Two signs together $+\,- = -\quad -\,- = +$$5+(-3)=5-3$; $4-(-6)=4+6$
Multiply / divide $\text{same signs}\to+,\ \text{different}\to-$$(-4)\times(-3)=12$; $(-20)\div4=-5$
Ordering $\ldots -3<-2<-1<0<1\ldots$the further LEFT on a number line, the smaller
BIDMAS still applies $\times,\div\text{ before }+,-$e.g. $-2+3\times(-4)=-2-12=-14$
Subtract a negative · $4-(-6)$
two minuses make a plus
$4+6=10$
Multiply · $(-3)\times(-8)$
same signs $\to$ positive
$=24$
Order · $-1,\ -5,\ 2,\ -3$
most negative first
$-5,\ -3,\ -1,\ 2$
Negative number: a number less than zero, e.g. $-4$.
Number line: a line showing order; numbers get smaller to the left.
Sum / difference: the result of adding / subtracting.
Product: the result of multiplying.
Directed number: a number with a $+$ or $-$ direction (positive or negative).
✗ $4-(-6)=-2$
✓ two minuses make a plus: $4+6=10$.
✗ $(-3)\times(-8)=-24$
✓ same signs give a positive: $+24$.
✗ $-5$ is bigger than $-2$
✓ $-5$ is further left, so it is SMALLER: $-5<-2$.
✗ Ignoring BIDMAS with negatives
✓ do $\times$ and $\div$ first: $-2+3\times(-4)=-2-12$.
• Adding a negative is the same as subtracting: $5+(-3)=5-3$.
• Subtracting a negative is the same as adding: $4-(-6)=4+6$.
• Two negatives multiplied (or divided) give a POSITIVE.
• Rewrite double signs first: $+\,-\to-$ and $-\,-\to+$.
• For $\times$ and $\div$: count the minus signs – an even number gives $+$, odd gives $-$.
• Use a number line for adding and subtracting.
mathedup.co.uk · sheet JUF0