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Fraction Word Problems: Multiplication and DivisionFraction Word Problems: Multiplication and Division
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Question 1 of 6
1. Question
How many `1 1 / 6` sections of rope are there in a total length of `42`m?- (36)
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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, list down the values stated in the problemTotal length of the rope `=` `42`m Sections it will be cut into `=` $$\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{6}}=\frac{(\color{#9a00c7}{6}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{6}}=\frac{6+1}{6}=\frac{7}{6}$$ Divide the two values`42-:7/6` `=` `42/1xx6/7` Reciprocate the divisor and change the operation to multiplication `=` `(7xx6)/1xx6/(7xx1)` `42` and `7` are both multiples of `7` `=` $$\frac{\color{#CC0000}{7}\times6}{1}\times\frac{6}{\color{#CC0000}{7}\times1}$$ Cancel diagonally `=` `6/1xx6/1` `=` `36/1` `=` `36` `36` -
Question 2 of 6
2. Question
A race track is `3 2/3`km long per lap. How many laps will a racer need to make in order to complete a `77`km race?- (21) laps
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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, list down the values stated in the problemTotal length of the race `=` `77`km Length of a lap `=` `3 2/3`km Divide the two valuesStart by converting the mixed fraction to an improper fraction$$77\div\color{#00880A}{3}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{77}{1}\div\frac{(\color{#9a00c7}{3}\times\color{#00880A}{3})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` `77/1-:(9+2)/3` `=` `77/1-:11/3` Get the reciprocal (flip) of the divisor`11/3` becomes `3/11` Proceed with multiplying this to the dividend.`77/1-:``11/3` `=` `77/1xx``3/11` `=` $$\frac{77\div\color{#CC0000}{11}}{1}\times\frac{3}{11\div\color{#CC0000}{11}}$$ Reduce the fractions `=` `7/1xx3/1` `=` `21/1` `=` `21` laps `21` laps -
Question 3 of 6
3. Question
How many `20`-minute periods are there in `5` hours?- (15) periods
Hint
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To divide fractions, flip the divisor and then multiply as normalMethod OneUse an illustration to represent the problem
`1` circle represents `1` hour or `60` minutes, so `5` circles are drawn.Since there are three `20` minutes in `60` minutes, each circle is divided into `3` parts.Count the total number of parts`5` circles `xx3` parts `=` `15` There are `15` `20`-minute periods in `5` hours`15` periodsMethod TwoFirst, list down the values stated in the problemTotal no. of hours `=` `5` hours Length of a period
(in hours)`=` `20` minutes `-:60` minutes`=20/60=1/3` Divide the two valuesStart by getting the reciprocal (flip) of the divisor`1/3` becomes `3/1` Proceed with multiplying this to the dividend.`5-:``1/3` `=` `5/1xx``3/1` `=` `15/1` `=` `15` There are `15` `20`-minute periods in `5` hours`15` periods -
Question 4 of 6
4. Question
Bill swims for exactly the same amount of time each day. If he swims for a total of `7 1/2` hours in `5` days, for how long did he swim each day?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, list down the values stated in the problemTotal no. of
swimming hours`=` `7 1/2` hours No. of days `=` `5` days Divide the two valuesStart by converting the mixed fraction to an improper fraction$$\color{#00880A}{7}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}\div5$$ `=` $$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{7})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}\div\frac{5}{1}$$ `=` `(14+1)/2-:5/1` `=` `15/2-:5/1` Get the reciprocal (flip) of the divisor`5/1` becomes `1/5` Proceed with multiplying this to the dividend.`15/2-:``5/1` `=` `15/2xx``1/5` `=` $$\frac{15\div\color{#CC0000}{5}}{2}\times\frac{1}{5\div\color{#CC0000}{5}}$$ Reduce the fractions `=` `3/2xx1/1` `=` `3/2` Convert the fraction from improper to mixedStart by dividing the numerator by the denominatorArrange the numbers for long division
`2` goes into `3` once. So write `1` above the line.
Multiply `1` to `2` and write the answer below `3`
Subtract `2` from `3` and write the answer one line below
Since `2` cannot go into `1` anymore, `1` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{3}}{\color{#9a00c7}{2}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{1}}{\color{#9a00c7}{2}}$$ Bill swam for `1 1/2` hours per day.`1 1/2` hours -
Question 5 of 6
5. Question
How many `1 1/3`m sections of cable can be cut from a `72`m roll?- (54) sections
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, list down the values stated in the problemTotal length of the rope `=` `72`m Sections it will be cut into `=` $$\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}=\frac{(\color{#9a00c7}{3}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}=\frac{3+1}{3}=\frac{4}{3}$$ Divide the two values`72-:4/3` `=` `72/1xx3/4` Reciprocate the divisor and change the operation to multiplication `=` $$\frac{72\div\color{#CC0000}{4}}{1}\times\frac{3}{4\div\color{#CC0000}{4}}$$ Reduce the fractions `=` `18/1xx3/1` Cancel diagonally `=` `54/1` `=` `54` A `72`m roll of cable can have `54` sections of `1 1/3`m.`54` -
Question 6 of 6
6. Question
A `$1600` TV has a `1/5` off discount. Find the following:-
`(i)` Discount: `$` (320)`(ii)` Sale Price: `$` (1280)
Hint
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To multiply fractions, simply multiply the numerators and denominators separately.`(i)` Find the discount price of the TV.First, list down the values stated in the problemOriginal Price `=` `$1600` Discount Rate `=` `1/5` Multiply the two values`1600xx1/5` `=` `1600/1xx1/5` `=` `1600/5` `=` `1600-:5` `=` `$320` The discount price is `$320``(ii)` Find the sale price of the TV.First, list down the known values in the problemOriginal Price `=` `$1600` Discount Price `=` `$320` Subtract the two valuesOriginal price `-` Discount price `=` Sale price `$1600` `-` `$320` `=` `$1280` The sale price is `$1280``(i) $320``(ii) $1280` -
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 LCM
- 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 Fractions 1
- Multiply and Divide Mixed Fractions 2
- Multiply and Divide Mixed Fractions 3
- Multiply and Divide Mixed Fractions 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