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Multiply and Divide Mixed Numbers>
Multiply and Divide Mixed Numbers 1Multiply and Divide Mixed Numbers 1
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Question 1 of 4
1. Question
Multiply the following:`2 1/4xx3 1/3`Hint
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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 numbers into improper formMultiply the denominator by the whole number and then add it to the numerator$$\color{#00880A}{2}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{4}}\times\color{#00880A}{3}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{4}\times\color{#00880A}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{4}} \times \frac{(\color{#9a00c7}{3}\times\color{#00880A}{3})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}$$ `=` `(8+1)/4 xx (9+1)/3` `=` `9/4 xx 10/3` Proceed with multiplying the fractions and then simplify.`9/4 xx 10/3` `=` `90/12` `=` $$\frac{90\color{#CC0000}{\div6}}{12\color{#CC0000}{\div6}}$$ Reduce to lowest terms `=` `15/2` `=` `(14+1)/2` Transform the fraction back to a mixed number `=` `7 1/2` `7 1/2` -
Question 2 of 4
2. Question
Multiply the following:`4 1/2xx2 2/3`- (12)
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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 numbers into improper formMultiply the denominator by the whole number and then add it to the numerator$$\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}\times\color{#00880A}{2}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{4})+\color{#007DDC}{1}}{\color{#9a00c7}{2}} \times \frac{(\color{#9a00c7}{3}\times\color{#00880A}{2})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` `(8+1)/2 xx (6+2)/3` `=` `9/2 xx 8/3` Proceed with multiplying the fractions and then simplify.`9/2 xx 8/3` `=` `72/6` `=` `72-:6` Reduce to lowest terms `=` `12` `12` -
Question 3 of 4
3. Question
Multiply the following:`3 3/4xx1 4/5`Hint
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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$$\color{#00880A}{3}\frac{\color{#007DDC}{3}}{\color{#9a00c7}{4}}\times\color{#00880A}{1}\frac{\color{#007DDC}{4}}{\color{#9a00c7}{5}}$$ `=` $$\frac{(\color{#9a00c7}{4}\times\color{#00880A}{3})+\color{#007DDC}{3}}{\color{#9a00c7}{4}}\times\frac{(\color{#9a00c7}{5}\times\color{#00880A}{1})+\color{#007DDC}{4}}{\color{#9a00c7}{5}}$$ `=` `(12+3)/4xx(5+4)/5` `=` `15/4 xx 9/5` Proceed with multiplying the fractions and then simplify.`15/4 xx 9/5` `=` $$\frac{15\div\color{#CC0000}{5}}{4} \times \frac{9}{5\div\color{#CC0000}{5}}$$ `15` and `5` are multiples of `5` `=` `3/4xx9/1` `=` `27/4` Convert the fraction from improper to mixedStart by dividing the numerator by the denominatorArrange the numbers for long division
`4` goes into `27` six times. So write `6` above the line.
Multiply `6` to `4` and write the answer below `27`
Subtract `24` from `27` and write the answer one line below
Since `4` cannot go into `3` anymore, `3` is left as the Remainder and `6` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{27}}{\color{#9a00c7}{4}}$$ `=` $$\color{#00880A}{6}\frac{\color{#e65021}{3}}{\color{#9a00c7}{4}}$$ `6 3/4` -
Question 4 of 4
4. Question
Multiply the following:`5 1/3xx4 1/2`- (24)
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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$$\color{#00880A}{5}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}\times\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}$$ `=` $$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{5})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}\times\frac{(\color{#9a00c7}{2}\times\color{#00880A}{4})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}$$ `=` `(15+1)/3xx(8+1)/2` `=` `16/3 xx 9/2` Proceed with multiplying the fractions and then simplify.`16/3 xx 9/2` `=` $$\frac{16\div\color{#CC0000}{2}}{3} \times \frac{9}{2\div\color{#CC0000}{2}}$$ Reduce the fractions `=` `8/3xx9/1` `=` $$\frac{8}{3\div\color{#CC0000}{3}} \times \frac{9\div\color{#CC0000}{3}}{1}$$ Reduce the fractions further `=` `8/1xx3/1` `=` `24/1` `=` `24` `24`
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