Substitute values into a formula

Cost in dollars

\(\displaystyle C=14+6h\)

Hire time in hours

\(\displaystyle h=2.5\)

Calculate the hire cost

Rate first, in dollars

\(\displaystyle C=14+6h\)

Sum first, in dollars

\(\displaystyle D=(14+6)h=20h\)

Hire time in hours

\(\displaystyle h\)

Compare the two calculations as the hire time changes. The first adds the fixed charge once; the second multiplies the whole sum

How do the bars compare across the slider range?

Calculate the subject

Here C is the cost in dollars and h is the hire time in hours. A formula relates variables. Its subject is isolated on one side. Use the substitution and order of operations you already know, then attach the unit of the calculated quantity

1. 1Match the variable Replace the time with its given value \(\displaystyle C=18+4(3.5)\)
2. 2Evaluate the product Keep the fixed charge while calculating the hourly charge \(\displaystyle C=18+14\)
3. 3Add and state the unit The subject represents the cost \(\displaystyle C=32\text{ dollars}\)
4. 4Keep brackets around negative inputs Square the whole input before multiplying by its coefficient. A negative coefficient keeps its sign \(\displaystyle -2(-3)^2=-2(9)=-18\)

Cost in dollars

\(\displaystyle C=3u+7v\)

First length in metres

\(\displaystyle u=2.4\)

Second length in metres

\(\displaystyle v=1.8\)

Calculate the total cost of the two supplies

Match each length to its letter before multiplying

Area formula

\(\displaystyle A=lw\)

Length

\(\displaystyle l=4.5\text{ m}\)

Width

\(\displaystyle w=2.8\text{ m}\)

Calculate the area of the rectangle

Replace both variables, then use the operation shown by the formula

Keep the numerator together

A fraction bar groups the whole numerator. Add its terms before dividing, and keep the sign of the denominator

1. 1Substitute into the fraction Keep both numerator terms above the fraction bar \(\displaystyle R=\frac{-1+4}{-2}\)
2. 2Add the numerator Leave the denominator unchanged \(\displaystyle R=\frac{3}{-2}\)
3. 3Divide A positive numerator divided by a negative denominator gives a negative result \(\displaystyle R=-\frac{3}{2}\)

Formula

\(\displaystyle F=\frac{a+b}{c}\)

Value of a

\(\displaystyle a=-\frac{7}{4}\)

Value of b

\(\displaystyle b=\frac{1}{2}\)

Value of c

\(\displaystyle c=-\frac{3}{2}\)

Calculate the subject. Give an exact value

Work out the whole numerator before dividing by the denominator

Formula

\(\displaystyle G=-2x^2+3y\)

Assigned values

\(\displaystyle x=-1.5,\quad y=2.4\)

Calculate the subject

The square applies to the input, not to its coefficient

Formula

\(\displaystyle E=2x^2+3y\)

Assigned values

\(\displaystyle x=-3,\quad y=4\)

Which line contains the first error?