# C4.9 Study Guide

## Your daily routine

Open your day's lesson, read the instructions and try the question on paper first. Enter each answer in its own field, then use the local checker. If you are stuck, read the safe hint or follow the separate worked example. The example uses different numbers: learn its method, then return to your own question.

## Daily focus

**Monday:** Count in halves and matching decimals. Connect equal sharing with fractions and percentages of a quantity. Read large numbers in groups, explain each digit and practise written arithmetic.

**Tuesday:** Count in quarters and matching decimals. Compare fractions using equal-sized parts, convert decimals into reduced fractions and combine useful multiplication parts.

**Wednesday:** Count in eighths and matching decimals. Keep the whole-number part when comparing a mixed number with a fraction. Use place value to expand large numbers and check calculations with inverse operations.

**Thursday:** Count in thirds and exact recurring decimals. A bar or bracketed repeating digit represents an endless pattern, not a rounded value. Use exact values throughout calculations and division.

**Friday:** Count in fifths and matching decimals. Compare decimal places carefully, use tens-and-ones partial products and connect positive multiples with written division.

## Methods to practise

### Counting and fractions

Start at the stated term and make equal jumps. Include the stopping point, but do not enter the starting term again when it is already given. On a fraction number line, each denominator-sized group makes a whole. For a fraction of a quantity, divide by the denominator and then multiply by the numerator. To compare fractions, use a common denominator or compare their whole-number parts first.

### Place value

Read large numbers in three-digit groups: millions, thousands and ones. “Complete millions” means all complete groups of that size, not just one digit. A digit's value is its digit multiplied by one unit of its column. In expanded form, enter the contribution from every place separately; a zero digit contributes zero.

For rounding, identify the neighbouring multiples of the requested place and compare with their halfway point. When multiplying or dividing by a power of ten, move digits in a place-value chart and use placeholder zeros where needed.

### Written arithmetic and money

Align decimal points before adding or subtracting. Work from the right-hand column and show regrouping above the appropriate place. Check an addition by subtraction, or a subtraction by addition. In a missing-money equation, find the gap between the amount at the start and the amount left; keep dollars and cents aligned.

### Multiplication and division

Calculate every useful part before combining it. Split a two-digit multiplier into its tens and ones, record both partial products and add their rows. Positive multiples begin with one group, not zero. Try division mentally and with a written algorithm; both methods should agree. If a remainder remains, continue to an exact decimal rather than rounding.

## Entering answers

Use `a/b` for a fraction and a space in a mixed number, such as `3 2/5`. Write a single reduced fraction when simplest fraction form is requested. For recurring decimals, put only the repeating digits in brackets, such as `0.(7)`. For money questions, enter the amount in dollars; the dollar sign may be omitted. Use `a` or `b` only when the question asks you to choose an option.

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