify your final answer!

STEP 2

1. Convert the mixed number to an improper fraction.2. Divide the fractions.3. Simplify the result.

STEP 3

STEP 4

Now, we're dividing 110\frac{1}{10}101​ by 193\frac{19}{3}319​.Remember, dividing by a fraction is the same as multiplying by its reciprocal.The reciprocal of a fraction is just flipping it upside down!So, the reciprocal of 193\frac{19}{3}319​ is 319\frac{3}{19}193​.

STEP 5

Let's **rewrite** our division problem as a multiplication problem: 110÷193=110⋅319 \frac{1}{10} \div \frac{19}{3} = \frac{1}{10} \cdot \frac{3}{19} 101​÷319​=101​⋅193​

STEP 6

Now, we **multiply** the numerators together and the denominators together: 110⋅319=1⋅310⋅19=3190 \frac{1}{10} \cdot \frac{3}{19} = \frac{1 \cdot 3}{10 \cdot 19} = \frac{3}{190} 101​⋅193​=10⋅191⋅3​=1903​

STEP 7

Let's see if we can **simplify** 3190\frac{3}{190}1903​.Since 333 is a prime number and doesn't divide 190190190, this fraction is already in its simplest form!Awesome!

STEP 8

Our final answer is 3190\frac{3}{190}1903​.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. Convert the mixed number to an improper fraction.
2. Divide the fractions.
3. Simplify the result.

Now, we're dividing $\frac{1}{10}$ by $\frac{19}{3}$ .
Remember, dividing by a fraction is the same as multiplying by its reciprocal.
The reciprocal of a fraction is just flipping it upside down!
So, the reciprocal of $\frac{19}{3}$ is $\frac{3}{19}$ .

Let's rewrite our division problem as a multiplication problem: $\frac{1}{10} \div \frac{19}{3} = \frac{1}{10} \cdot \frac{3}{19}$

Now, we multiply the numerators together and the denominators together: $\frac{1}{10} \cdot \frac{3}{19} = \frac{1 \cdot 3}{10 \cdot 19} = \frac{3}{190}$

Let's see if we can simplify $\frac{3}{190}$ .
Since $3$ is a prime number and doesn't divide $190$ , this fraction is already in its simplest form!
Awesome!

Our final answer is $\frac{3}{190}$ .