SQA National 5 Applications of Mathematics

## Notation Applications of Mathematics problems are written in words and symbols, and the first job is to read the symbols correctly. | Symbol | Meaning | |---|---| | $=$ | is equal to | | $+$, $-$ | add, subtract | | $\times$ | multiply | | $/$ or $\div$ | divide | | $<$, $>$ | is less than, is greater than | | $( \ )$ | do the calculation inside first | | $\%$ | per cent, meaning out of 100 | | $:$ | ratio, as in 2 : 3 | | $.$ | decimal point, separating whole numbers from parts | When a calculation has several operations, brackets are done first, then multiplication and division from left to right, then addition and subtraction from left to right. So $4 + 6 \times 3 = 22$, since the multiplication comes first, but $(4 + 6) \times 3 = 30$. A simple formula is a rule written with letters. To use it, replace each letter with its value and work out the result. If the cost in pounds of hiring a van for $d$ days is $C = 25 + 40d$, then for 3 days $$ C = 25 + 40 \times 3 = 25 + 120 = 145 $$ so the hire costs £145. The multiplication is done before the addition. The inequality symbols compare amounts. A result of 7.4 is less than 8, written $7.4 < 8$, and a mass of 12 kg is greater than 9.5 kg, written $12 > 9.5$. The open end of the symbol faces the larger number. ## Units A number in a real situation is almost always attached to a unit, and the unit has to be written with the answer. The units used most often are below. | Quantity | Units and relationships | |---|---| | Money…