## Go Math! Practice Fluency Workbook Grade 6, California 1st Edition, Chapter 6: Representing Ratios and Rates

**Question. Read the table and find the ratio for lion and elephant by using the method of ratio and proportion.**

Given table is

To find the ratio for lion and elephant.

Using the method of ratio and proportion.

The number of lions in the zoo is 9 and the number of elephants in the zoo is 12

now to find the ratio of a lion to elephant,

ratio of lion to elephant = lion / elephant,

Now substitute all the values in the above formula,

= \(\frac{9}{12}\)

simplify,

= \(\frac{3}{4}\)

The ratio of a lion to elephant is 3:4

**Question. Read the table and find the ratio of giraffes and otters by using the method of ratio and proportion.**

Given table is

To find the ratio of giraffes and otters.

Using the method of ratio and proportion.

The number of giraffes in the zoo is 8 and the number of otters in the zoo is 16

now to find the ratio of giraffes to otters,

the ratio of giraffes to otters = giraffes/otters

Now substitute all the values in the above formula,

= \(\frac{8}{16}\)

simplify,

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

The ratio of giraffes to otters is 1:2

**Question. Read the table find the ratio of lions and seals by using the method of ratio and proportion.**

Given table is

To find the ratio of lions and seals.

Using the method of ratio and proportion.

The number of lions in the zoo is 9 and the number of seals in the zoo is 10

now to find the ratio,

the ratio of the lions to seals = lion/seals

Now substitute all the values in the above formula,

= \(\frac{9}{10}\)

The ratio of lions to seals is 9:10

**Question. Read the table find the ratio of seals to elephants by using the method of ratio and proportion.**

Given table is

To find the ratio of seals to elephants.

Using the method of ratio and proportion.

The number of seals in the zoo is 10 and the number of elephants in the zoo is 12

now to find the ratio,

the ratio of the seals to elephants = seals/elephants

Now substitute all the values in the above formula,

= \(\frac{10}{12}\)

simplify,

= \(\frac{5}{6}\)

The ratio of the seals to elephants is 5:6

**Question. Read the table find the ratio of elephants to lions by using the method of ratio and proportion.**

Given table is

To find the ratio of elephants to lions.

Using the method of ratio and proportion.

The number of elephants in the zoo is 12 and the number of lions in the zoo is 9 to find the ratio,

the ratio of the elephant to lion = elephant/lion

Now substitute all the values in the above formula,

= \(\frac{12}{9}\)

simplify,

= \(\frac{4}{3}\)

The ratio of elephants to lions is 4:3

**Question. Find the three equivalent ratios for the 4/3 expression using the method of ratio.**

Given table is

The given expression is 4/3

To find the three equivalent ratios for the given expression.

Using the method of ratio.

To find the three equivalent ratios for the given expression, 4/3

This ratio is in reduced form, the equivalent ratio can be found by multiplying both parts of the ratios by the same constants.

\(\frac{4 \times 2}{3 \times 2}=\frac{8}{6}\)

Likewise, do the same procedure for the next two ratios,

\(\begin{aligned}& \frac{4 \times 3}{3 \times 3}=\frac{12}{9} \\

& \frac{4 \times 4}{3 \times 4}=\frac{16}{12}

\end{aligned}\)

The three equivalent ratios for the given ratio of 4/3

are 8:3 or 12:9 or 16:12

**Question. Find the three equivalent ratios for the 12/14 expression. Using the method of ratio.**

The given expression is 12/14

To find the three equivalent ratios for the given expression.

Using the method of ratio.

The given ratio is 12/14

to write the reduced form of this ratio,

\(\frac{6 \times 2}{7 \times 2}=\frac{12}{14}\)

so its reduced form is 6/7

multiply and divide the ratio by the same constant,

\(\frac{6 \times 3}{7 \times 3}=\frac{18}{21}\)

Now do the same procedure for the next two ratios,

\(\begin{aligned}& \frac{6 \times 4}{7 \times 4}=\frac{24}{28} \\

& \frac{6 \times 5}{7 \times 5}=\frac{30}{35}

\end{aligned}\)

The three equivalent ratios for the given ratio12 by 14

is 18:21 or 24:28 or 30:35

**Question. Find the three equivalent ratios for the 6/9 expression using the method of ratio.**

The given expression is 6/9

To find the three equivalent ratios for the given expression.

Using the method of ratio.

The given ratio is 6/9

to find its reduced form,

\(\frac{6}{9}=\frac{2 \times 3}{3 \times 3}\)

so its reduced form is 2/3

now multiply and divide the ratio by the same constant,

\(\frac{2 \times 2}{3 \times 2}=\frac{4}{6}\)

Now do the procedure to find the next two ratios,

\(\begin{aligned}& \frac{2 \times 4}{3 \times 4}=\frac{8}{12} \\

& \frac{2 \times 5}{3 \times 5}=\frac{10}{15}

\end{aligned}\)

The three equivalent ratios for the given ratio 6/9 are

\(\frac{4}{6}\) or 4:6

\(\frac{8}{12}[\latex] or 8:12

[latex]\frac{10}{15}\) or 10:15

**Question. Find the three ratios equivalent to the ratio of cats to dogs in a park is 3 to 4 using the method of ratio.**

Given the ratio of cats to dogs in a park is 3 to 4

To find the three ratios equivalent to the given ratio.

Using the method of ratio.

The given ratio of cats to dogs is 3:4

now multiply and divide the ratio by the same constant,

= \(\frac{3 \times 2}{4 \times 2}\)

= \(\frac{6}{8}\)

Now do the same procedure to find the next two ratios,

\(\begin{aligned}& \frac{3 \times 3}{4 \times 3}=\frac{9}{12} \\

& \frac{3 \times 4}{4 \times 4}=\frac{12}{16}

\end{aligned}\)

The three ratios of cats to dogs in a park are

\(\frac{6}{8}\) or 6 : 8

\(\frac{9}{12}\) or 9 : 12

\(\frac{12{16}\) or 12 : 16

**Question. Find the three ratios of rainy days to sunny days is 5/7 using the method of ratios.**

Given the ratio of rainy days to sunny days is 5/7

To find the three ratios of rainy days to sunny days.

Using the method of ratios.

The ratio of rainy days to sunny days is 5/7

now multiply and divide the ratio by the same constant,

= \(\frac{5 \times 2}{7 \times 2}\)

simplify,

= \(\frac{10}{14}\)

Now repeat the same procedure to find the ratios of the next two,

\(\begin{aligned}& \frac{5 \times 3}{7 \times 3}=\frac{15}{21} \\

& \frac{5 \times 4}{7 \times 4}=\frac{20}{28}

\end{aligned}\)

The three equivalent ratios of rainy days to sunny days are

\(\frac{10}{14}\) or 10 : 14

\(\frac{15}{21}\) or 15 : 21

\(\frac{20}{28}\) or 20 : 28

**Question. Find the three equivalent ratios for the protein to fiber in a granola bar is 9/2 using the method of ratio.**

Given the ratio of protein to fiber in a granola bar is 9/2

To find the three equivalent ratios for the protein to fiber in a granola bar.

Using the method of ratio.

The given ratio of the protein to fiber in a granola bar is 9/2

now to multiply and divide the ratio by the same constant,

= \(\frac{9 \times 2}{2 \times 2}\)

= \(\frac{18}{4}\)

Now repeat the same procedure to find the next two ratios,

\(\begin{aligned}& \frac{9 \times 3}{2 \times 3}=\frac{27}{6} \\

& \frac{9 \times 4}{2 \times 4}=\frac{36}{8}

\end{aligned}\)

The three equivalent ratios of protein to fiber in a granola bar are

\(\frac{18}{4}\) or 18 : 4

\(\frac{27}{6}\) or 27 : 6

\(\frac{36}{8}\) or 36 : 8

**Question. Find how many angelfishes are there in the pet shop. Using the method of ratio.**

Given the ratio of the clownfish to angelfish is 5:4

and the angelfish to golden fish is 4:3

To find how many angelfishes are there in the pet shop. Using the method of ratio.

The given ratio of clownfish to angelfish is 5:4 and the ratio of angelfish to goldfish is 4:3 there are 60 fishes are there in the pet shop.

from this, it is clear that clownfish=5

angelfish=4

goldfish=3

Using the above values now find the total number of angelfish in the pet shop,

= \(\frac{60}{5}\)

= 12

multiply by 4

= 12 x 4

= 48

There are 48 angelfishes are there in the pet shop.

**Question. Find the ratio between the days of May month to days in a particular year.**

**Given:** Days in May to days in a year.

**To find:** We have to find the ratio between the days of May month to days in a particular year.

Just find out the number of days present in May month.

Then find the number of days in a year.

Then divide the days of May month by days in a year to get the ratio.

The May month consists of 31 days.

and in a year, there are usually 365 days.

Now if we divide these days, we get

Ratio = \(\frac{31}{365}\)

Ratio = 31 : 365

The ratio between the days of May month to days in a particular year is 31:365.

**Question. Find the ratio between the numbers of sides of a triangle to the number of sides a square.**

**Given:** Sides of a triangle to sides of a square.

**To find: **We have to find the ratio between the number of sides of a triangle to the number of sides a square has.

Just find out the number of sides of a triangle.

Then find the number of sides of a square.

Then divide them to find the ratio.

As we know, any triangle has “3” sides.

and any square always has “4” sides.

Now let’s take the division of the number of sides of a triangle and the number of sides of a square, we get the ratio as,

Ratio = \(\frac{3}{4}\)

Ratio = 3 : 4

The ratio of the sides of a triangle to the sides of a square is 3:4.

**Question. Find the ratio between 8 triangles to 12 circles.**

**Given:** There are 8 triangles and 12 circles are given.

**To find:** We have to find the ratio between 8 triangles to 12 circles.

Take division of them.

Then simplify them to obtain different ratios.

We have given 8 triangles and 12 circles.

The ratio for the above statement is 8/12 i.e. 8:12.

Dividing the ratio 8:12 i.e. 8 by 12 by 4 in both numerator and denominator, we get,

\(\frac{\frac{8}{4}}{\frac{12}{4}}=\frac{2}{3}\)i.e. the ratio is 2:3.

Dividing the ratio 8:12 i.e. 8 by12 by 2 in both numerator and denominator, we get

\(\frac{\frac{8}{2}}{\frac{12}{2}}=\frac{4}{6}\)i.e. the ratio is 4:6.

Multiplying the ratio 8:12 i.e. 8 by12 by 2 in both numerator and denominator, we get

\(\frac{8}{12} \times \frac{2}{2}\),

= \(\frac{16}{24}\)

i.e. the ratio is 16:24.

The three equivalent ratios of 8 triangles and 12 circles are,

2 : 3

4 : 6

16 : 24

**Question. Find the three equivalent ratios between 20 pencils and 25 erasers.**

**Given:** There are 20 pencils and 25 erasers are given.

**To find:** We have to find the three equivalent ratios between 20 pencils and 25 erasers.

Take division of them.

Then simplify them to obtain different ratios.

We have been given 20 pencils and 25 erasers.

The ratio for the above statement is 20:25.

If we multiply and divide the numerator and denominator of the ratio 20/25 by “2”, we get

Ratio =20

= \(\frac{20}{25} \times \frac{2}{2}\)

= \(\frac{40}{50}\)

= 40 : 50

Dividing the ratio 40/50, by 10 in both the numerator and denominator, we get

\(\frac{\frac{40}{10}}{\frac{50}{10}}=\frac{4}{5}\)i.e. the ratio is 4:5.

Dividing the ratio 40/50, by 5 in both the numerator and denominator, we get

\(\frac{\frac{40}{5}}{\frac{50}{5}}=\frac{8}{10}\)i.e. the ratio is 8:10.

Three equivalent ratios of 20 pencils and 25 erasers are

40 : 50

4 : 5

8 : 10

**Question. Find the three equivalent ratios between 5 girls and 6 boys.**

**To find: **There are 5 girls and 6 boys are given.

**To find: **We have to find the three equivalent ratios between 5 girls and 6 boys.

Take division of them.

Then simplify them to obtain different ratios.

We have given 5 girls and 6 boys.

Now divide them to get the different ratios.

Now let’s divide the number of girls and the number of boys, we get

= \(\frac{5}{6}\)

Ratio = 5 : 6

Now if we multiply and divide this ratio by “2”, we get

\(\frac{5}{6} \times \frac{2}{2}\)= \(\frac{10}{12}\)

Ratio = 10 : 12

Now if we multiply and divide this ratio by “3”, we get

\(\frac{15}{18}\)Ratio = 15 : 18

Three equivalent ratios of 5 girls and 6 boys are,

⇒ 5 : 6

⇒ 10 : 12

⇒ 15 : 18

**Question. Find the three equivalent ratios between 10 pants and 14 shirts.**

**Given:** There are 10 pairs of pants and 14 shirts given.

**To find:** We have to find the three equivalent ratios between 10 pants and 14 shirts.

Take division of them.

Then simplify them to obtain different ratios.

We have given 10 pairs of pants and 14 shirts.

The ratio is expressed as 10:14.

If we multiply the numerator and denominator by “2”, we get

= \(\frac{10}{14} \times \frac{2}{2}\)

= \(\frac{20}{28}\)

Ratio = 20 : 28

The ratio obtained after the simplification of 20:28 is determined by dividing the numerator and denominator of 20/28 by 4, thus, we obtain

\(\frac{20}{28}\)= \(\frac{5}{7}\)

i.e. the ratio is 5:7

The ratio 10:14, i.e. 10 by 14 is multiplied by 3 in both the numerator and denominator.

We obtain

\(\frac{10}{14} \times \frac{3}{3},\)= \(\frac{30}{42}\)

i.e. the ratio is 30:42.

Three equivalent ratios of10 pants and14 shirts are,

20 : 28

5 : 7

30 : 42

**Go Math Answer Key**

- Go Math! Practice Fluency Workbook Grade 6 Chapter 1: Integers Exercise 1.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 1: Integers Exercise 1.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 1: Integers Exercise 1.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 2: Factors and Multiples Exercise 2.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 2: Factors and Multiples Exercise 2.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 3: Rational Numbers Exercise 3.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 3: Rational Numbers Exercise 3.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 3: Rational Numbers Exercise 3.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 4: Operations with Fractions Exercise 4.4 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.4 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 5: Operations with Decimals Exercise 5.5 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 8: Percents Exercise 8.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 8: Percents Exercise 8.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6 Chapter 8: Percents Exercise 8.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 6: Representing Ratios and Rates Exercise 6.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 6: Representing Ratios and Rates Exercise 6.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 6: Representing Ratios and Rates Exercise 6.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 7: Applying Ratios and Rates Exercise 7.1 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 7: Applying Ratios and Rates Exercise 7.2 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 7: Applying Ratios and Rates Exercise 7.3 Answer Key
- Go Math! Practice Fluency Workbook Grade 6, Chapter 7: Applying Ratios and Rates Exercise 7.4 Answer Key