Complete equivalent ratios

Equivalent ratios

\(\displaystyle 4:9=12:x\)

Find the missing term

Both methods start with the ratio three to seven. The same-factor method multiplies both terms by the batch count. The same-addition method adds the increase in the first term to both terms. Move to three batches and compare the second terms

What happens to the second terms at that setting?

Follow the corresponding pair

Find the factor between known terms in the same position. Apply it to the other term in the same direction. A factor can be less than one

Same factor

The terms a and b use the same positive scale factor k

Three terms

A second known pair can check your factor

Fraction notation

The terms a and b correspond to c and d. For positive terms, the ratio equality can also be written as equal fractions

Use a factor below one

Find the missing term

Divide the known target term by its corresponding term in the complete ratio

Apply this multiplier to the term corresponding to x

Substitute the missing term to check the completed ratios

Start with the complete ratio

Check a second known pair

Required equivalent ratio

\(\displaystyle 5:12=20:x\)

What is the first error in the student's method?

Read equivalent fraction notation

Recognise an equivalent ratio

Complete a three-term ratio

Use a rational multiplier