Podcast
Questions and Answers
What operation is equivalent to dividing by a fraction?
What operation is equivalent to dividing by a fraction?
- Adding the fraction to itself
- Dividing the fraction by itself
- Multiplying by the fraction's reciprocal (correct)
- Subtracting the fraction from itself
How can a whole number be rewritten as a fraction?
How can a whole number be rewritten as a fraction?
- Subtract it from 1
- Write it over 1 (correct)
- Divide it by 2
- Multiply it by a fraction
What is the first step in dividing mixed numbers?
What is the first step in dividing mixed numbers?
- Multiply the whole number by the denominator of the fraction part
- Turn them into improper fractions (correct)
- Find the common denominator
- Add the whole numbers together
When dividing mixed numbers and fractions, what should you do first?
When dividing mixed numbers and fractions, what should you do first?
What is the key idea when dividing with mixed numbers and fractions?
What is the key idea when dividing with mixed numbers and fractions?
What is the term for the number written in the form a/b, where a is the numerator and b is the denominator?
What is the term for the number written in the form a/b, where a is the numerator and b is the denominator?
When multiplying two fractions, what should be multiplied to create a new fraction?
When multiplying two fractions, what should be multiplied to create a new fraction?
What is another term for a mixed number?
What is another term for a mixed number?
What happens when you divide by a number?
What happens when you divide by a number?
Why can dividing fractions and mixed numbers be challenging?
Why can dividing fractions and mixed numbers be challenging?
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Study Notes
Dividing Fractions and Mixed Numbers
- A fraction is a number written in the form a/b, where a is the numerator and b is the denominator.
- Multiplying two fractions involves multiplying the numerators and denominators to create a new fraction.
- Dividing fractions is not as straightforward and can be confusing.
Dividing Fractions
- Dividing by a number is the same as multiplying by its reciprocal.
- Dividing by a fraction is the same as multiplying by its reciprocal.
- For example, dividing by 2 is the same as multiplying by 1/2.
- The strategy for dividing fractions is to multiply by the reciprocal of the divisor.
Examples of Dividing Fractions
- To divide a fraction, multiply by the reciprocal of the divisor.
- For example, ? = × =
- A whole number can be rewritten as a fraction, making it easier to perform the operation.
- For example, 2 = 2/1, making it easier to divide by a fraction.
Dividing Mixed Numbers
- A mixed number is a whole number plus a fraction, and can be converted into an improper fraction.
- To convert a mixed number to an improper fraction:
- Take the whole number and turn it into a fraction with denominator 1.
- Multiply the numerator and denominator of the whole number by the denominator of the fraction portion.
- Add the two fractions together.
Examples of Dividing Mixed Numbers
- To divide mixed numbers, convert them into improper fractions and then divide.
- For example, ? = ? =
- Convert the mixed numbers into fractions, then divide the fractions.
Division of Mixed Numbers and Fractions
- When both fractions and mixed numbers are involved, division can appear complicated.
- The process is the same as above: turn all mixed numbers into improper fractions and then divide the fractions.
- Divide mixed numbers and fractions by converting mixed numbers to improper fractions and then dividing using the reciprocal method.
Examples of Division of Mixed Numbers and Fractions
- To divide mixed numbers and fractions, convert the mixed numbers to improper fractions and then divide.
- For example, ? = ? =
- Convert the mixed number to a fraction, then divide the fractions.
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