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Fraction Word Problems: Addition and Subtraction 3Fraction Word Problems: Addition and Subtraction 3
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Question 1 of 4
1. Question
Adrian juices some oranges and apples. He got `2 3/4` glasses of orange juice and `4 5/8` glasses of apple juice. How many glasses of juice did he get altogether?Hint
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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 remainderA mixed number consists of a whole number and a fraction.First, list down the values stated in the problemOrange Juice `=` `3 1/2` Apple Juice `=` `4 5/8` Add these `2` fractions to get the total number of glasses Adrian juiced.First, add the whole numbers`2``+``4` `=` `6` Now add the fractionsSince `8` is a multiple of `4`, `8` is the `LCD``3/4``+``5/8` `=` $$\frac{3\times\color{#CC0000}{2}}{4\times\color{#CC0000}{2}}+\frac{5}{8}$$ Multiply by `2` so that the denominator becomes `8` `=` $$\frac{6}{8}+\frac{5}{8}$$ Add the numerators `=` $$\frac{11}{8}$$ Keep the same denominator Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`8` goes into `11` once. So write `1` above the line.
Multiply `1` to `8` and write the answer below `11`
Subtract `8` from `11` and write the answer one line below
Since `8` cannot go into `3` anymore, `3` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{11}}{\color{#9a00c7}{8}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{3}}{\color{#9a00c7}{8}}$$ Finally, add the two sums (whole number and mixed fraction).`6+1 3/8` `=` `7 3/8` `7 3/8` -
Question 2 of 4
2. Question
At a party, 2 groups ordered a total of 6 pizzas. The first group ate `1 7/8` of the pizzas and the second group ate `3 1/4` of the pizzas. How many pizzas were left?Hint
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Excellent!
Incorrect
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 remainderA mixed number consists of a whole number and a fraction.First, list down the values stated in the problemPizzas Eaten by 1st Group `=` `1 7/8` Pizzas Eaten by 2nd Group `=` `3 1/4` First, add the whole numbers`1``+``3` `=` `4` Now add the fractionsSince `8` is a multiple of `4`, `8` is the `LCD``7/8``+``1/4` `=` $$\frac{5}{8}+\frac{1\times\color{#CC0000}{2}}{4\times\color{#CC0000}{2}}$$ Multiply by `2` so that the denominator becomes `8` `=` $$\frac{7}{8}+\frac{2}{8}$$ Add the numerators `=` $$\frac{9}{8}$$ Keep the same denominator Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`8` goes into `9` once. So write `1` above the line.
Multiply `1` to `8` and write the answer below `9`
Subtract `8` from `9` and write the answer one line below
Since `8` cannot go into `9` anymore, `1` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{9}}{\color{#9a00c7}{8}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{1}}{\color{#9a00c7}{8}}$$ Next, add the two sums (whole number and mixed fraction).`4+1 1/8` `=` `5 1/8` Convert `5 1/8` into an improper fraction Finally, subtract the sum of the fractions from the total number of pizzas, which is `6`.It will be easier to compute if you change the sum of the fractions into an improper fraction.`6-5 1/8` `=` `6-41/8` Convert `5 1/8` into an improper fraction `=` `6/1-41/8` `4+1 1/8` `=` `5 1/8` Since `8` is a multiple of `1`, `8` is the `LCD``6/1-41/8` `=` $$\frac{6\times\color{#CC0000}{8}}{1\times\color{#CC0000}{8}}-\frac{41}{8}$$ Multiply by `8` so that the denominator becomes `8` `=` $$\frac{48}{8}-\frac{41}{8}$$ Add the numerators `=` $$\frac{7}{8}$$ Keep the same denominator `7/8` -
Question 3 of 4
3. Question
From a reel of ribbon that is `9 1/2`m long, a `1 2/3`m long piece is cut. How much of the ribbon remains?Hint
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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 remainderTransforming 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 ribbon `=` `9 1/2`m Removed piece `=` `1 2/3`m Subtract these `2` fractions to get the remaining length of ribbon.First, transform the mixed fractions to improper fractions$$\color{#00880A}{9}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\color{#00880A}{1} \frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{9})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\frac{(\color{#9a00c7}{3}\times\color{#00880A}{1})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{18+1}{2}-\frac{3+2}{3}$$ `=` $$\frac{19}{2}-\frac{5}{3}$$ Use cross method to subtract the two fractions.First, multiply the two denominators. Use the product as a denominator for a new fraction.`19/2-5/3` `=` `☐/(2times3)` `=` `☐/6` To get the numerator, cross multiply the given addition problem and add the products.$$\frac{\color{#00880A}{19}}{\color{#9a00c7}{2}}-\frac{\color{#9a00c7}{5}}{\color{#00880A}{3}}$$ `=` $$\frac{(\color{#00880A}{19\times3})-(\color{#9a00c7}{2\times5})}{6}$$ `=` `(57-10)/6` `=` `47/6` Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`6` goes into `47` seven times. So write `7` above the line.
Multiply `7` to `6` and write the answer below `47`
Subtract `42` from `47` and write the answer one line below
Since `6` cannot go into `5` anymore, `5` is left as the Remainder and `7` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{47}}{\color{#9a00c7}{6}}$$ `=` $$\color{#00880A}{7}\frac{\color{#e65021}{5}}{\color{#9a00c7}{6}}$$ `7 5/6`m -
Question 4 of 4
4. Question
Doug plans to dig a hole `4 1/3`m deep. So far, he has dug `3 4/5`m deep. How much deeper does he need to dig?Write fractions in the form “a/b”- (8/15)m
Hint
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Exceptional!
Incorrect
Transforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ A mixed number consists of a whole number and a fraction.First, list down the values stated in the problemTarget depth `=` `4 1/3`m Dug so far `=` `3 4/5`m Subtract these `2` fractions to get the remaining depth to be dug.First, transform the mixed fractions to improper fractions$$\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}-\color{#00880A}{3} \frac{\color{#007DDC}{4}}{\color{#9a00c7}{5}}$$ `=` $$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{4})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}-\frac{(\color{#9a00c7}{5}\times\color{#00880A}{3})+\color{#007DDC}{4}}{\color{#9a00c7}{5}}$$ `=` $$\frac{12+1}{3}-\frac{15+4}{5}$$ `=` $$\frac{13}{3}-\frac{19}{5}$$ Use cross method to subtract the two fractions.First, multiply the two denominators. Use the product as a denominator for a new fraction.`13/3-19/5` `=` `☐/(3times5)` `=` `☐/15` To get the numerator, cross multiply the given addition problem and add the products.$$\frac{\color{#00880A}{13}}{\color{#9a00c7}{3}}-\frac{\color{#9a00c7}{19}}{\color{#00880A}{5}}$$ `=` $$\frac{(\color{#00880A}{13\times5})-(\color{#9a00c7}{3\times19})}{15}$$ `=` `(65-57)/15` `=` `8/15` `8/15`m
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