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Multiply 4/9

−3

. Write the answer as a mixed number in simplest form.

7 answers

To multiply \( \frac{4}{9} \) by \( -3 \), we can express \( -3 \) as a fraction:

\[ -3 = \frac{-3}{1} \]

Now, we multiply these two fractions:

\[ \frac{4}{9} \times \frac{-3}{1} = \frac{4 \times -3}{9 \times 1} = \frac{-12}{9} \]

Next, we simplify \( \frac{-12}{9} \). The greatest common divisor (GCD) of 12 and 9 is 3, so we divide both the numerator and denominator by 3:

\[ \frac{-12 \div 3}{9 \div 3} = \frac{-4}{3} \]

Now, we can express \( \frac{-4}{3} \) as a mixed number. Since \(-4\) is less than \(-3\) and more than \(-5\), we get:

\[ -4 \div 3 = -1 \text{ with a remainder of } -1 \]

Thus, we have:

\[ \frac{-4}{3} = -1 \frac{1}{3} \]

So the final answer is:

\[ \boxed{-1 \frac{1}{3}} \]

Multiply 2/3
by 1 1/4
Write the answer in simplest form.

To multiply \( \frac{2}{3} \) by \( 1 \frac{1}{4} \), we first need to convert the mixed number \( 1 \frac{1}{4} \) into an improper fraction.

  1. Convert \( 1 \frac{1}{4} \):
    • Multiply the whole number 1 by the denominator 4: \( 1 \times 4 = 4 \).
    • Add the numerator 1: \( 4 + 1 = 5 \).
    • The improper fraction is \( \frac{5}{4} \).

Now we can multiply the fractions \( \frac{2}{3} \) and \( \frac{5}{4} \):

\[ \frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} \]

Next, we need to simplify \( \frac{10}{12} \). The GCD of 10 and 12 is 2, so we divide both the numerator and denominator by 2:

\[ \frac{10 \div 2}{12 \div 2} = \frac{5}{6} \]

Thus, the answer in simplest form is:

\[ \boxed{\frac{5}{6}} \]

Multiply 9.6
by 0.2. Write the answer as a decimal.

To multiply \( 9.6 \) by \( 0.2 \), we can perform the multiplication as follows:

\[ 9.6 \times 0.2 \]

First, we can ignore the decimal point and multiply \( 96 \) by \( 2 \):

\[ 96 \times 2 = 192 \]

Now, we need to consider the decimal places. The number \( 9.6 \) has one decimal place and \( 0.2 \) has one decimal place, so in total, we have \( 1 + 1 = 2 \) decimal places to account for in the final answer.

We place the decimal point in \( 192 \) to get:

\[ 1.92 \]

Thus, the final answer is:

\[ \boxed{1.92} \]

Multiply 2.6 by −1.3

To multiply \( 2.6 \) by \( -1.3 \), we perform the multiplication as follows:

\[ 2.6 \times -1.3 \]

First, let's ignore the negative sign and multiply \( 2.6 \) by \( 1.3 \).

Multiply:

\[ 2.6 \times 1.3 \]

We can calculate it by breaking it down:

\[ 2.6 \times 1.3 = 2.6 \times \left(1 + 0.3\right) = 2.6 \times 1 + 2.6 \times 0.3 \]

Calculating each part:

  • \( 2.6 \times 1 = 2.6 \)
  • \( 2.6 \times 0.3 = 0.78 \) (since \( 2.6 \times 3 = 7.8 \) and we shift the decimal one position to the left)

Now add the two results:

\[ 2.6 + 0.78 = 3.38 \]

Now, since we initially ignored the negative sign, we conclude that:

\[ 2.6 \times -1.3 = -3.38 \]

Thus, the final answer is:

\[ \boxed{-3.38} \]