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.

${3}\over{2}$

${9}\over{6}$

$1 {{1} \over {2}}$ ✓

$2 {{1} \over {2}}$

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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.