Go Math! Practice Fluency Workbook Grade 6 Chapter 4 Operations with Fractions Exercise 4.1 Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition Chapter 4 Operations with Fractions

Page 17 Problem 1 Answer

we have to use the greatest common factor to write each answer in the simplest form. To multiply two fractions, multiply the numerators and then multiply the denominators

⇒ $\frac{2}{3} \cdot \frac{6}{7}=\frac{2 \cdot 6}{3 \cdot 7}=\frac{12}{21}$

Since 12 and 21 have a GCF of 3, We can reduce the fraction by dividing the numerator and denominator by 3 :

⇒ $\frac{12}{21}=\frac{12 \div 3}{21 \div 3}=\frac{4}{7}$

From the above step, we will get the answer 4/7

Page 17 Problem 2 Answer

we have to use the greatest common factor to write each answer in the simplest form. To multiply two fractions, multiply the numerators and then multiply the denominators.

⇒ $\frac{3}{4} \cdot \frac{2}{3}=\frac{3 \cdot 2}{4 \cdot 3}=\frac{6}{12}$

Since 6 and 12 have a GCF of 6, We can reduce the fraction by dividing the numerator and denominator by 3 :

⇒ $\frac{6}{12}=\frac{6 \div 6}{12 \div 6}=\frac{1}{2}$

From the above step, we will get the answer1/2.

$Go Math! Practice Fluency Workbook Grade 6 Chapter 4 Operations with Fractions Exercise 4.1 Answer Key$

Page 17 Problem 3 Answer

we have to use the greatest common factor to write each answer in the simplest form. To multiply two fractions, multiply the numerators and then multiply the denominators

⇒ $\frac{8}{21} \cdot \frac{7}{10}=\frac{8 \cdot 7}{21 \cdot 10}=\frac{56}{210}$

Since 56 and 210 have a GCF of 14, We can reduce the fraction by dividing the numerator and denominator by 3 :

⇒ $\frac{56}{210}=\frac{56 \div 14}{210 \div 14}=\frac{4}{15}$

From the above step, we will get the answer on 4/15

Page 17 Problem 4 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators

When multiplying a whole number and a fraction, if the denominator of the fraction divides evenly into the whole number, you can complete this division and then multiply the quotient by the numerator of the original fraction:

⇒ $24 \cdot \frac{5}{6}=\frac{24}{6} \cdot 5=4 \cdot 5=20$

From the above step, we will get the answer20

Page 17 Problem 5 Answer

We have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators

⇒ $32 \cdot \frac{3}{8}=\frac{32}{8} \cdot 3=4 \cdot 3=12$

From the above step, we will get the answer 12.

Page 17 Problem 6 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators

⇒ $21 \cdot \frac{3}{7}=\frac{21}{7} \cdot 3=3 \cdot 3=9$

From the above step, we will get the answer 9

Page 17 Problem 7 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator.

The LCM of 15 and 6 is 30 s0 rewrite the fractions to have a denominator of 30:

⇒ $\frac{4}{15}+\frac{5}{6}=\frac{4 \cdot 2}{15 \cdot 2}+\frac{5 \cdot 5}{6 \cdot 5}=\frac{8}{30}+\frac{25}{30}$

Now that the fractions have a common denominator, you can add the numerators to add the fractions:

⇒ $\frac{8}{30}+\frac{25}{30}=\frac{8+25}{30}=\frac{33}{30}$

Reducing the fraction by dividing the numerator and denominator by the GCF of 3 gives:

⇒ $\frac{33}{30}=\frac{33 \div 3}{30 \div 3}=\frac{11}{10}$

Converting the improper fraction to a mixed number then gives:

⇒ $\frac{11}{10}=1 \frac{1}{10}$

From the above step, we will get the answer 11/10.

Page 17 Problem 8 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator

The LCM of 12 and 20 is 60 so rewrite the fractions to have a denominator of 30:

⇒$\frac{5}{12}-\frac{3}{20}=\frac{5 \cdot 5}{12 \cdot 5}-\frac{3 \cdot 3}{20 \cdot 3}=\frac{25}{60}-\frac{9}{60}$

Now that the fractions have a common denominator, you can add the numerators to add the fractions:

⇒$\frac{25}{60}-\frac{9}{60}=\frac{25-9}{60}=\frac{16}{60}$

Reducing the fraction by dividing the numerator and denominator by

⇒$\frac{16}{60}=\frac{16 \div 4}{60 \div 4}=\frac{4}{15}$

From the above step, we will get the answer 4/15.

Page 17 Problem 9 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator.

The LCM of 12 and 20 is 60 so rewrite the fractions to have a denominator of 30:

⇒ $\frac{3}{5}+\frac{3}{20}=\frac{3 \cdot 4}{5 \cdot 4}+\frac{3}{20}=\frac{12}{20}+\frac{3}{20}$

Now that the fractions have a common denominator, you can add the numerators to add the fractions:

⇒ $\frac{12}{20}+\frac{3}{20}=\frac{12+3}{20}=\frac{15}{20}$

Reducing the fraction by dividing the numerator and denominator by

⇒ $\frac{15}{20}=\frac{15 \div 5}{20 \div 5}=\frac{3}{4}$

From the above step, we will get the answer 3/4.

Page 17 Problem 10 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator

The LCM of 8 and 24 is 24 so rewrite the fractions to have a denominator of 24:

⇒$\frac{5}{8}-\frac{5}{24}=\frac{5 \cdot 3}{8 \cdot 3}-\frac{5}{24}=\frac{15}{24}-\frac{5}{24}$

Now that the fractions have a common denominator, you can add the numerators to add the fractions:

⇒$\frac{15}{24}-\frac{5}{24}=\frac{15-5}{24}=\frac{10}{24}$

Reducing the fraction by dividing the numerator and denominator by then the GCF of 2 gives.

⇒$\frac{10}{24}=\frac{10 \div 2}{24 \div 2}=\frac{5}{12}$

From the above step, we will get the answer 5/12.

Page 17 Problem 11 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator

The LCM of 12 and 8 is 24 so rewrite the fractions to have a denominator of 24:

⇒ $3 \frac{5}{12}+1 \frac{3}{8}=3 \frac{5 \cdot 2}{12 \cdot 2}+1 \frac{3 \cdot 3}{8 \cdot 3}=3 \frac{10}{24}+1 \frac{9}{24}$

Now the fraction has a common denominator, you can add the mixed numbers by adding the whole numbers and adding the numerators.

⇒ $3 \frac{10}{24}+1 \frac{9}{24}=4 \frac{10+9}{24}=4 \frac{19}{24}$

From the above step, we will get the answer 4×19/24.

Page 17 Problem 12 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator.

The LCM of 10 and 18 is 90 so rewrite the fractions to have a denominator of 90:

⇒$2 \frac{9}{10}-1 \frac{7}{18}=2 \frac{9 \cdot 9}{10 \cdot 9}-1 \frac{7 \cdot 5}{18 \cdot 5}=2 \frac{81}{90}-1 \frac{35}{90}$

Now the fraction has a common denominator, you can add the mixed numbers by adding the whole numbers and adding the numerators.

⇒$2 \frac{81}{90}-1 \frac{35}{90}=1 \frac{81-35}{90}=1 \frac{46}{90}$

Reducing the fraction by dividing the numerator and denominator by then the GCF of 2 gives.

⇒$1 \frac{46}{90}=1 \frac{46 \div 2}{90 \div 2}=1 \frac{23}{45}$

From the above step, we will get the answer 1×23/45.

Page 17 Problem 13 Answer

We have to solve the given question: Louis spent 12 hours last week practicing guitar. If 1/4

of the time was spent practicing chords, To find: how much time did Louis spend practicing chords?

It is given that Loius spent 12 hours last week practicing guitar and that 1/4

of that time was spent practicing chords. To find the number of hours he spent practicing chords, we must find:12×1/4

⇒ $12 \cdot \frac{1}{4}=\frac{12}{4} \cdot 1=3 \cdot 1=3$hours

From the above step, we will get the answer 3 hours

Page 17 Problem 14 Answer

It is given that Angie and her friends ate 3/4

of the pizza and her brother ate 2/3 of what was left. To find how much of the original pizza that her brother ate, we must first find how much was left after Angie and her friends ate pizza.

They started with a whole pizza so we can subtract $\frac{3}{4}$from a whole to find how much is left. Remember that you need to get a common denominator before you can subtract:

⇒ $1-\frac{3}{4}=\frac{4}{4}-\frac{3}{4}=\frac{4-3}{4}=\frac{1}{4}$

Her brother then at $\frac{2}{3}$ of the remaining $\frac{1}{4}$ of the pizza. To find what fraction of the original pizza he ate, we can then find:

⇒ $\frac{1}{4}.\frac{2}{3}$

To multiply two fractions multiply the numerators and then multiply the denominators:

⇒ $\frac{1}{4} \cdot \frac{2}{3}=\frac{1 \cdot 2}{4 \cdot 3}=\frac{2}{12}$

Since 2 and 12 have a GCF of 2, we can reduce the fraction by dividing the numerators and denominators by 2:

⇒ $\frac{2}{12}=\frac{2 \div 2}{12 \div 2}=\frac{1}{6}$ of the pizza.

From the above step, we will get the answer 1/6 of the pizza.

Page 18 Exercise 1 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators.

⇒$\frac{3}{4} \cdot \frac{7}{9}=\frac{3 \cdot 7}{4 \cdot 9}=\frac{21}{36}$

Since 21 and 36 have a GCF of 3, we can reduce the fraction by dividing the numerators and denominators by 3:

⇒$\frac{21}{36}=\frac{21 \div 3}{36 \div 3}=\frac{7}{12}$

From the above step, we will get the answer/12

Page 18 Exercise 2 Answer

we have to use the greatest common factor to write each answer in simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators.

⇒ $\frac{2}{7} \cdot \frac{7}{9}=\frac{2 \cdot 7}{7 \cdot 9}=\frac{14}{63}$

Since 14 and 63 have a GCF of 7, we can reduce the fraction by dividing the numerators and denominators by 7:

⇒ $\frac{14}{63}=\frac{14 \div 7}{63 \div 7}=\frac{2}{9}$

From the above step, we will get the answer 2/9

Page 18 Exercise 3 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators.

⇒ $\frac{7}{11} \cdot \frac{22}{28}=\frac{7 \cdot 22}{11 \cdot 28}=\frac{154}{308}$

Since 154 and 308 have a GCF of 154, we can reduce the fraction by dividing the numerators and denominators by 154:

⇒ $\frac{154}{308}=\frac{154 \div 154}{308 \div 154}=\frac{1}{2}$

From the above step, we will get the answer1/2

Page 18 Exercise 4 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators.

Remember that a whole number can be written as a fraction with 1 as the denominator:

⇒ $8 \cdot \frac{3}{10}=\frac{8}{1} \cdot \frac{3}{10}=\frac{8 \cdot 3}{1 \cdot 10}=\frac{24}{10}$

Since 24 and 10 have a GCF of 2, we can reduce the fraction by dividing the numerators and denominators by 2:

⇒ $\frac{24}{10}=\frac{24 \div 2}{10 \div 2}=\frac{12}{5}$

Rewriting the improper fraction as a mixed number then gives:

⇒ $\frac{12}{5}=2 \frac{2}{5}$

From the above step, we will get the answer 2×2/5.

Page 18 Exercise 5 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators.

⇒ $\frac{4}{9} \cdot \frac{3}{4}=\frac{4 \cdot 3}{9 \cdot 4}=\frac{12}{36}$

Since 12 and 36 have a GCF of 12, we can reduce the fraction by dividing the numerators and denominators by 12:

⇒ $\frac{12}{36}=\frac{12 \div 12}{36 \div 12}=\frac{1}{3}$

From the above step, we will get the answer 1/3.

Page 18 Exercise 6 Answer

we have to use the greatest common factor to write each answer in the simplest form.

To multiply two fractions, multiply the numerators and then multiply the denominators

⇒ $\frac{3}{7} \cdot \frac{2}{3}=\frac{3 \cdot 2}{7 \cdot 3}=\frac{6}{21}$

Since 6 and 21 have a GCF of 3, we can reduce the fraction by dividing the numerators and denominators by 3:

⇒ $\frac{6}{21}=\frac{6 \div 3}{21 \div 3}=\frac{2}{7}$

From the above step, we will get the answer2/7

Page 18 Exercise7 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator.

The LCM of 9 and 12 is 36 so rewrite the fractions to have a denominator of 36:

⇒$\frac{7}{9}+\frac{5}{12}=\frac{7 \cdot 4}{9 \cdot 4}+\frac{5 \cdot 3}{12 \cdot 3}=\frac{28}{36}+\frac{15}{36}$

Now the fraction has a common denominator, you can add the mixed numbers by adding the whole numbers and adding the numerators.

⇒$\frac{28}{36}+\frac{15}{36}=\frac{28+15}{36}=\frac{43}{36}$

Converting the improper fraction to a mixed number then gives:

⇒$\frac{43}{36}=1 \frac{7}{36}$

From the above step, we will get the answer1x7/36

Page 18 Exercise 8 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator.

The LCM of 24 and 8 is 24 so rewrite the fractions to have a denominator of 24:

⇒$\frac{21}{24}-\frac{3}{8}=\frac{21}{24}-\frac{3 \cdot 3}{8 \cdot 3}=\frac{21}{24}-\frac{9}{24}$

Now the fraction has a common denominator, you can add the mixed numbers by adding the whole numbers and adding the numerators.

⇒$\frac{21}{24}-\frac{9}{24}=\frac{21-9}{24}=\frac{12}{24}$

Reducing the fraction by dividing the numerator and denominator by then the GCF of 2 gives.

⇒$\frac{12}{24}=\frac{12 \div 12}{24 \div 12}=\frac{1}{2}$

From the above step, we will get the answer 1/2.

Page 18 Exercise 9 Answer

We have to add and subtract the given equation using the least common multiple as the denominator.

To add fractions with unlike denominators, you must first rewrite the fractions to have a common denominator.

The LCM of 15 and 12 is 60 so rewrite the fractions to have a denominator of 60:

⇒ $\frac{11}{15}+\frac{7}{12}=\frac{11 \cdot 4}{15 \cdot 4}+\frac{7 \cdot 5}{12 \cdot 5}=\frac{44}{60}+\frac{35}{60}$

Now the fraction has a common denominator, you can add the mixed numbers by adding the whole numbers and adding the numerators.

⇒ $\frac{44}{60}+\frac{35}{60}=\frac{44+35}{60}=\frac{79}{60}$

Converting the improper fraction to a mixed number then gives:

⇒ $\frac{79}{60}=1 \frac{19}{60}$

From the above step, we will get the answer 1×19/60.

Go Math Answer Key

Go Math! Practice Fluency Workbook Grade 6 California 1st Edition Chapter 4 Operations with Fractions

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