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Multiply and Divide Mixed Numbers>
Multiply and Divide Mixed Numbers 2Multiply and Divide Mixed Numbers 2
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Question 1 of 5
1. Question
Multiply the following:`2 5/6xx1 1/3`Hint
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Correct!
Incorrect
Transforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ Transforming an Improper to Mixed Fraction
$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}=\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$`(``b``-:``c``)=``Q` and `R` is the remainderFirst, convert the mixed numbers into improper formMultiply the denominator by the whole number and then add it to the numerator$$\color{#00880A}{2}\frac{\color{#007DDC}{5}}{\color{#9a00c7}{6}}\times\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{6}\times\color{#00880A}{2})+\color{#007DDC}{5}}{\color{#9a00c7}{6}} \times \frac{(\color{#9a00c7}{3}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}$$ `=` `(12+5)/6 xx (3+1)/3` `=` `17/6 xx 4/3` Proceed with multiplying the fractions and then simplify.`17/6 xx 4/3` `=` `68/18` `=` $$\frac{68\color{#CC0000}{\div2}}{18\color{#CC0000}{\div2}}$$ Reduce to lowest terms `=` `34/9` Convert the fraction from improper to mixedStart by dividing the numerator by the denominatorArrange the numbers for long division
`9` goes into `34` three times. So write `3` above the line.
Multiply `3` to `9` and write the answer below `34`
Subtract `27` from `34` and write the answer one line below
Since `9` cannot go into `7` anymore, `7` is left as the Remainder and `3` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{34}}{\color{#9a00c7}{9}}$$ `=` $$\color{#00880A}{3}\frac{\color{#e65021}{7}}{\color{#9a00c7}{9}}$$ `3 7/9` -
Question 2 of 5
2. Question
Multiply the following:`7xx4 3/4`Hint
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Well Done!
Incorrect
Transforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ Transforming an Improper to Mixed Fraction
$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}=\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$`(``b``-:``c``)=``Q` and `R` is the remainderFirst, convert the mixed number into improper formMultiply the denominator by the whole number and then add it to the numerator$$7\times\color{#00880A}{4}\frac{\color{#007DDC}{3}}{\color{#9a00c7}{4}}$$ `=` $$7\times\frac{(\color{#9a00c7}{4}\times\color{#00880A}{4})+\color{#007DDC}{3}}{\color{#9a00c7}{4}}$$ `=` `7xx(16+3)/4` `=` `7xx 19/4` Proceed with multiplying the fractions and then simplify.`7xx 19/4` `7/1xx 19/4` A whole number can be a fraction with `1` as the denominator `=` `133/4` Convert the fraction from improper to mixedStart by dividing the numerator by the denominatorArrange the numbers for long division
`4` goes into `13` three times. So write `3` above the line.
Multiply `3` to `4` and write the answer below `13`
Subtract `12` from `13` and write the answer one line below
Drop down `3`
`4` goes into `13` three times. So again write `3` above the line.
Multiply `3` to `4` and write the answer below `13`
Subtract `12` from `13` and write the answer one line below
Since `4` cannot go into `1` anymore, `1` is left as the Remainder and `33` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{133}}{\color{#9a00c7}{4}}$$ `=` $$\color{#00880A}{33}\frac{\color{#e65021}{1}}{\color{#9a00c7}{4}}$$ `33 1/4` -
Question 3 of 5
3. Question
Multiply the following:`7 1/5xx2 1/2`- (18)
Hint
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Excellent!
Incorrect
Transforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ First, convert the mixed number into improper formMultiply the denominator by the whole number and then add it to the numerator$$\color{#00880A}{7}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{5}}\times\color{#00880A}{2}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}$$ `=` $$\frac{(\color{#9a00c7}{5}\times\color{#00880A}{7})+\color{#007DDC}{1}}{\color{#9a00c7}{5}}\times\frac{(\color{#9a00c7}{2}\times\color{#00880A}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}$$ `=` `(35+1)/5xx(4+1)/2` `=` `36/5 xx 5/2` Proceed with multiplying the fractions and then simplify.`36/5 xx 5/2` `=` $$\frac{36}{5\div\color{#CC0000}{5}} \times \frac{5\div\color{#CC0000}{5}}{2}$$ Reduce the fractions `=` `36/1xx1/2` `=` $$\frac{36\div\color{#CC0000}{2}}{1} \times \frac{1}{2\div\color{#CC0000}{2}}$$ Reduce the fractions further `=` `18/1xx1/1` `=` `18/1` `=` `18` `18` -
Question 4 of 5
4. Question
Multiply the following:`2xx1 2/3xx2 1/5`Hint
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Great Work!
Incorrect
Transforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ Transforming an Improper to Mixed Fraction
$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}=\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$`(``b``-:``c``)=``Q` and `R` is the remainderFirst, convert the mixed number into improper formMultiply the denominator by the whole number and then add it to the numerator$$2\times\color{#00880A}{1}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}\times\color{#00880A}{2}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{5}}$$ `=` $$\frac{2}{1}\times\frac{(\color{#9a00c7}{3}\times\color{#00880A}{1})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}\times\frac{(\color{#9a00c7}{5}\times\color{#00880A}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{5}}$$ `=` `2/1xx(3+2)/3xx(10+1)/5` `=` `2/1xx5/3 xx 11/5` Proceed with multiplying the fractions and then simplify.`2/1xx5/3 xx 11/5` `=` `(2xx5xx11)/(1xx3xx5)` `=` `110/15` `=` $$\frac{110\div\color{#CC0000}{5}}{15\div\color{#CC0000}{5}}$$ Simplify the fraction `=` `22/3` Convert the fraction from improper to mixedStart by dividing the numerator by the denominatorArrange the numbers for long division
`3` goes into `22` seven times. So write `7` above the line.
Multiply `7` to `3` and write the answer below `22`
Subtract `21` from `22` and write the answer one line below
Since `3` cannot go into `1` anymore, `1` is left as the Remainder and `7` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{22}}{\color{#9a00c7}{3}}$$ `=` $$\color{#00880A}{7}\frac{\color{#e65021}{1}}{\color{#9a00c7}{3}}$$ `7 1/3` -
Question 5 of 5
5. Question
Divide the following:`2 2/3-:1/3`- (8)
Hint
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Correct!
Incorrect
Transforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ To divide fractions, flip the divisor and then multiply as normalFirst, convert the mixed numbers into improper formMultiply the denominator by the whole number and then add it to the numerator$$\color{#00880A}{2}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}\div\frac{1}{3}$$ `=` $$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{2})+\color{#007DDC}{2}}{\color{#9a00c7}{3}} \div \frac{1}{3}$$ `=` `(6+2)/3 -: 1/3` `=` `8/3 -: 1/3` First, get the reciprocal (flip) of the divisor`1/3` becomes `3/1` Proceed with multiplying this to the dividend.`8/3-:``1/3` `=` `8/3xx``3/1` `=` `24/3` `=` `24-:3` `=` `8` `8`
Quizzes
- Shaded Fractions 1
- Shaded Fractions 2
- Equivalent Fractions 1
- Equivalent Fractions 2
- Equivalent Fractions 3
- Equivalent Fractions 4
- Simplify Fractions 1
- Simplify Fractions 2
- Simplify Fractions 3
- Find the Lowest Common Denominator
- Comparing Fractions 1
- Comparing Fractions 2
- Comparing Fractions 3
- Mixed and Improper Fractions 1
- Mixed and Improper Fractions 2
- Mixed and Improper Fractions 3
- Add and Subtract Fractions 1
- Add and Subtract Fractions 2
- Add and Subtract Fractions 3
- Add and Subtract Fractions 4
- Multiply and Divide Fractions 1
- Multiply and Divide Fractions 2
- Multiply and Divide Fractions 3
- Add and Subtract Mixed Numbers 1
- Add and Subtract Mixed Numbers 2
- Add and Subtract Mixed Numbers 3
- Multiply and Divide Mixed Numbers 1
- Multiply and Divide Mixed Numbers 2
- Multiply and Divide Mixed Numbers 3
- Multiply and Divide Mixed Numbers 4
- Fraction Word Problems: Addition and Subtraction 1
- Fraction Word Problems: Addition and Subtraction 2
- Fraction Word Problems: Addition and Subtraction 3
- Fraction Word Problems: Addition and Subtraction 4
- Fraction Word Problems: Multiplication and Division
- Find the Fraction of a Quantity
- Find the Quantity of a Quantity 1
- Find the Quantity of a Quantity 2
- Find the Fraction of a Quantity: Word Problems 1
- Find the Fraction of a Quantity: Word Problems 2
- Find the Fraction of a Quantity: Word Problems 3
- Find the Fraction of a Quantity: Word Problems 4
- Find the Quantity of a Quantity: Word Problems
- Order of Operations Involving Fractions 1
- Order of Operations Involving Fractions 2