Good Learning Co.
SavannahYear 8
← Maths
MathsNumber sense28 min★★ difficulty

Written methods with fractions and decimals

A recipe that needs 2 3/4 cups of flour and a bill split three ways both come down to the same four operations you already know — just with fractions and decimals in the mix.

Part of your national curriculum
  • Number: Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

Lesson overview

What you'll learn in this lesson

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

Key learning points

  • • Adding mixed numbers
  • • Multiplying fractions
  • • Decimal division

This lesson at a glance

  • 28 minutes
  • 13 parts to scroll through
  • 3 quick checks
  • Marked quiz at the end
  • Gentle pace: short sittings with pauses

Words to know

operationsformalwrittenmethodsapplied

Scroll down — the lesson carries on below

Part 1 of 13 · Discover8%
1

Watch & discover

Part 1 of 13

Watch first

Written methods with fractions and decimals

An English teaching video on this topic from MathTalk. Watch it, then scroll down for the lesson.

In a nutshell

Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

2

Learning cycle

Part 2 of 13

Learning cycle 1 of 2

Part 1 · Adding mixed numbers

A short piece of teaching, then a check to make sure it has landed.

3

Explore the idea

Part 3 of 13

Learn

Adding mixed numbers

Add 1 2/3 + 2 1/6. Convert to a common denominator of 6: 1 4/6 + 2 1/6 = 3 5/6. Whole numbers add separately from the fraction parts once denominators match.

4

Explore the idea

Part 4 of 13

Learn

Multiplying fractions

Multiply 3/4 × 2/5 by multiplying numerators and denominators: (3×2)/(4×5) = 6/20, which simplifies to 3/10.

5

Quick check

Part 5 of 13

Quick check

What is 1 2/3 + 2 1/6?

6

Reset break

Part 6 of 13

Pause

That's sitting 1 of 2 done

Stretch, get a drink, look out of the window. There is no timer and nothing is counting down — your place is saved, so you can come back in five minutes or tomorrow.

Stop here for now
7

Quick check

Part 7 of 13

Quick check

What is 3/4 × 2/5?

8

Learning cycle

Part 8 of 13

Learning cycle 2 of 2

Part 2 · Decimal division

A short piece of teaching, then a check to make sure it has landed.

9

Explore the idea

Part 9 of 13

Learn

Decimal division

Divide 12.6 by 0.3 by multiplying both numbers by 10 to clear the decimal: 126 ÷ 3 = 42. So 12.6 ÷ 0.3 = 42.

10

Quick check

Part 10 of 13

Quick check

What is 12.6 ÷ 0.3?

11

Challenge round

Part 11 of 13

Game · Sort it

Which of these are true?

Drag each card into the right column. Tap a card first if dragging is fiddly.

True

Not true

12

Mastery quiz

Part 12 of 13

Marked quiz

End of lesson quiz: Written methods with fractions and decimals

3 questions, marked with the reasoning shown. No timer.

  1. 1. What is 1 2/3 + 2 1/6?

  2. 2. What is 3/4 × 2/5?

  3. 3. What is 12.6 ÷ 0.3?

13

Lesson round-up

Part 13 of 13

Lesson round-up

Ready when you are

Quiz score

Not sat

Games

Not played

Points this lesson

0

Best run

0 in a row

Luna: 0 out of 3 on the practice checks. Only if you feel up to it — one more?

Ask Luna

Do the work

Your written work for this lesson

This is the part you'd do in your book at school. Pick the pieces below, write here or on paper, and photograph anything you draw or work out.

Article

The cost of a school trip

A school is planning a trip to a wildlife park. The coach costs £480 however many people go. Entry costs £9.50 for each pupil and each adult goes free. The school says every pupil must pay the same amount, and the trip must not lose money.

If 60 pupils go, the coach works out at £8 each, so the total for each pupil is £17.50. If only 40 pupils go, the coach works out at £12 each, so the price rises to £21.50. The teacher explains that the coach is a fixed cost and the entry is a cost per person — which is why the price per pupil changes when the number changes.

The school decides to charge £20 and to use anything left over for a second trip later in the year.

Written for Good Learning Co.

Reading questions

  1. Work out the total cost of the trip if 50 pupils go.
  2. Show why the price per pupil falls when more pupils go, using numbers.
  3. At £20 each, how many pupils must go before the trip makes money? Show your working.

  • Working out

    Working out

    Do the practice questions on paper, showing every step — not just the answer. Mark them yourself and circle anything you got wrong.

    10–15 questions

  • Worked example, explained

    Writing

    Copy one question out and write underneath, in words, why each step works.

    1 question, 4–5 sentences

  • Problem in words

    Working out

    Write your own real-life problem that uses today's method, then solve it.

    1 problem + solution

Saved as you type.

Part 1 of 13 · Watch & discover

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    Use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers

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