Question

• a ratio relates two or more numbers with the same units. • in ratios, order is important. example: there are 8 apples and 5 oranges in a fruit basket. write the ratio of apples to oranges. ➔ we can write ratios in three different ways: as a fraction \\(\frac{8}{5}\\), as a ratio 8:5, using words 8 to 5 1) look at the figures below. there are 5 circles, 4 squares, and 3 triangles. find the ratios of: figures of circles, squares, triangles a) circles to squares b) triangles to circles c) squares to total number of figure equivalent ratios equivalent ratios can be found by simply multiplying (or dividing) each term of the ratio by the same number. diagram of equivalent ratios: \\(\frac{1}{2}\\) = \\(\frac{2}{4}\\) = \\(\frac{4}{8}\\) = \\(\frac{8}{16}\\) with ×2 operations 2) write two equivalent ratios for each given ratio: a) 4:7 b) \\(\frac{5}{25}\\) c) 6:12

Explanation:

Step1: Solve 1a: Circles to squares

There are 5 circles and 4 squares. Write the ratio in three forms:
Fraction: $\frac{5}{4}$
Ratio: $5:4$
Word form: 5 to 4

Step2: Solve 1b: Triangles to circles

There are 3 triangles and 5 circles. Write the ratio in three forms:
Fraction: $\frac{3}{5}$
Ratio: $3:5$
Word form: 3 to 5

Step3: Solve 1c: Squares to total figures

First calculate total figures: $5+4+3=12$. There are 4 squares. Write the ratio in three forms:
Fraction: $\frac{4}{12}=\frac{1}{3}$
Ratio: $4:12=1:3$
Word form: 4 to 12 (or 1 to 3)

Step4: Solve 2a: Equivalent ratios for 4:7

Multiply both terms by 2: $4\times2:7\times2=8:10$
Multiply both terms by 3: $4\times3:7\times3=12:21$

Step5: Solve 2b: Equivalent ratios for $\frac{5}{25}$

Divide both terms by 5: $\frac{5\div5}{25\div5}=\frac{1}{5}$
Multiply both terms by 2: $\frac{5\times2}{25\times2}=\frac{10}{50}$

Step6: Solve 2c: Equivalent ratios for 6:12

Divide both terms by 6: $6\div6:12\div6=1:2$
Multiply both terms by 2: $6\times2:12\times2=12:24$

Answer:

1)
a) $\frac{5}{4}$, $5:4$, 5 to 4
b) $\frac{3}{5}$, $3:5$, 3 to 5
c) $\frac{1}{3}$, $1:3$, 1 to 3 (or $\frac{4}{12}$, $4:12$, 4 to 12)
2)
a) $8:14$, $12:21$ (answers may vary)
b) $\frac{1}{5}$, $\frac{10}{50}$ (answers may vary)
c) $1:2$, $12:24$ (answers may vary)