Solve problems involving addition and subtraction of mixed numbers | Maths

Starter quiz

Look at this calculation: ${4} \over {10}$ − ${3} \over {10}$ What is the unit we are working with?

thirds

quarters

fifths

tenths ✓
$2{{4} \over {5}}$ + $1{{3} \over {5}}$ =

${37} \over {5}$

$3{7} \over {10}$

$4{{2} \over {5}}$ ✓

$4{{2} \over {10}}$

$1{{1} \over {5}}$
$3{{4} \over {5}}$ − $1{{3} \over {5}}$ =

$4{{7} \over {5}}$

$4{{7} \over {10}}$

${1} \over {5}$

${1} \over {0}$

$2{{1} \over {5}}$ ✓
Use ‘finding the difference’ by counting on to solve $8{{2} \over {9}}$ − $7{{8} \over {9}}$

$15{{10} \over {9}}$

$15{{10} \over {18}}$

$1{{6} \over {9}}$

${3} \over {9}$ ✓

$1{{3} \over {9}}$
Match the mixed number to their equivalent improper fraction.

$1{{4} \over {5}}$

⇔

${9} \over {5}$ ✓

$4{{4} \over {5}}$

⇔

${24} \over {5}$ ✓

$2{{4} \over {5}}$

⇔

${14} \over {5}$ ✓

$5{{1} \over {5}}$

⇔

${26} \over {5}$ ✓

$3{{3} \over {5}}$

⇔

${18} \over {5}$ ✓
By expressing the mixed numbers as improper fractions, calculate this: $7{{3} \over {8}}$ − $2{{5} \over {8}}$ =

$4{{6} \over {8}}$ ✓

$9{{8} \over {8}}$

10

$5{{2} \over {8}}$

6

Exit quiz

Which bar model represents this problem? Izzy eats one and one-quarter slices of pizza. How much less pizza does she eat than Andeep who has eaten two and three-quarter slices of pizza?
Look at the table. How far does Izzy walk over Monday and Tuesday in all?

${45} \over {5}$

5 ✓

$5{{3} \over {5}}$

$3{{4} \over {5}}$
Look at the table. How far does Izzy walk over Tuesday and Wednesday in total?

${56} \over {5}$

6

$6{{1} \over {5}}$ ✓

$5{{1} \over {5}}$
Look at the table. How much further does Izzy walk on Wednesday than Thursday?

$4{{5} \over {5}}$

5

$2{{1} \over {5}}$

$1{{4} \over {5}}$ ✓
Andeep has a five and five-tenths metres of rope. He cuts a piece off. He has three and two-tenth metres left. What length of rope did he cut off?

$2{{7} \over {10}}$

$2{{3} \over {10}}$ ✓

$8{{7} \over {10}}$

$2{{3} \over {0}}$

$1{{3} \over {10}}$
Izzy spends two and three-quarter hours in the park on Saturday and another two and two-quarter hours on Sunday. How long does she spend in the park in total?

$4{{5} \over {8}}$

$2{{5} \over {8}}$

$5{{1} \over {4}}$ ✓

${1} \over {4}$

$4{{6} \over {4}}$

Worksheet

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Lesson Details

Key learning points

Improper fractions can be added and subtracted in the same way as proper fractions.
When interpreting data or solving problems, number-sense is needed to determine the most efficient strategy to use.
Decide on the most efficient strategy by looking at the fractions of the minuend and subtrahend.
Bar models are a useful tool to represent word problems and support in forming an equation to solve.

Common misconception

Children may not always choose an efficient strategy when adding or subtracting mixed numbers. This may result in calculation errors being made.

Look at the numbers in the calculation. What do you notice? Which strategy would be most efficient to use with these numbers? Check your answer using a different strategy. If you get the same answer, you are likely to be correct.

Keywords

Mixed number - A mixed number is a whole number and a fraction combined.
Improper fraction - An improper fraction is a fraction where the numerator is greater than or equal to the denominator.