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Add and Subtract Mixed Numbers>
Add and Subtract Mixed Numbers 2Add and Subtract Mixed Numbers 2
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Question 1 of 3
1. Question
Add the following:`8 1/2+10 3/4`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.Method OneFirst, add the whole numbers`8+10` `=` `18` Notice that the fractions have different denominators.Find the `LCD` of `2` and `4` so we can add the fractions.Multiples of `2`:$$2\;\;\color{#004ec4}{4}\;\;6\;\;8$$Multiples of `4`:$$\color{#004ec4}{4}\;\;8\;\;12\;\;16$$The `LCD` of `2` and `4` is `4`Use the `LCD` as the denominator for both fractions then proceed with adding.`1/2+3/4` `=` $$\frac{1\times\color{#CC0000}{2}}{2\times\color{#CC0000}{2}}+\frac{3}{4}$$ Multiply by `2` so that the denominator becomes `4` `=` $$\frac{2}{\color{#004ec4}{4}}+\frac{3}{\color{#004ec4}{4}}$$ Add the numerators `=` $$\frac{5}{4}$$ Keep the same denominator Change the improper fraction to a mixed fractionDivide the numerator by the denominatorArrange the numbers for long division
`4` goes into `5` one time. So write `1` above the line.
Multiply `1` to `4` and write the answer below `5`
Subtract `4` from `5` and write the answer one line below
Since `4` cannot go into `1` anymore, `1` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{5}}{\color{#9a00c7}{4}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{1}}{\color{#9a00c7}{4}}$$ `=` `1 1/4` Finally, combine the sum of the whole numbers and the sum of the fractions`8 1/2+10 3/4` `=` `18+1 1/4` `=` `19 1/4` `19 1/4`Method TwoFirst, add the whole numbers`8+10` `=` `18` Add the fractions using cross method.Start by multiplying the two denominators. Use the product as a denominator for a new fraction.`1/2+3/4` `=` `☐/(2times4)` `=` `☐/8` To get the numerator, cross multiply the given addition problem and add the products.$$\frac{\color{#00880A}{1}}{\color{#9a00c7}{2}}+\frac{\color{#9a00c7}{3}}{\color{#00880A}{4}}$$ `=` $$\frac{(\color{#00880A}{1\times4})+(\color{#9a00c7}{2\times3})}{8}$$ `=` `(4+6)/8` `=` `10/8` `=` $$\frac{10\div\color{#CC0000}{2}}{8\div\color{#CC0000}{2}}$$ Express in lowest terms `=` `5/4` `=` `1 1/4` We know this from Method One Finally, combine the sum of the whole numbers and the sum of the fractions`8 1/2+10 3/4` `=` `18+1 1/4` `=` `19 1/4` `19 1/4` -
Question 2 of 3
2. Question
Add the following:`7 2/3+3 5/7`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, add the whole numbers`7+3` `=` `10` Add the fractions using cross method.Start by multiplying the two denominators. Use the product as a denominator for a new fraction.`2/3+5/7` `=` `☐/(3times7)` `=` `☐/21` To get the numerator, cross multiply the given addition problem and add the products.$$\frac{\color{#00880A}{2}}{\color{#9a00c7}{3}}+\frac{\color{#9a00c7}{5}}{\color{#00880A}{7}}$$ `=` $$\frac{(\color{#00880A}{2\times7})+(\color{#9a00c7}{3\times5})}{21}$$ `=` `(14+15)/21` `=` `29/21` Change the improper fraction to a mixed fractionDivide the numerator by the denominatorArrange the numbers for long division
`21` goes into `29` one time. So write `1` above the line.
Multiply `1` to `21` and write the answer below `29`
Subtract `21` from `29` and write the answer one line below
Since `21` cannot go into `8` anymore, `8` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{29}}{\color{#9a00c7}{21}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{8}}{\color{#9a00c7}{21}}$$ `=` `1 8/21` Finally, combine the sum of the whole numbers and the sum of the fractions`7 2/3+3 5/7` `=` `10+1 8/21` `=` `11 8/21` `11 8/21` -
Question 3 of 3
3. Question
Subtract the following:`4 1/2-2 1/10`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, transform the mixed fractions to improper fractions$$\color{#00880A}{4}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\color{#00880A}{2} \frac{\color{#007DDC}{1}}{\color{#9a00c7}{10}}$$ `=` $$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{4})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}-\frac{(\color{#9a00c7}{10}\times\color{#00880A}{2})+\color{#007DDC}{1}}{\color{#9a00c7}{10}}$$ `=` $$\frac{8+1}{2}-\frac{20+1}{10}$$ `=` $$\frac{9}{2}-\frac{21}{10}$$ Notice that the fractions have different denominators.Find the `LCD` of `2` and `10` so we can subtract the fractions.Multiples of `2`:$$2\;\;4\;\;6\;\;8\;\;\color{#004ec4}{10}\;\;12$$Multiples of `10`:$$\color{#004ec4}{10}\;\;20\;\;30$$The `LCD` of `2` and `10` is `10`Next, we get the same denominator and subtract the fractions`9/2-21/10` `=` $$\frac{9\times\color{#CC0000}{5}}{2\times\color{#CC0000}{5}}-\frac{21}{10}$$ Multiply `5` so that the denominator becomes `10` `=` $$\frac{45}{\color{#004ec4}{10}}-\frac{21}{\color{#004ec4}{10}}$$ `=` $$\frac{24}{10}$$ Transform the fraction back to a mixed fractionStart by dividing the numerator by the denominatorArrange the numbers for long division
`10` goes into `24` two times. So write `2` above the line.
Multiply `2` to `10` and write the answer below `24`
Subtract `20` from `24` and write the answer one line below
[add colors: `2`]Since `10` cannot go into `4` anymore, `4` is left as the Remainder and `2` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{24}}{\color{#9a00c7}{10}}$$ `=` $$\color{#00880A}{2}\frac{\color{#e65021}{4}}{\color{#9a00c7}{10}}$$ `=` $$2\frac{4\div\color{#CC0000}{2}}{10\div\color{#CC0000}{2}}$$ Reduce to lowest terms `=` `2 2/5` `2 2/5`
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 LCM
- 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 Fractions 1
- Multiply and Divide Mixed Fractions 2
- Multiply and Divide Mixed Fractions 3
- Multiply and Divide Mixed Fractions 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