Solved on Nov 05, 2023

Calculate the given fractions. Show your work. (4 marks) a) $-\frac{3}{4} \times\left(-\frac{1}{9}\right)$ b) $\frac{7}{9}\left(-\frac{6}{11}\right)$ c) $-\frac{3}{8} \div \frac{7}{10}$ d) $-2 \frac{1}{8} \div 1 \frac{1}{4}$

STEP 1

Assumptions1. We are given four different fraction problems to solve. . We will solve each problem one by one.
3. The operations involved are multiplication and division.
4. The order of operations will be followed.

STEP 2

Let's start with problem a) $-\frac{}{4} \times\left(-\frac{1}{9}\right)$ When multiplying fractions, we simply multiply the numerators together and the denominators together. Also, the product of two negative numbers is a positive number.
$-\frac{}{4} \times\left(-\frac{1}{9}\right) = \frac{- \times -1}{4 \times9}$

STEP 3

Calculate the multiplication.
$-\frac{3}{} \times\left(-\frac{1}{9}\right) = \frac{3}{36}$

STEP 4

implify the fraction.
$-\frac{3}{4} \times\left(-\frac{1}{9}\right) = \frac{1}{12}$

STEP 5

Next, let's solve problem b) $\frac{7}{9}\left(-\frac{}{11}\right)$ Again, we multiply the numerators together and the denominators together. Here, the product of a positive number and a negative number is a negative number.
$\frac{7}{9}\left(-\frac{}{11}\right) = \frac{7 \times -}{9 \times11}$

STEP 6

Calculate the multiplication.
$\frac{}{9}\left(-\frac{6}{11}\right) = -\frac{42}{99}$

STEP 7

The fraction $-\frac{42}{99}$ cannot be simplified further, so this is our final answer for problem b.

STEP 8

Now, let's solve problem c) $-\frac{3}{8} \div \frac{7}{10}$ When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.
$-\frac{3}{8} \div \frac{7}{10} = -\frac{3}{8} \times \frac{10}{7}$

STEP 9

Calculate the multiplication.
$-\frac{3}{8} \div \frac{7}{} = -\frac{30}{56}$

STEP 10

implify the fraction.
$-\frac{3}{8} \div \frac{7}{10} = -\frac{15}{28}$

STEP 11

Finally, let's solve problem d) $- \frac{}{8} \div \frac{}{4}$ First, we need to convert the mixed numbers into improper fractions.
$- \frac{}{8} = -\frac{17}{8}$ $\frac{}{4} = \frac{5}{4}$ So, the problem becomes $-\frac{17}{8} \div \frac{5}{4}$

STEP 12

Again, we multiply the first fraction by the reciprocal of the second fraction.
$-\frac{17}{8} \div \frac{5}{4} = -\frac{17}{8} \times \frac{4}{5}$

STEP 13

Calculate the multiplication.
$-\frac{17}{8} \div \frac{5}{} = -\frac{68}{40}$

STEP 14

implify the fraction.
$-\frac{17}{8} \div \frac{}{4} = -\frac{17}{10}$ So, the solutions to the problems area) $\frac{}{12}$ b) $-\frac{42}{99}$ c) $-\frac{}{28}$ d) $-\frac{17}{10}$

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Calculate the given fractions. Show your work. (4 marks) a) $-\frac{3}{4} \times\left(-\frac{1}{9}\right)$ b) $\frac{7}{9}\left(-\frac{6}{11}\right)$ c) $-\frac{3}{8} \div \frac{7}{10}$ d) $-2 \frac{1}{8} \div 1 \frac{1}{4}$

STEP 1

Assumptions1. We are given four different fraction problems to solve. . We will solve each problem one by one.
3. The operations involved are multiplication and division.
4. The order of operations will be followed.

STEP 2

STEP 3

Calculate the multiplication.
$-\frac{3}{} \times\left(-\frac{1}{9}\right) = \frac{3}{36}$

STEP 4

implify the fraction.
$-\frac{3}{4} \times\left(-\frac{1}{9}\right) = \frac{1}{12}$

STEP 5

Next, let's solve problem b) $\frac{7}{9}\left(-\frac{}{11}\right)$ Again, we multiply the numerators together and the denominators together. Here, the product of a positive number and a negative number is a negative number.
$\frac{7}{9}\left(-\frac{}{11}\right) = \frac{7 \times -}{9 \times11}$

STEP 6

Calculate the multiplication.
$\frac{}{9}\left(-\frac{6}{11}\right) = -\frac{42}{99}$

STEP 7

The fraction $-\frac{42}{99}$ cannot be simplified further, so this is our final answer for problem b.

STEP 8

Now, let's solve problem c) $-\frac{3}{8} \div \frac{7}{10}$ When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction.
$-\frac{3}{8} \div \frac{7}{10} = -\frac{3}{8} \times \frac{10}{7}$

STEP 9

Calculate the multiplication.
$-\frac{3}{8} \div \frac{7}{} = -\frac{30}{56}$

STEP 10

implify the fraction.
$-\frac{3}{8} \div \frac{7}{10} = -\frac{15}{28}$

STEP 11

Finally, let's solve problem d) $- \frac{}{8} \div \frac{}{4}$ First, we need to convert the mixed numbers into improper fractions.
$- \frac{}{8} = -\frac{17}{8}$ $\frac{}{4} = \frac{5}{4}$ So, the problem becomes $-\frac{17}{8} \div \frac{5}{4}$

STEP 12

Again, we multiply the first fraction by the reciprocal of the second fraction.
$-\frac{17}{8} \div \frac{5}{4} = -\frac{17}{8} \times \frac{4}{5}$

STEP 13

Calculate the multiplication.
$-\frac{17}{8} \div \frac{5}{} = -\frac{68}{40}$

STEP 14

implify the fraction.
$-\frac{17}{8} \div \frac{}{4} = -\frac{17}{10}$ So, the solutions to the problems area) $\frac{}{12}$ b) $-\frac{42}{99}$ c) $-\frac{}{28}$ d) $-\frac{17}{10}$

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STEP 1

Assumptions1. We are given four different fraction problems to solve. . We will solve each problem one by one.3. The operations involved are multiplication and division.4. The order of operations will be followed.

STEP 2

STEP 3

Calculate the multiplication.−3×(−19)=336-\frac{3}{} \times\left(-\frac{1}{9}\right) = \frac{3}{36}−3​×(−91​)=363​

STEP 4

implify the fraction.−34×(−19)=112-\frac{3}{4} \times\left(-\frac{1}{9}\right) = \frac{1}{12}−43​×(−91​)=121​

STEP 5

STEP 6

Calculate the multiplication.9(−611)=−4299\frac{}{9}\left(-\frac{6}{11}\right) = -\frac{42}{99}9​(−116​)=−9942​

STEP 7

The fraction −4299-\frac{42}{99}−9942​ cannot be simplified further, so this is our final answer for problem b.

STEP 8

STEP 9

Calculate the multiplication.−38÷7=−3056-\frac{3}{8} \div \frac{7}{} = -\frac{30}{56}−83​÷7​=−5630​

STEP 10

implify the fraction.−38÷710=−1528-\frac{3}{8} \div \frac{7}{10} = -\frac{15}{28}−83​÷107​=−2815​

STEP 11

STEP 12

Again, we multiply the first fraction by the reciprocal of the second fraction.−178÷54=−178×45-\frac{17}{8} \div \frac{5}{4} = -\frac{17}{8} \times \frac{4}{5}−817​÷45​=−817​×54​

STEP 13

Calculate the multiplication.−178÷5=−6840-\frac{17}{8} \div \frac{5}{} = -\frac{68}{40}−817​÷5​=−4068​

STEP 14

implify the fraction.−178÷4=−1710-\frac{17}{8} \div \frac{}{4} = -\frac{17}{10}−817​÷4​=−1017​So, the solutions to the problems area) 12\frac{}{12}12​ b) −4299-\frac{42}{99}−9942​ c) −28-\frac{}{28}−28​ d) −1710-\frac{17}{10}−1017​

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Assumptions1. We are given four different fraction problems to solve. . We will solve each problem one by one.
3. The operations involved are multiplication and division.
4. The order of operations will be followed.

Calculate the multiplication.
$-\frac{3}{} \times\left(-\frac{1}{9}\right) = \frac{3}{36}$

implify the fraction.
$-\frac{3}{4} \times\left(-\frac{1}{9}\right) = \frac{1}{12}$

Calculate the multiplication.
$\frac{}{9}\left(-\frac{6}{11}\right) = -\frac{42}{99}$

The fraction $-\frac{42}{99}$ cannot be simplified further, so this is our final answer for problem b.

Calculate the multiplication.
$-\frac{3}{8} \div \frac{7}{} = -\frac{30}{56}$

implify the fraction.
$-\frac{3}{8} \div \frac{7}{10} = -\frac{15}{28}$

Again, we multiply the first fraction by the reciprocal of the second fraction.
$-\frac{17}{8} \div \frac{5}{4} = -\frac{17}{8} \times \frac{4}{5}$

Calculate the multiplication.
$-\frac{17}{8} \div \frac{5}{} = -\frac{68}{40}$

implify the fraction.
$-\frac{17}{8} \div \frac{}{4} = -\frac{17}{10}$ So, the solutions to the problems area) $\frac{}{12}$ b) $-\frac{42}{99}$ c) $-\frac{}{28}$ d) $-\frac{17}{10}$