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Order of Operations Involving Fractions 2Order of Operations Involving Fractions 2
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Question 1 of 3
1. Question
Solve the following.`3/4xx2/3+(3-2/3)`Hint
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Order of Operations (BODMAS)
B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – SubtractionTransforming 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 remainderAccording to BODMAS, Bracket is prioritized over Multiplication, then followed by Addition.Ignore the other operations for now and only do the operation inside the bracket, which is subtraction.$$\color{#9E9E9E}{\frac{3}{4}\times\frac{2}{3}+}\color{#00880A}{\left({3-\frac{2}{3}}\right)}$$ First, make `3` into a fraction. Recall that all whole numbers has `1` as a denominator`3` `=` `3/1` To proceed with Subtraction, find the `LCD` of `1` and `3`Multiples of `1`:$$1\;\;2\;\;\color{#004ec4}{3}\;\;4\;\;5$$Multiples of `3`:$$\color{#004ec4}{3}\;\;6\;\;9\;\;12\;\;15$$The `LCD` of `1` and `3` is `3`Use the `LCD` as the denominator and then subtract.`3/1-2/3` `=` $$\frac{(\color{#004ec4}{3}\div1)\times3}{\color{#004ec4}{3}}-\frac{(\color{#004ec4}{3}\div3)\times2}{\color{#004ec4}{3}}$$ `=` `(3xx3)/3-(1xx2)/3` `=` `9/2-2/3` `=` `7/3` Next, ignore the addition for now and only do Multiplication.$$\color{#CC0000}{\frac{3}{4}\times\frac{2}{3}}\color{#9E9E9E}{+\frac{7}{3}}$$ `=` $$\frac{6}{12}\color{#9E9E9E}{+\frac{7}{3}}$$ `=` $$\frac{1}{2}\color{#9E9E9E}{+\frac{7}{3}}$$ Simplify` Next, to proceed with Addition, find the `LCD` of `2` and `3`Multiples of `2`:$$2\;\;4\;\;\color{#004ec4}{6}\;\;8\;\;10$$Multiples of `3`:$$3\;\;\color{#004ec4}{6}\;\;9\;\;12\;\;15$$The `LCD` of `2` and `3` is `6`Use the `LCD` as the denominator and then add.`1/2+7/3` `=` $$\frac{(\color{#004ec4}{6}\div2)\times1}{\color{#004ec4}{6}}+\frac{(\color{#004ec4}{6}\div3)\times7}{\color{#004ec4}{6}}$$ `=` `(3xx1)/6+(2xx7)/6` `=` `3/6+14/6` `=` `17/6` Finally, convert the improper fraction into a mixed number.Arrange the numbers for long division
`6` goes into `17` two times. So write `2` above the line.
Multiply `2` to `6` and write the answer below `17`
Subtract `12` from `17` and write the answer one line below
Since `6` cannot go into `5` anymore, `5` is left as the Remainder and `2` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{17}}{\color{#9a00c7}{6}}$$ `=` $$\color{#00880A}{2}\frac{\color{#e65021}{5}}{\color{#9a00c7}{6}}$$ `2 5/6` -
Question 2 of 3
2. Question
Solve the following.`4/5+3 2/3-:1/6`Hint
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Order of Operations (BODMAS)
B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – SubtractionTransforming a Fraction from Mixed to Improper
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ First, convert the mixed number in a fraction by multiplying the denominator by the whole number and then adding the numerator$$\color{#00880A}{3}\frac{\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{3})+\color{#007DDC}{2}}{\color{#9a00c7}{3}}$$ `=` $$\frac{9+2}{3}$$ `=` $$\frac{11}{3}$$ According to BODMAS, Division is prioritized over Addition.Ignore the addition for now and only do division.$$\color{#9E9E9E}{\frac{4}{5}+}\frac{11}{3}\div\frac{1}{6}$$ `=` $$\color{#9E9E9E}{\frac{4}{5}+}\color{#e85e00}{\frac{11}{3}\div\frac{6}{1}}$$ Find the reciprocal of `1/6` then proceed with multiplication `=` $$\color{#9E9E9E}{\frac{4}{5}+}\frac{66}{3}$$ `=` $$\color{#9E9E9E}{\frac{4}{5}+}22$$ Simplify Simply combine the two remaining values to make a mixed number`4/5+22` `=` `22 4/5` `22 4/5` -
Question 3 of 3
3. Question
Solve the following.`5/8+1 1/2-:1 1/3`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
`=` $$\frac{(\color{#9a00c7}{c}\times\color{#00880A}{A})+\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ Order of Operations (BODMAS)
B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – SubtractionFirst, convert the mixed numbers in fractions by multiplying the denominator by the whole number and then adding the numerator`1 1/2`$$\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{2}}$$ `=` $$\frac{(\color{#9a00c7}{2}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{2}}$$ `=` $$\frac{2+1}{2}$$ `=` $$\frac{3}{2}$$ `1 1/3`$$\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{3}}$$ `=` $$\frac{(\color{#9a00c7}{3}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{3}}$$ `=` $$\frac{3+1}{3}$$ `=` $$\frac{4}{3}$$ According to BODMAS, Division is prioritized over Addition.Ignore the addition for now and only do division.$$\color{#9E9E9E}{\frac{5}{8}+}\color{#e85e00}{\frac{3}{2}\div\frac{4}{3}}$$ `=` $$\color{#9E9E9E}{\frac{5}{8}+}\frac{3}{2}\times\frac{3}{4}$$ Find the reciprocal of `4/3` then proceed with multiplication `=` $$\color{#9E9E9E}{\frac{5}{8}+}\frac{9}{8}$$ Next, proceed with the AdditionSince the denominators of the remaining values are the same, add only the numerators$$\frac{5}{8}+\frac{9}{8}$$ `=` $$\frac{14}{8}$$ Finally, convert the improper fraction into a mixed number.Arrange the numbers for long division
`8` goes into `14` one time. So write `1` above the line.
Multiply `1` to `8` and write the answer below `14`
Subtract `8` from `14` and write the answer one line below
Since `8` cannot go into `6` anymore, `6` is left as the Remainder and `1` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{14}}{\color{#9a00c7}{8}}$$ `=` $$\color{#00880A}{1}\frac{\color{#e65021}{6}}{\color{#9a00c7}{8}}$$ `=` `1 3/4` Simplify the fraction `1 3/4`
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