Question
\( \begin{array}{ll}\text { a. } 2 \times \frac{3}{5}= & \text { b. } 4 \times \frac{5}{6}= \\ \text { c. } 11 \times \frac{3}{10}= & \text { d. } 9 \times \frac{1}{2}= \\ \)\begin{tabular}{ll}\text { e. }\( \frac{2}{3} \times 2= \) & \( 8 \times \frac{6}{7}= \) \\ \hline\end{tabular} & \begin{tabular}{l}\text { f. } 8 \\ \hline\end{tabular}\end{array}
Ask by Cummings Valdez. in South Africa
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
Here are the results:
- a. \( 2 \times \frac{3}{5} = 1.2 \)
- b. \( 4 \times \frac{5}{6} \approx 3.33 \)
- c. \( 11 \times \frac{3}{10} = 3.3 \)
- d. \( 9 \times \frac{1}{2} = 4.5 \)
- e. \( \frac{2}{3} \times 2 \approx 1.33 \)
- f. \( 8 \times \frac{6}{7} \approx 6.86 \)
Solution
Calculate the value by following steps:
- step0: Calculate:
\(9\times \frac{1}{2}\)
- step1: Multiply:
\(\frac{9}{2}\)
Calculate or simplify the expression \( 11 * (3/10) \).
Calculate the value by following steps:
- step0: Calculate:
\(11\times \frac{3}{10}\)
- step1: Multiply:
\(\frac{11\times 3}{10}\)
- step2: Multiply:
\(\frac{33}{10}\)
Calculate or simplify the expression \( 8 * (6/7) \).
Calculate the value by following steps:
- step0: Calculate:
\(8\times \frac{6}{7}\)
- step1: Multiply:
\(\frac{8\times 6}{7}\)
- step2: Multiply:
\(\frac{48}{7}\)
Calculate or simplify the expression \( (2/3) * 2 \).
Calculate the value by following steps:
- step0: Calculate:
\(\frac{2}{3}\times 2\)
- step1: Multiply:
\(\frac{2\times 2}{3}\)
- step2: Multiply:
\(\frac{4}{3}\)
Calculate or simplify the expression \( 2 * (3/5) \).
Calculate the value by following steps:
- step0: Calculate:
\(2\times \frac{3}{5}\)
- step1: Multiply:
\(\frac{2\times 3}{5}\)
- step2: Multiply:
\(\frac{6}{5}\)
Calculate or simplify the expression \( 4 * (5/6) \).
Calculate the value by following steps:
- step0: Calculate:
\(4\times \frac{5}{6}\)
- step1: Reduce the numbers:
\(2\times \frac{5}{3}\)
- step2: Multiply:
\(\frac{2\times 5}{3}\)
- step3: Multiply:
\(\frac{10}{3}\)
Let's solve each multiplication step by step:
### a. \( 2 \times \frac{3}{5} \)
To calculate this, we multiply the whole number by the fraction:
\[
2 \times \frac{3}{5} = \frac{2 \times 3}{5} = \frac{6}{5} = 1.2
\]
### b. \( 4 \times \frac{5}{6} \)
Similarly, we multiply:
\[
4 \times \frac{5}{6} = \frac{4 \times 5}{6} = \frac{20}{6} = \frac{10}{3} \approx 3.33
\]
### c. \( 11 \times \frac{3}{10} \)
Now for this multiplication:
\[
11 \times \frac{3}{10} = \frac{11 \times 3}{10} = \frac{33}{10} = 3.3
\]
### d. \( 9 \times \frac{1}{2} \)
Next, we calculate:
\[
9 \times \frac{1}{2} = \frac{9 \times 1}{2} = \frac{9}{2} = 4.5
\]
### e. \( \frac{2}{3} \times 2 \)
For this multiplication:
\[
\frac{2}{3} \times 2 = \frac{2 \times 2}{3} = \frac{4}{3} \approx 1.33
\]
### f. \( 8 \times \frac{6}{7} \)
Finally, we calculate:
\[
8 \times \frac{6}{7} = \frac{8 \times 6}{7} = \frac{48}{7} \approx 6.86
\]
### Summary of Results:
- a. \( 2 \times \frac{3}{5} = \frac{6}{5} = 1.2 \)
- b. \( 4 \times \frac{5}{6} = \frac{10}{3} \approx 3.33 \)
- c. \( 11 \times \frac{3}{10} = \frac{33}{10} = 3.3 \)
- d. \( 9 \times \frac{1}{2} = \frac{9}{2} = 4.5 \)
- e. \( \frac{2}{3} \times 2 = \frac{4}{3} \approx 1.33 \)
- f. \( 8 \times \frac{6}{7} = \frac{48}{7} \approx 6.86 \)
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Simplify this solution Bonus Knowledge
When multiplying a whole number by a fraction, you can think of it as taking a certain number of parts from the whole. For instance, \( 2 \times \frac{3}{5} = \frac{6}{5} \), which can also be understood as taking two pieces of a pie that is cut into five equal slices, giving you one and one-fifth pieces. In real-world applications, knowing how to multiply fractions can be incredibly helpful! For example, if you're cooking and a recipe calls for \( \frac{3}{5} \) of a cup of sugar and you want to make double the recipe, you’d need \( 2 \times \frac{3}{5} \) cups of sugar, which equals \( \frac{6}{5} \) cups, or one and one-fifth cups. Happy cooking!
