Question
EXERCISE 13.5 1. Calculate these numbers. Afterwards, check your answers using your calculator. a) \( 5 \div \frac{1}{2} \) b) \( 3 \div \frac{5}{6} \) c) \( 22 \div \frac{2}{3} \) d) \( 45 \div \frac{7}{5} \) 2. What do I have to multiply 5 with to get 7 ? 3. How many times does \( \frac{2}{3} \) go into 4 ?
Ask by Harper Matthews. in South Africa
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
1. a) 10, b) 3.6, c) 33, d) 32.14
2. Multiply 5 by 1.4 to get 7.
3. \( \frac{2}{3} \) goes into 4 six times.
Solution
Solve the equation by following steps:
- step0: Solve for \(x\):
\(\frac{2}{3}x=4\)
- step1: Multiply by the reciprocal:
\(\frac{2}{3}x\times \frac{3}{2}=4\times \frac{3}{2}\)
- step2: Multiply:
\(x=6\)
Calculate or simplify the expression \( 22 \div \frac{2}{3} \).
Calculate the value by following steps:
- step0: Calculate:
\(22\div \frac{2}{3}\)
- step1: Multiply by the reciprocal:
\(22\times \frac{3}{2}\)
- step2: Reduce the numbers:
\(11\times 3\)
- step3: Multiply the numbers:
\(33\)
Calculate or simplify the expression \( 45 \div \frac{7}{5} \).
Calculate the value by following steps:
- step0: Calculate:
\(45\div \frac{7}{5}\)
- step1: Multiply by the reciprocal:
\(45\times \frac{5}{7}\)
- step2: Multiply:
\(\frac{45\times 5}{7}\)
- step3: Multiply:
\(\frac{225}{7}\)
Solve the equation \( 5x=7 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(5x=7\)
- step1: Divide both sides:
\(\frac{5x}{5}=\frac{7}{5}\)
- step2: Divide the numbers:
\(x=\frac{7}{5}\)
Calculate or simplify the expression \( 5 \div \frac{1}{2} \).
Calculate the value by following steps:
- step0: Calculate:
\(5\div \frac{1}{2}\)
- step1: Multiply by the reciprocal:
\(5\times 2\)
- step2: Multiply the numbers:
\(10\)
Calculate or simplify the expression \( 3 \div \frac{5}{6} \).
Calculate the value by following steps:
- step0: Calculate:
\(3\div \frac{5}{6}\)
- step1: Multiply by the reciprocal:
\(3\times \frac{6}{5}\)
- step2: Multiply:
\(\frac{3\times 6}{5}\)
- step3: Multiply:
\(\frac{18}{5}\)
Let's solve the problems step by step.
### 1. Calculate these numbers.
a) \( 5 \div \frac{1}{2} \)
To divide by a fraction, we multiply by its reciprocal:
\[
5 \div \frac{1}{2} = 5 \times 2 = 10
\]
b) \( 3 \div \frac{5}{6} \)
Using the same method:
\[
3 \div \frac{5}{6} = 3 \times \frac{6}{5} = \frac{18}{5} = 3\frac{3}{5} = 3.6
\]
c) \( 22 \div \frac{2}{3} \)
Again, multiplying by the reciprocal:
\[
22 \div \frac{2}{3} = 22 \times \frac{3}{2} = 33
\]
d) \( 45 \div \frac{7}{5} \)
Using the reciprocal:
\[
45 \div \frac{7}{5} = 45 \times \frac{5}{7} = \frac{225}{7} \approx 32\frac{1}{7} \approx 32.14
\]
### Summary of Results:
- a) \( 10 \)
- b) \( 3.6 \)
- c) \( 33 \)
- d) \( 32\frac{1}{7} \) or approximately \( 32.14 \)
### 2. What do I have to multiply 5 with to get 7?
We can set up the equation:
\[
5x = 7
\]
Solving for \( x \):
\[
x = \frac{7}{5} = 1.4
\]
### 3. How many times does \( \frac{2}{3} \) go into 4?
We can set up the equation:
\[
\frac{2}{3}x = 4
\]
Solving for \( x \):
\[
x = 4 \times \frac{3}{2} = 6
\]
### Final Answers:
1. a) \( 10 \), b) \( 3.6 \), c) \( 33 \), d) \( 32\frac{1}{7} \)
2. \( 1.4 \)
3. \( 6 \)
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Bonus Knowledge
To solve the division problems, remember that dividing by a fraction is the same as multiplying by its reciprocal! So here we go: a) \( 5 \div \frac{1}{2} = 5 \times 2 = 10 \) b) \( 3 \div \frac{5}{6} = 3 \times \frac{6}{5} = \frac{18}{5} = 3.6 \) c) \( 22 \div \frac{2}{3} = 22 \times \frac{3}{2} = 33 \) d) \( 45 \div \frac{7}{5} = 45 \times \frac{5}{7} = \frac{225}{7} \approx 32.14 \) To find what to multiply 5 by to get 7, you can simply rearrange the equation \( 5x = 7 \) to find that \( x = \frac{7}{5} = 1.4 \). Now, to determine how many times \( \frac{2}{3} \) goes into 4, you divide: \( 4 \div \frac{2}{3} = 4 \times \frac{3}{2} = 6 \). So, \( \frac{2}{3} \) goes into 4 exactly 6 times!
