Currency Exchange

Grade 8 · mathematics · 100 practice problems · read aloud

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💰 Currency Exchange

What is it and Why is it Useful?

Currency exchange is the process of converting money from one currency to another (like US Dollars to Euros). It's essential for international travel, online shopping from other countries, and understanding the global economy. You use a special number called an exchange rate to do the conversion.

How to Solve Exchange Problems

  1. Identify the Exchange Rate: Find the rate (e.g., 1 USD = 0.85 EUR).
  2. Set Up Your Calculation: Decide if you are multiplying or dividing by the rate.
  3. Convert the Currency: Perform the multiplication or division.
  4. Label Your Answer: Always write the correct currency symbol!

Visual Examples

Example 1: USD to EUR
If 1 USD = 0.92 EUR, how many Euros do you get for 50 USD?

Step 1: Rate is 1 USD : 0.92 EUR
Step 2: Multiply USD by the rate. 50 × 0.92
Step 3: Calculate. 50 × 0.92 = 46
Answer: 50 USD = 46 EUR 💶

Example 2: EUR to USD
If 1 USD = 0.92 EUR, how many USD do you get for 100 EUR?

Step 1: Rate is 1 USD : 0.92 EUR
Step 2: Divide EUR by the rate. 100 ÷ 0.92
Step 3: Calculate. 100 ÷ 0.92 ≈ 108.70
Answer: 100 EUR ≈ 108.70 USD 💵

Common Mistakes to Avoid

❌ Multiplying when you should divide: Always think: "Will my answer be a bigger or smaller number?" If you're converting TO the currency in the rate (e.g., USD to EUR using 1 USD = 0.92 EUR), you multiply. If you're converting FROM it, you divide.

❌ Forgetting the currency label: A number without a currency label is meaningless! Always write USD, EUR, etc.

❌ Misplacing the decimal: Double-check your decimal placement when multiplying or dividing by decimals.

Tips & Tricks

Think of the rate as a fraction: 1 USD / 0.92 EUR. To convert, set up your problem so the original currency unit cancels out.

Estimate first! If 1 USD is about 0.9 EUR, then 30 USD should be a little less than 30 EUR (about 27). If your calculation gives you 300, you know you made a mistake.

Use the "Big Mac" method: Imagine if a Big Mac costs 5 USD here and 4.50 EUR there. The rate is 4.50/5.00 = 0.90. This can help you remember which way the rate goes.

How to Practice

  • Use real, current exchange rates from financial websites for practice problems.
  • Practice with a partner: One person names an amount and a currency, the other converts it.
  • Create a "travel budget" for a dream vacation to another country and convert your spending money.
  • Look for items in online stores from other countries and calculate their cost in your local currency.

Practice problems

6 of the 100, worked through step by step — try them before opening the answer.

1 5² + √(81) - 2³ = ?

Hint: Remember to evaluate exponents and square roots before performing addition and subtraction operations.

Show the answer

Answer: 26

  1. Calculate 5². 5² means 5 × 5 = 25.
  2. Calculate √(81). The square root of 81 is 9, because 9 × 9 = 81.
  3. Calculate 2³. 2³ means 2 × 2 × 2 = 8.
  4. Substitute these values into the expression: 25 + 9 - 8
  5. Perform the addition first: 25 + 9 = 34
  6. Then subtract 8: 34 - 8 = 26 Final answer: 26

Let's solve step by step. We have: 5² + √(81) - 2³

2 3² × (4 + 2) - √(64) = ?

Hint: Remember to follow the order of operations: parentheses first, then exponents, then multiplication/division from left to right, and finally addition/subtraction from left to right.

Show the answer

Answer: 46

  1. Solve inside the parentheses: 4 + 2 = 6
  2. Calculate the exponent: 3² = 9
  3. Multiply: 9 × 6 = 54
  4. Calculate the square root: √(64) = 8
  5. Subtract: 54 - 8 = 46

The answer is 46.

3 (6 × 10⁸) ÷ (2 × 10³) = ?

Hint: Separate the coefficients and the powers of ten, then simplify each part before combining them.

Show the answer

Answer: 300000

  1. Write the expression as (6 ÷ 2) × (10⁸ ÷ 10³).
  2. Simplify the coefficients: 6 ÷ 2 = 3.
  3. Simplify the powers of ten: 10⁸ ÷ 10³ = 10^(8-3) = 10⁵.
  4. Combine the results: 3 × 10⁵.
  5. Convert to standard form: 3 × 10⁵ = 3 × 100000 = 300000.

The answer is 300000.

4 (2.5 × 10⁴) ÷ (5 × 10²) = ?

Hint: When dividing numbers in scientific notation, handle the coefficients and exponents separately. Remember that dividing powers with the same base means subtracting exponents.

Show the answer

Answer: 50

  1. Break the division into two parts** We can write it as: (2.5 ÷ 5) × (10⁴ ÷ 10²) --- **
  2. Simplify the first part** 2.5 ÷ 5 = 0.5 So now we have: 0.5 × (10⁴ ÷ 10²) --- **
  3. Simplify the powers of 10** Using the rule: 10⁴ ÷ 10² = 10^(4 − 2) = 10² = 100 So now we have: 0.5 × 100 --- **
  4. Multiply** 0.5 × 100 = 50 --- **Final Answer:** 50

Let's solve step by step. We have: (2.5 × 10⁴) ÷ (5 × 10²) --- **

5 (3.6 × 10⁸) ÷ (9 × 10³) = ?

Hint: Separate the coefficients and exponents, then apply the laws of exponents for division

Show the answer

Answer: 40000

  1. Separate the coefficients and powers of 10: (3.6 ÷ 9) × (10⁸ ÷ 10³)
  2. Divide the coefficients: 3.6 ÷ 9 = 0.4
  3. Apply the exponent rule for division: 10⁸ ÷ 10³ = 10^(8-3) = 10⁵
  4. Multiply the results: 0.4 × 10⁵ = 0.4 × 100,000 = 40,000

The answer is 40000.

6 (4 × 10³) × (2.5 × 10⁴) = ?

Hint: Multiply the coefficients and add the exponents when multiplying terms in scientific notation.

Show the answer

Answer: 100000000

  1. Multiply the coefficients: 4 × 2.5 = 10
  2. Add the exponents: 3 + 4 = 7
  3. Combine the results: 10 × 10⁷
  4. Convert to standard form: 10 × 10,000,000 = 100,000,000

The answer is 100000000.

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