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Fraction Word Problems: Addition and Subtraction 1Fraction Word Problems: Addition and Subtraction 1
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Question 1 of 4
1. Question
Three people share a sum of money. The `1`st person receives `2/5` of the sum and the `2`nd person receives `1/2`. What fraction of the money does the `3`rd person receive?Write fractions in the format “a/b”- (1/10)
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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 problem`1`st person `=` `2/5` `2`nd person `=` `1/2` Use cross method to add the two fractions.First, multiply the two denominators. Use the product as a denominator for a new fraction.`2/5``+``1/2` `=` `☐/(5times2)` `=` `☐/10` To get the numerator, cross multiply the given addition problem and add the products.$$\frac{\color{#00880A}{2}}{\color{#9a00c7}{5}}+\frac{\color{#9a00c7}{1}}{\color{#00880A}{2}}$$ `=` $$\frac{(\color{#00880A}{2\times2})+(\color{#9a00c7}{5\times1})}{10}$$ `=` `(4+5)/10` `=` `9/10` Finally, subtract this fraction from `1`. `1` represents the whole sum of money`1-9/10` `=` `10/10-9/10` Subtract the numerators `=` `1/10` Keep the same denominator The `3`rd person gets `1/10` of the money.`1/10` -
Question 2 of 4
2. Question
A rain tank is three fifths full. Heavy rain over a period of `3` nights filled it with one tenths of water each night. What fraction of the tank’s capacity is filled after the `3` nights of rainfall?Write fractions in the format “a/b”- (9/10)
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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 problemStarting amount of water `=` `3/5` Additional amount of water `=` `3times1/10=3/1times1/10=``3/10` Add the two values to get the total amount of water after 3 daysSince `10` is a multiple of `5`, it is the `LCD` of `5` and `10``3/5``+``3/10` `=` $$\frac{3\color{#CC0000}{\times2}}{5\color{#CC0000}{\times2}}+\frac{3}{10}$$ Multiply `2` to `5` so it becomes `10` `=` `6/10+3/10` `=` `9/10` Keep the same denominator `9/10` -
Question 3 of 4
3. Question
A concrete truck contains a concrete mixture that consists of `1/4` cement, `1/3` sand, `1/6` water and the rest is gravel. What fraction of the mixture is gravel?Write fractions in the format “a/b”- (1/4)
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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 problemCement `=` `1/4` Sand `=` `1/3` Water `=` `1/6` Add the three fractions.Start by finding the `LCD` of the `4`, `3` and `6`Multiples of `4`:$$4\;\;8\;\;\color{#004ec4}{12}\;\;16\;\;20$$Multiples of `3`:$$3\;\;6\;\;9\;\;\color{#004ec4}{12}\;\;15\;\;18$$Multiples of `6`:$$6\;\;\color{#004ec4}{12}\;\;18\;\;24$$The `LCD` of `4`, `3` and `6` is `12`Use the `LCD` as the denominator for the three fractions then add them.`1/4``+``1/3``+``1/6` `=` $$\frac{1\times\color{#CC0000}{3}}{4\times\color{#CC0000}{3}}+\frac{1\times\color{#CC0000}{4}}{4\times\color{#CC0000}{4}}+\frac{1\times\color{#CC0000}{2}}{6\times\color{#CC0000}{2}}$$ Multiply the fractions so that the denominator becomes `12` `=` $$\frac{3}{\color{#004ec4}{12}}+\frac{4}{\color{#004ec4}{12}}+\frac{2}{\color{#004ec4}{12}}$$ Add only the numerators `=` $$\frac{9}{12}$$ Keep the same denominator `=` $$\frac{9\div\color{#CC0000}{3}}{12\div\color{#CC0000}{3}}$$ Express in lowest terms `=` $$\frac{3}{4}$$ Finally, subtract this fraction from `1`. Here, `1` represents the whole mixture`1-3/4` `=` `4/4-3/4` Subtract the numerators `=` `1/4` Keep the same denominator `1/4` of the concrete mixture is gravel.`1/4` -
Question 4 of 4
4. Question
Eddie ordered `2` pizzas, each sliced in `8` pieces. He ate `5` pieces. Find the following:Write fractions in the format “a/b”-
`(i)` Fraction that Eddie ate: (5/16)`(ii)` Fraction of remaining pizza: (11/16)
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`(i)` Find the fraction of pizza that Eddie ate.First, list down the values stated in the problemSlices Eddie ate `=` `5` Total slices of pizza `=` `2` pizzas`xx8` slices`=``16` Since we are looking for the fraction that Eddie ate, the numerator must be the no. of slices he ate while the denominator must be the total no. of slices$$\mathsf{\frac{\color{#9E8600}{no.\;of\;slices\;he\;ate}}{\color{#007DDC}{total\;no.\;of\;slices}}}$$ `=` $$\frac{\color{#9E8600}{5}}{\color{#007DDC}{16}}$$ Eddie ate `5/16` of the pizza he ordered.`(ii)` Find the fraction of pizza that remains.Simply subtract the fraction that Eddie ate from `1`. Here, `1` represents the total pizza that he ordered.`1-5/16` `=` `16/16-5/16` Subtract the numerators `=` `11/16` Keep the same denominator `11/16` of the pizza Eddie ordered remains.`(i) 5/16``(ii) 11/16` -
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- Equivalent Fractions 4
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- Simplify Fractions 2
- Simplify Fractions 3
- Find the LCM
- Comparing Fractions 1
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- Comparing Fractions 3
- Mixed and Improper Fractions 1
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- Mixed and Improper Fractions 3
- Add and Subtract Fractions 1
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- Add and Subtract Fractions 3
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- Multiply and Divide Fractions 1
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- Add and Subtract Mixed Numbers 1
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- Add and Subtract Mixed Numbers 3
- Multiply and Divide Mixed Fractions 1
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