Question

write ratios to describe the pictures. 1. circles to shapes 2. triangles to circles 3. circles to squares 4. squares to triangles 5. shaded parts to total parts 6. shaded parts to white parts write an equivalent ratio for each. circle each ratio that is in simplified form. 7. $\frac{2}{6}$ = _ 8. $\frac{1}{5}$ = _ 9. $\frac{12}{24}$ = _ 10. $\frac{3}{4}$ = _ 11. $\frac{16}{18}$ = _ 12. $\frac{4}{6}$ = _ 13. $\frac{2}{10}$ = _ 14. $\frac{12}{16}$ = _ 15. $\frac{5}{8}$ = _ 16. $\frac{2}{3}$ = _ 17. $\frac{12}{20}$ = _ 18. $\frac{25}{30}$ = _ ★ tell how you know that two ratios are equivalent.

Explanation:

Step1: Count shapes for first - set of ratios

There are 5 circles, 6 triangles, and 4 squares. Total shapes = 5 + 6+4 = 15.

Step2: Calculate circles to shapes ratio

Number of circles is 5 and total shapes is 15. Ratio is $\frac{5}{15}=\frac{1}{3}$.

Step3: Calculate triangles to circles ratio

Number of triangles is 6 and circles is 5. Ratio is $\frac{6}{5}$.

Step4: Calculate circles to squares ratio

Number of circles is 5 and squares is 4. Ratio is $\frac{5}{4}$.

Step5: Calculate squares to triangles ratio

Number of squares is 4 and triangles is 6. Ratio is $\frac{4}{6}=\frac{2}{3}$.

Step6: For the pie - chart (assuming 8 parts in total and 3 shaded)

Shaded parts to total parts ratio is $\frac{3}{8}$.

Step7: Shaded parts to white parts ratio

White parts = 8 - 3=5. Ratio is $\frac{3}{5}$.

Step8: Find equivalent ratios

• For $\frac{2}{6}$, multiply numerator and denominator by 2 to get $\frac{4}{12}$.
• For $\frac{1}{5}$, multiply numerator and denominator by 2 to get $\frac{2}{10}$.
• For $\frac{12}{24}$, divide numerator and denominator by 2 to get $\frac{6}{12}$.
• For $\frac{3}{4}$, multiply numerator and denominator by 2 to get $\frac{6}{8}$.
• For $\frac{16}{18}$, divide numerator and denominator by 2 to get $\frac{8}{9}$.
• For $\frac{4}{6}$, divide numerator and denominator by 2 to get $\frac{2}{3}$.
• For $\frac{2}{10}$, divide numerator and denominator by 2 to get $\frac{1}{5}$.
• For $\frac{12}{16}$, divide numerator and denominator by 4 to get $\frac{3}{4}$.
• For $\frac{5}{8}$, multiply numerator and denominator by 2 to get $\frac{10}{16}$.
• For $\frac{2}{3}$, multiply numerator and denominator by 2 to get $\frac{4}{6}$.
• For $\frac{12}{20}$, divide numerator and denominator by 4 to get $\frac{3}{5}$.
• For $\frac{25}{30}$, divide numerator and denominator by 5 to get $\frac{5}{6}$.

Answer:

1. $\frac{1}{3}$
2. $\frac{6}{5}$
3. $\frac{5}{4}$
4. $\frac{2}{3}$
5. $\frac{3}{8}$
6. $\frac{3}{5}$
7. $\frac{4}{12}$
8. $\frac{2}{10}$
9. $\frac{6}{12}$
10. $\frac{6}{8}$
11. $\frac{8}{9}$
12. $\frac{2}{3}$
13. $\frac{1}{5}$
14. $\frac{3}{4}$
15. $\frac{10}{16}$
16. $\frac{4}{6}$
17. $\frac{3}{5}$
18. $\frac{5}{6}$