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Find the Fraction of a Quantity: Word Problems 3Find the Fraction of a Quantity: Word Problems 3
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Question 1 of 5
1. Question
Jack brings `$40` to the cinema. He spends `1/4` of that amount on one movie ticket and `3/5` on snacks. What is the remaining amount of money?- `$` (6)
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To multiply fractions, simply multiply the numerators and denominators separately.First, find the fraction for the money spent by adding the two given fractions.Fraction for snacks: `3/5`Fraction for ticket: `1/4`$$\frac{\color{#00880A}{3}}{\color{#9a00c7}{5}}+\frac{\color{#007DDC}{1}}{\color{#9a00c7}{4}}$$ `=` $$\frac{(\color{#00880A}{3}\times\color{#9a00c7}{4})+(\color{#007DDC}{1}\times\color{#9a00c7}{5})}{\color{#9a00c7}{5\times4}}$$ `=` `(12+5)/20` `=` `17/20` Proceed to compute for the actual money that Jack spentTo get a fraction of a quantity, simply multiply the fraction to the quantity.Fraction of money spent: `17/20`Total money: `$40``17/20``xx``40` `=` `17/20xx40/1` `=` $$\frac{17}{20\div\color{#CC0000}{20}}\times\frac{40\div\color{#CC0000}{20}}{1}$$ Reduce the fractions `=` `17/1xx2/1` `=` `34/1` `=` `$34` Jack spent $34 in the cinema.Finally, subtract the money spent from the total money to get the remaining amount.`$40-$34` `=` `$6` There is `$6` left from Jack’s money.`$6` -
Question 2 of 5
2. Question
A petrol tank has a capacity of `60L`. It is currently `1/3` full. How many more litres need to be added before the tank becomes full?- (40)`L`
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To multiply fractions, simply multiply the numerators and denominators separately.First, compute for the exact amount of fuel in the tank at the momentTo get a fraction of a quantity, simply multiply the fraction to the quantity.Fraction of current fuel amount: `1/3`Total tank capacity: `60L``1/3``xx``60` `=` `1/3xx60/1` `=` $$\frac{1}{3\div\color{#CC0000}{3}}\times\frac{60\div\color{#CC0000}{3}}{1}$$ Reduce the fractions `=` `1/1xx20/1` `=` `20/1` `=` `20L` The tank currently contains `20L` of petrol.Finally, subtract the current amount of petrol from the total capacity to get how much petrol needs to be added.`60L-20L` `=` `40L` `40L` of petrol needs to be added for the tank to be full.`40L` -
Question 3 of 5
3. Question
A `1` metre pole is placed in a pond. `1/5` of it is in the ground and `2/3` of it is in the water. What fraction of the pole is above the water?Write fractions in the format “a/b”- (2/15)
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Subtract the given fractions from the full length of the pole.Length of the pole: `1`mLength of pole in water: `2/3`Length of pole in the ground: `1/5``1-(\frac{\color{#00880A}{2}}{\color{#9a00c7}{3}}+\frac{\color{#007DDC}{1}}{\color{#9a00c7}{5}})` `=` $$1-\frac{(\color{#00880A}{2}\times\color{#9a00c7}{5})+(\color{#007DDC}{1}\times\color{#9a00c7}{3})}{\color{#9a00c7}{3\times5}}$$ Use cross method to add the fractions `=` $$1-\frac{10+3}{15}$$ `=` $$\frac{15}{15}-\frac{13}{15}$$ `=` $$\frac{2}{15}$$ `2/15` of the pole is above water.`2/15` -
Question 4 of 5
4. Question
From a squad of `15` players, `1/3` are injured. How many are not injured?- (10) players
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To multiply fractions, simply multiply the numerators and denominators separately.First, get the fraction of players that are not injured.Total squad of players: `3/3`Fraction of injured players: `1/3``3/3-1/3` `=` `2/3` `2/3` of the players are not injured.To get a fraction of a quantity, simply multiply the fraction to the quantity.Fraction of injured players: `2/3`Total no. of players: `15``2/3``xx``15` `=` `2/3xx15/1` `=` $$\frac{2}{3\div\color{#CC0000}{3}}\times\frac{15\div\color{#CC0000}{3}}{1}$$ Reduce the fractions `=` `2/1xx5/1` `=` `10/1` `=` `10` players `10` players in the squad are not injured.`10` players -
Question 5 of 5
5. Question
Jason buys eight `500`g cans of dog food. Eventually, `1 1/5`kg worth is eaten. How much dog food remains?Hint
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To multiply fractions, simply multiply the numerators and denominators separately.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 remainderTo get a fraction of a quantity, simply multiply the fraction to the quantity.`1` can of dog food: `500`g or `1/2`kgNo. of cans: `8`kg`1/2``xx``8` `=` `1/2xx8/1` `=` `8/2` `=` `8-:2` `=` `4`kg Jason bought `4`kg of dog food in totalSubtract the amount of eaten dog food from the total amount of dog food.Total amount: `4`kgAmount eaten: `1 1/5`kg$$4-\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{5}}$$ Convert the fraction from mixed to improper `=` $$4-\frac{(\color{#9a00c7}{5}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{5}}$$ `=` $$4-\frac{5+1}{5}$$ `=` $$4-\frac{6}{5}$$ `=` $$\frac{20}{5}-\frac{6}{5}$$ Reduce the fractions `=` `14/5` Convert the fraction from improper to mixed by dividing the numerator by the denominatorArrange the numbers for long division
`5` goes into `14` once. So write `2` above the line.
Multiply `2` to `5` and write the answer below `14`
Subtract `10` from `14` and write the answer one line below
Since `5` cannot go into `4` anymore, `4` is left as the Remainder and `2` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{14}}{\color{#9a00c7}{5}}$$ `=` $$\color{#00880A}{2}\frac{\color{#e65021}{4}}{\color{#9a00c7}{5}}$$ `2 4/5`kg of dog food remains.`2 4/5`kg
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- Simplify Fractions 3
- Find the LCM
- Comparing Fractions 1
- Comparing Fractions 2
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- Mixed and Improper Fractions 1
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- Mixed and Improper Fractions 3
- Add and Subtract Fractions 1
- Add and Subtract Fractions 2
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- Add and Subtract Fractions 4
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- Add and Subtract Mixed Numbers 1
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- Multiply and Divide Mixed Fractions 1
- Multiply and Divide Mixed Fractions 2
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- Fraction Word Problems: Addition and Subtraction 1
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