lesson
Keep the sign of the whole mixed number
1 · Learn
A negative mixed number such as -1 1/2 means -(1 + 1/2), so it is -3/2, not -1 + 1/2. Convert mixed numbers to improper fractions before a multi-step calculation. Keep the negative sign attached to the whole numerator.
For addition and subtraction, use a common denominator. For -1 1/2 + 3/4, write -6/4 + 3/4 = -3/4. Subtracting the same positive fraction instead gives -6/4 - 3/4 = -9/4. On a number line, adding 3/4 moves right; subtracting it moves left.
For multiplication, multiply numerators and denominators and apply the sign rule: (-3/2) × (3/4) = -9/8. For division by a non-zero fraction, multiply by its reciprocal: (-3/2) ÷ (3/4) = (-3/2) × (4/3) = -2. Check by multiplying -2 by 3/4 to recover -3/2.
Simplify exact answers by dividing numerator and denominator by a common factor. Do not add denominators when adding fractions. Two negative factors give a positive product, but adding two negative numbers gives a negative sum: the operation matters.
2 · Worked example
Calculate (-2 1/3) × (-3/4). Convert the mixed number to -7/3, then multiply: (-7/3) × (-3/4) = 21/12 = 7/4. The product is positive because both factors are negative. This does not mean their sum is positive.
3 · Your turn
Let A = -(1 + 1/2) and B = 3/4. Find A + B, A - B, A × B and A ÷ B. Give exact simplified fractions or integers.
Check your answer
A + B = -3/4; A - B = -9/4; A × B = -9/8; A ÷ B = -2. Multiplying the quotient -2 by B = 3/4 returns A = -3/2.
4 · Apply your learning
Use the worked number line to compare A + B and A - B. Then change B to -3/4 and predict the direction of each move before calculating. Explain why a sign rule from multiplication cannot simply be copied into addition.
Adult guidance and safety
Ask pupils to justify classifications and operations, not just repeat a rule. Use a number line and exact fractions before decimal approximations. Check the scope of a negative sign and distinguish a principal root from all solutions of an equation.
Open your writing and drawing pad
Write, draw or show your working. Use a mouse, pen or finger. This pad is not a submitted answer.
Not saved to your account. Download your drawing as PNG and your typed notes as TXT before leaving or refreshing. They are separate files. Do not enter private information.
Open a picture saved on this device to draw on it again. Opening replaces the drawing, but Undo can restore it. PNG only, up to 4 MB and 4096 × 4096 pixels. The picture stays in this browser; it is not uploaded. Paper lines in a saved picture become part of that picture.
Clear the drawing? Your typed notes will stay. You can undo this action.
Your pad is empty.
Open a UTF-8 TXT file from this device, up to 40 KB and 10,000 characters. It stays in this browser. Opening can be undone until you type again. Downloads keep a new copy; they do not change the file you opened.
Replace the notes on this page with the opened file? Download the current notes first if you want to keep them.
Typed notes are not submitted answers.
Check a calculation · Year 5 onward
Use this only when your teacher or adult allows a calculator for the task. Show your thinking first. It does not replace mental or written arithmetic and does not mark your lesson answer.
Powers, roots and trigonometry · Year 7 onward
Use only when the task allows a calculator. Choose one operation at a time and record your working. Trigonometry here always uses degrees (DEG), not radians. Inverse sine, cosine and tangent return an angle, not a reciprocal. Keep exact fractions and π in answers when requested.
Approximate numerical results use up to 12 significant digits. Inverse sine returns −90° to 90°, inverse cosine 0° to 180°, and inverse tangent −90° to 90°; these are principal values, not every possible solution of a trigonometric equation.
Practice this lesson
Lesson resources
Browse the available practice activities and worksheets for this lesson.
Your progress