Securing understanding of addition and subtraction with fractions | Maths

Starter quiz

When subtracting fractions you must have ______.
- a common numerator
- a common denominator ✓
- the largest fraction first
Which of the following are not common denominators of ${1}\over{4}$ and ${7}\over{20}$ ?
- 4 ✓
- 20
- 24 ✓
- 40
Which symbol is missing here? $\frac{2}{9} + \frac{1}{8} \square \frac{2}{9} + \frac{1}{7}$ .
- < ✓
- >
- =
- ?
Calculate ${7}\over{12}$ - ${1}\over{3}$ .
- ${4}\over{9}$
- ${3}\over{12}$ ✓
- ${4}\over{12}$
- ${8}\over{15}$
Which of the following is not a correct alternative for ${3}\over{8}$ - ${3}\over{4}$ + ${7}\over{16}$ ?
- ${3}\over{8}$ + ${7}\over{16}$ - ${3}\over{4}$
- ${3}\over{8}$ + ${7}\over{16}$ + $\left(-\frac34\right)$
- ${3}\over{8}$ - $\left(\frac{3}{4} + \frac{7}{16}\right)$ ✓
Calculate ${3}\over{8}$ - ${3}\over{4}$ + ${7}\over{16}$ .
- $\left(-\frac4{16}\right)$
- ${7}\over{4}$
- ${7}\over{12}$
- ${1}\over{16}$ ✓

What is the name of a number that has both an integer part and a fractional part?
- 'mixed number' ✓
Which of the following is $3 {{2} \over {3}}$ as an improper fraction?
- ${32}\over{3}$
- ${18}\over{3}$
- ${11}\over{3}$ ✓
- ${8}\over{3}$
Which of the following show a correct first step to calculate $3 {{1} \over {3}}$ - $1 {{5} \over {6}}$ ?
- ${10}\over{3}$ - ${11}\over{6}$ ✓
- ${7}\over{3}$ - ${11}\over{6}$
- (3 - 1) + $\left(\frac13-\frac56\right)$ ✓
- (3 - 1) - $\left(\frac13-\frac56\right)$
Which of the following can be simplified before calculating?
- ${5}\over{8}$ + ${3}\over{7}$
- ${4}\over{9}$ - ${5}\over{15}$ ✓
- ${2}\over{5}$ + ${4}\over{16}$ ✓
- ${2}\over{3}$ - ${2}\over{7}$
What is the missing digit in this calculation $1 {{1} \over {3}}$ + $2 {{\square} \over {6}}$ = $4 {{1} \over {6}}$ ?
- 1
- 2
- 3
- 4
- 5 ✓
Calculate $3 {{1} \over {3}}$ - $1 {{5} \over {6}}$ , give your answer in its simplest form.
- ${3}\over{2}$
- ${9}\over{6}$
- $1 {{1} \over {2}}$ ✓
- $2 {{1} \over {2}}$

To make the denominators the same, you may need to scale up or down.
It can be easier to add/subtract the wholes and then add/subtract the fractions.
Improper fractions can help when exchanging/regrouping is required.

When partitioning mixed numbers and subtracting incorrectly subtracting the fractional part.

Use an integer example to show the structure of partitioning. E.g. 28 - 15 = (20 + 8) - (10 + 5) = (20 - 10) + (8 - 5) not (20 - 10)-(8 - 5)

Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Mixed number - A mixed number is an improper fraction written as its integer part plus the fractional part where the fractional part is a proper fraction.
Lcm - LCM is an abbreviation for lowest common multiple.