Add and Subtract Mixed Numbers 3
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Question 1 of 4
1. Question
Add the following:`9 7/8+3 5/24`Hint
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Well Done!
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, add the whole numbers`9+3` `=` `12` Notice that the fractions have different denominators.Find the `LCD` of `8` and `24` so we can add the fractions.Multiples of `8`:$$8\;\;16\;\;\color{#004ec4}{24}\;\;32$$Multiples of `24`:$$\color{#004ec4}{24}\;\;48\;\;72$$The `LCD` of `8` and `24` is `24`Proceed with adding the fractions`7/8+5/24` `=` $$\frac{7\times\color{#CC0000}{3}}{8\times\color{#CC0000}{3}}+\frac{5}{24}$$ Multiply by `3` so that the denominator becomes `24` `=` $$\frac{21}{\color{#004ec4}{24}}+\frac{5}{\color{#004ec4}{24}}$$ `=` $$\frac{26}{24}$$ Change the improper fraction to a mixed fractionDivide the numerator by the denominatorArrange the numbers for long division
`24` goes into `26` one time. So write `1` above the line.
Multiply `1` to `24` and write the answer below `26`
Subtract `24` from `26` and write the answer one line below
[add colors: `1`, `2`]Since `24` cannot go into `2` anymore, `2` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{26}}{\color{#9a00c7}{24}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{2}}{\color{#9a00c7}{24}}$$ `=` $$1\frac{2\div\color{#CC0000}{2}}{24\div\color{#CC0000}{2}}$$ Express in lowest terms `=` `1 1/12` Finally, combine the sum of the whole numbers and the sum of the fractions`9 7/8+3 5/24` `=` `12+1 1/12` `=` `13 1/12` `13 1/12` -
Question 2 of 4
2. Question
Subtract the following:`7-3 3/8`Hint
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Great Work!
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 remainderTransforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ First, transform the mixed fractions to improper fractions$$7-\color{#00880A}{3} \frac{\color{#007DDC}{3}}{\color{#9a00c7}{8}}$$ `=` $$\frac{7}{1}-\frac{(\color{#9a00c7}{8}\times\color{#00880A}{3})+\color{#007DDC}{3}}{\color{#9a00c7}{8}}$$ `=` $$\frac{7}{1}-\frac{24+3}{8}$$ `=` $$\frac{7}{1}-\frac{27}{8}$$ Use cross method to subtract the fractions.Start by multiplying the two denominators. Use the product as a denominator for a new fraction.`7/1-27/8` `=` `☐/(1times8)` `=` `☐/8` To get the numerator, cross multiply the given addition problem and subtract the products.$$\frac{\color{#00880A}{7}}{\color{#9a00c7}{1}}-\frac{\color{#9a00c7}{27}}{\color{#00880A}{8}}$$ `=` $$\frac{(\color{#00880A}{7\times8})-(\color{#9a00c7}{1\times27})}{8}$$ `=` `(56-27)/8` `=` `29/8` Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`8` goes into `29` six times. So write `6` above the line.
Multiply `3` to `8` and write the answer below `29`
Subtract `24` from `29` and write the answer one line below
Since `8` cannot go into `5` anymore, `5` is left as the Remainder and `3` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{29}}{\color{#9a00c7}{8}}$$ `=` $$\color{#00880A}{3}\frac{\color{#e65021}{5}}{\color{#9a00c7}{8}}$$ `3 5/8` -
Question 3 of 4
3. Question
Subtract the following:`5 1/4-3 2/3`Hint
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Fantastic!
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 remainderTransforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ First, transform the mixed fractions to improper fractions$$\color{#00880A}{5}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{4}}-\color{#00880A}{3} \frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{4}\times\color{#00880A}{5})+\color{#007DDC}{1}}{\color{#9a00c7}{4}}-\frac{(\color{#9a00c7}{3}\times\color{#00880A}{3})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{20+1}{4}-\frac{9+2}{3}$$ `=` $$\frac{21}{4}-\frac{11}{3}$$ Notice that the fractions have different denominators.Find the `LCD` of `4` and `3` so we can subtract the fractions.Multiples of `4`:$$4\;\;8\;\;\color{#004ec4}{12}\;\;16\;\;20$$Multiples of `3`:$$3\;\;6\;\;9\;\;\color{#004ec4}{12}\;\;15\;\;18$$The `LCD` of `4` and `3` is `12`Next, we get the same denominator and subtract the fractions`21/4-11/3` `=` $$\frac{21\times\color{#CC0000}{3}}{4\times\color{#CC0000}{3}}-\frac{11\times\color{#CC0000}{4}}{3\times\color{#CC0000}{4}}$$ Multiply each fraction so that the denominator becomes `12` `=` $$\frac{63}{\color{#004ec4}{12}}-\frac{44}{\color{#004ec4}{12}}$$ `=` $$\frac{19}{12}$$ Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`12` goes into `19` once. So write `1` above the line.
Multiply `1` to `12` and write the answer below `19`
Subtract `12` from `19` and write the answer one line below
Since `12` cannot go into `7` anymore, `7` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{19}}{\color{#9a00c7}{12}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{7}}{\color{#9a00c7}{12}}$$ `1 7/12` -
Question 4 of 4
4. Question
Subtract the following:`9-2 7/10`Hint
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Correct!
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 remainderTransforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ First, transform the mixed fractions to improper fractions$$9-\color{#00880A}{2} \frac{\color{#007DDC}{7}}{\color{#9a00c7}{10}}$$ `=` $$\frac{9}{1}-\frac{(\color{#9a00c7}{10}\times\color{#00880A}{2})+\color{#007DDC}{7}}{\color{#9a00c7}{10}}$$ `=` $$\frac{9}{1}-\frac{20+7}{10}$$ `=` $$\frac{9}{1}-\frac{27}{10}$$ Use cross method to subtract the fractions.Start by multiplying the two denominators. Use the product as a denominator for a new fraction.`9/1-27/10` `=` `☐/(1times10)` `=` `☐/10` To get the numerator, cross multiply the given addition problem and subtract the products.$$\frac{\color{#00880A}{9}}{\color{#9a00c7}{1}}-\frac{\color{#9a00c7}{27}}{\color{#00880A}{10}}$$ `=` $$\frac{(\color{#00880A}{9\times10})-(\color{#9a00c7}{1\times27})}{10}$$ `=` `(90-27)/10` `=` `63/10` Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`10` goes into `63` six times. So write `6` above the line.
Multiply `6` to `10` and write the answer below `63`
Subtract `60` from `63` and write the answer one line below
Since `10` cannot go into `3` anymore, `3` is left as the Remainder and `6` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{63}}{\color{#9a00c7}{10}}$$ `=` $$\color{#00880A}{6}\frac{\color{#e65021}{3}}{\color{#9a00c7}{10}}$$ `6 3/10`
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