Complete an equivalent ratio

Equivalent ratios

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

Find the missing term

Start with 3:7. To make the first term 9, will adding 6 to both terms give the same ratio as multiplying both terms by 3?

Both methods start with 3:7. The Multiply row scales both terms by the batch count. The Add row adds the increase in the first term to both terms. Try one, three and four batches. At three batches, compare the second terms

At three batches, what happens to the second terms?

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

1. 1Same factor The terms a and b use the same positive scale factor k \(\displaystyle a:b=ka:kb\quad(k>0)\)
2. 2Three terms A second known pair can check your factor
3. 3Fraction notation The terms a and b correspond to c and d. For positive terms, the ratio equality can also be written as equal fractions \(\displaystyle a:b=c:d\quad\Longleftrightarrow\quad\frac{a}{b}=\frac{c}{d}\)

Equivalent ratios

\(\displaystyle x:56=3:8\)

Find the missing term

Match the two known second terms

Equivalent ratios

\(\displaystyle 8:14:18=6:x:13.5\)

Find the missing term

Find the factor from the first term on the left to the first term on the right

Required equivalent ratio

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

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