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Order of Operations Involving Fractions 1Order of Operations Involving Fractions 1
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Question 1 of 4
1. Question
Solve the following.`2/3-1/2xx3/4`Write fractions in the format “a/b”- (7/24)
Hint
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Order of Operations (BODMAS)
B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – SubtractionAccording to BODMAS, Multiplication is prioritized over Subtraction.Ignore the subtraction for now and only do multiplication.$$\color{#9E9E9E}{\frac{2}{3}-}\color{#CC0000}{\frac{1}{2}\times\frac{3}{4}}$$ `=` $$\color{#9E9E9E}{\frac{2}{3}-}\frac{3}{8}$$ To proceed with Subtraction, find the `LCD` of `3` and `8`Multiples of `3`:$$3\;\;6\;\;9\;\;12\;\;15\;\;18\;\;21\;\;\color{#004ec4}{24}\;\;27$$Multiples of `8`:$$8\;\;16\;\;\color{#004ec4}{24}\;\;32\;\;40\;\;48$$The `LCD` of `3` and `8` is `24`Use the `LCD` as the denominator and then subtract.`2/3-3/8` `=` $$\frac{(\color{#004ec4}{24}\div3)\times2}{\color{#004ec4}{24}}-\frac{(\color{#004ec4}{24}\div8)\times3}{\color{#004ec4}{24}}$$ `=` `(8xx2)/24-(3xx3)/24` `=` `16/24-9/24` `=` `7/24` `7/24` -
Question 2 of 4
2. Question
Solve the following.`3/7+1/4xx3+1/4`Hint
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Order of Operations (BODMAS)
B – Bracket
O – Over (Powers, Exponents)
D – Division
M – Multiplication
A – Addition
S – SubtractionAccording to BODMAS, Multiplication is prioritized over Addition.Ignore the addition for now and only do multiplication.$$\color{#9E9E9E}{\frac{3}{7}+}\color{#CC0000}{\frac{1}{4}\times3}\color{#9E9E9E}{+\frac{1}{4}}$$ `=` $$\color{#9E9E9E}{\frac{3}{7}+}\frac{3}{4}\color{#9E9E9E}{+\frac{1}{4}}$$ Next, proceed with the AdditionSince the denominators of the second and third value are the same, add only the numerators$$\color{#9E9E9E}{\frac{3}{7}+}\color{#A57200}{\frac{3}{4}+\frac{1}{4}}$$ `=` $$\color{#9E9E9E}{\frac{3}{7}+}\frac{4}{4}$$ `=` $$\color{#9E9E9E}{\frac{3}{7}+}1$$ Simply combine the two remaining values to make a mixed number`3/7+1` `=` `1 3/7` `1 3/7` -
Question 3 of 4
3. Question
Solve the following.`5-2/5-:7/10`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, Division is prioritized over Subtraction.Ignore the subtraction for now and only do division.$$\color{#9E9E9E}{5-}\color{#e85e00}{\frac{2}{5}\div\frac{7}{10}}$$ `=` $$\color{#9E9E9E}{5-}\frac{2}{5}\times\frac{10}{7}$$ Find the reciprocal of `7/10` then proceed with multiplication `=` $$\color{#9E9E9E}{5-}\frac{2}{1}\times\frac{2}{7}$$ Simplify `=` $$\color{#9E9E9E}{5-}\frac{4}{7}$$ Make `5` into a fraction. Recall that all whole numbers has `1` as a denominator`5` `=` `5/1` To proceed with Subtraction, find the `LCD` of `1` and `7`Multiples of `1`:$$1\;\;2\;\;3\;\;4\;\;5\;\;6\;\;\color{#004ec4}{7}$$Multiples of `7`:$$\color{#004ec4}{7}\;\;14\;\;21\;\;28\;\;35$$The `LCD` of `1` and `7` is `7`Use the `LCD` as the denominator and then subtract.`5/1-4/7` `=` $$\frac{(\color{#004ec4}{7}\div1)\times5}{\color{#004ec4}{7}}-\frac{(\color{#004ec4}{7}\div7)\times4}{\color{#004ec4}{7}}$$ `=` `(7xx5)/7-(1xx4)/7` `=` `35/7-4/7` `=` `31/7` Finally, convert the improper fraction into a mixed number.Arrange the numbers for long division
`7` goes into `31` four times. So write `4` above the line.
Multiply `4` to `7` and write the answer below `31`
Subtract `28` from `31` and write the answer one line below
Since `7` cannot go into `3` anymore, `3` is left as the Remainder and `4` is the QuotientSubstitute values into the given formula$$\frac{\color{#007DDC}{b}}{\color{#9a00c7}{c}}$$ `=` $$\color{#00880A}{Q}\frac{\color{#e65021}{R}}{\color{#9a00c7}{c}}$$ $$\frac{\color{#007DDC}{31}}{\color{#9a00c7}{7}}$$ `=` $$\color{#00880A}{4}\frac{\color{#e65021}{3}}{\color{#9a00c7}{7}}$$ `4 3/7` -
Question 4 of 4
4. Question
Solve the following.`1 1/5-:2+4`Hint
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Correct!
Incorrect
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$$\color{#00880A}{1}\frac{\color{#007DDC}{1}}{\color{#9a00c7}{5}}$$ `=` $$\frac{(\color{#9a00c7}{5}\times\color{#00880A}{1})+\color{#007DDC}{1}}{\color{#9a00c7}{5}}$$ `=` $$\frac{5+1}{5}$$ `=` $$\frac{6}{5}$$ Next, make `2` into a fractions. Recall that all whole numbers has `1` as a denominator`2` `=` `2/1` According to BODMAS, Division is prioritized over Addition.Ignore the addition for now and only do division.$$\color{#e85e00}{\frac{6}{5}\div\frac{2}{1}}\color{#9E9E9E}{+4}$$ `=` $$\frac{6}{5}\times\frac{1}{2}\color{#9E9E9E}{+4}$$ Find the reciprocal of `2/1` then proceed with multiplication `=` $$\frac{6}{10}\color{#9E9E9E}{+4}$$ `=` $$\frac{3}{5}\color{#9E9E9E}{+4}$$ Simplify Simply combine the two remaining values to make a mixed number`3/5+4` `=` `4 3/5` `4 3/5`
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 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