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Fraction Word Problems: Addition and Subtraction 4Fraction Word Problems: Addition and Subtraction 4
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Question 1 of 4
1. Question
At a federal court, a jury was deciding whether a person accused was guilty or not. `2/3` believed the accused was guilty, `1/6` believed he was not guilty while the rest were undecided. What fraction of the jury were undecided?Write fractions in the format “a/b”- (1/6)
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Add fractions with unlike denominators by transforming the fractions so that they have like denominatorsFirst, list down the values stated in the problemBelieves accused is guilty `=` `2/3` Believes accused is not guilty `=` `1/6` Add the two fractions.Since `6` is a multiple of `3`, `6` is the `LCD``2/3``+``1/6` `=` $$\frac{2\times\color{#CC0000}{2}}{3\times\color{#CC0000}{2}}+\frac{1}{6}$$ Multiply by `2` so that the denominator becomes `6` `=` $$\frac{4}{6}+\frac{1}{6}$$ Add the numerators `=` $$\frac{5}{6}$$ Keep the same denominator Finally, subtract this fraction from `1`. Here, `1` represents the whole jury`1-5/6` `=` `6/6-5/6` Subtract the numerators `=` `1/6` Keep the same denominator `1/6` of the jury were undecided.`1/6` -
Question 2 of 4
2. Question
Jack likes to run to stay fit. He runs `3 1/2`km on Sunday, `2 1/4`km on Monday, and `4 2/3`km on Wednesday. How far does Jack run over those `3` days?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 problemSunday `=` `3 1/2`km Monday `=` `2 1/4`km Wednesday `=` `4 2/3`km Add these `3` fractions to get the total distance that Jack ran.First, add the whole numbers`3``+``2``+``4` `=` `9` Now add the fractionsStart by finding the `LCD` of `2`, `4` and `3`Multiples of `2`:$$2\;\;4\;\;6\;\;8\;\;10\;\;\color{#004ec4}{12}\;\;14\;\;16$$Multiples of `4`:$$4\;\;8\;\;\color{#004ec4}{12}\;\;16\;\;20$$Multiples of `3`:$$3\;\;6\;\;9\;\;\color{#004ec4}{12}\;\;15\;\;18$$The `LCD` of `2`, `4` and `3` is `12`Use the `LCD` as the denominator for the three fractions then add them.`1/2``+``1/4``+``2/3` `=` $$\frac{1\times\color{#CC0000}{6}}{2\times\color{#CC0000}{6}}+\frac{1\times\color{#CC0000}{3}}{4\times\color{#CC0000}{3}}+\frac{2\times\color{#CC0000}{4}}{3\times\color{#CC0000}{4}}$$ Multiply the fractions so that the denominator becomes `12` `=` $$\frac{6}{\color{#004ec4}{12}}+\frac{3}{\color{#004ec4}{12}}+\frac{8}{\color{#004ec4}{12}}$$ Add only the numerators `=` $$\frac{17}{12}$$ Keep the same denominator Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`12` goes into `17` once. So write `1` above the line.
Multiply `1` to `12` and write the answer below `17`
Subtract `12` from `17` and write the answer one line below
Since `12` cannot go into `5` anymore, `5` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{17}}{\color{#9a00c7}{12}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{5}}{\color{#9a00c7}{12}}$$ Finally, add the two sums (whole number and mixed fraction).`9+1 5/12` `=` `10 5/12`km `10 5/12`km -
Question 3 of 4
3. Question
From a `10 1/2`m roll of fabric, `2 1/4`m is cut. How much fabric 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 length of fabric `=` `10 1/2` Fabric that was cut `=` `2 3/4` Subtract the two fractions to get the remaining length of fabricFirst, transform the mixed fractions to improper fractions$$\color{#00880A}{10}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\color{#00880A}{2} \frac{\color{#007DDC}{3}}{\color{#9a00c7}{4}}$$ `=` $$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{10})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\frac{(\color{#9a00c7}{4}\times\color{#00880A}{2})+\color{#007DDC}{3}}{\color{#9a00c7}{4}}$$ `=` $$\frac{20+1}{2}-\frac{8+3}{4}$$ `=` $$\frac{21}{2}-\frac{11}{4}$$ Make sure that the fractions have the same denominators before subtractingSince `4` is a multiple of `2`, `4` is the `LCD``21/2-11/4` `=` $$\frac{21\times\color{#CC0000}{2}}{2\times\color{#CC0000}{2}}-\frac{11}{4}$$ Multiply by `2` so that the denominator becomes `4` `=` $$\frac{42}{4}-\frac{11}{4}$$ Subtract the numerators `=` $$\frac{31}{4}$$ Keep the same denominator Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`4` goes into `31` seven times. So write `7` above the line.
Multiply `7` to `4` and write the answer below `31`
Subtract `28` from `31` and write the answer one line below
Since `4` cannot go into `3` anymore, `3` is left as the Remainder and `7` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{31}}{\color{#9a00c7}{4}}$$ `=` $$\color{#00880A}{7}\frac{\color{#e65021}{3}}{\color{#9a00c7}{4}}$$ `7 3/4`m -
Question 4 of 4
4. Question
A cake needs `2/3` cup of sugar, `1 1/2` cups of cocoa, `3/4` cup of butter and `3 1/2` cups of flour. How many cups of ingredients are needed in total?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 problemSugar `=` `2/3` Cocoa `=` `1 1/2` Butter `=` `3/4` Flour `=` `3 1/2` First, add the whole numbers`3+1` `=` `4` Next, notice that the cocoa and the flour both have `1/2` cup worth of ingredient.These two halves can be added together to get a sum of `1`.`1/2+1/2` `=` `1` Now add the fractionsSince `3` and `4` are both multiples of `12`, `12` is the `LCD``2/3+3/4` `=` $$\frac{2\times\color{#CC0000}{4}+3\times\color{#CC0000}{3}}{12}$$ Cross multiply the fractions to get the new numerators `=` $$\frac{8+9}{12}$$ Add the numerators `=` $$\frac{17}{12}$$ Keep the same denominator Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`17` goes into `12` once. So write `1` above the line.
Multiply `1` to `12` and write the answer below `17`
Subtract `12` from `17` and write the answer one line below
Since `5` cannot go into `12` anymore, `5` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{17}}{\color{#9a00c7}{12}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{5}}{\color{#9a00c7}{12}}$$ Finally, add the sums of the values(whole number and mixed fraction).`4+1+1 5/12` `=` `6 5/12` `6 5/12`
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