Pre-Technical Studies Notes

Key Concepts

Whole numbers, fractions, and decimals help us count, measure, and compare things. You need these skills to solve problems with money, lengths, food, and scores.

• Place value tells the value of a digit. In 4,582, the 5 means 500.
• Compare whole numbers from the left. The first different digit decides.
• To order numbers, arrange them from smallest to largest or largest to smallest.
• Fractions show equal parts. In 3/4, 3 is the numerator and 4 is the denominator.
• Equivalent fractions have the same value, such as 1/2 = 2/4.
• Add or subtract fractions with the same denominator by working with the numerators.
• Decimals use place values: tenths, hundredths, and thousandths.
• Add zeros to compare decimals: 0.6 = 0.60.

Before you continue: Can you explain why 0.7 is greater than 0.65?

Key Terms

Place value - The value of a digit because of its position.

Numerator - The top number in a fraction.

Denominator - The bottom number in a fraction.

Equivalent fractions - Fractions with the same value.

Decimal - A number with a decimal point.

Ascending order - Arranging numbers from smallest to largest.

Descending order - Arranging numbers from largest to smallest.

Active Recall

Place value

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Numerator

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Denominator

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Equivalent fractions

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Decimal

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Worked Examples

1. Compare whole numbers

Compare 4,305 and 4,350.

1. Thousands are equal: 4 = 4.

2. Hundreds are equal: 3 = 3.

3. Tens differ: 0 is less than 5.

4. Therefore, 4,305 < 4,350.

Now you try: Compare 7,208 and 7,280.

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2. Add fractions

Find 2/7 + 3/7.

1. The denominators are the same.

2. Add the numerators: 2 + 3 = 5.

3. Keep the denominator: 2/7 + 3/7 = 5/7.

Now you try: Find 1/9 + 4/9.

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3. Order decimals

Arrange 0.8, 0.35, and 0.56 from smallest to largest.

1. Write equal places: 0.80, 0.35, 0.56.

2. Compare the tenths: 3, 5, and 8.

3. Order: 0.35, 0.56, 0.80.

Now you try: Order 0.4, 0.09, and 0.27.

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Practice Questions

1. (Easy) What is the place value of 6 in 6,214?

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2. (Easy) Circle the greater number: 3,901 or 3,109.

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3. (Medium) Arrange 45, 54, 405, and 504 in ascending order.

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4. (Medium) Find 3/8 + 2/8.

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5. (Medium) Find 7/10 - 3/10.

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6. (Hard) Arrange 0.7, 0.07, 0.77, and 0.17 from largest to smallest.

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Answer Key

1. Thousands

2. 3,901

3. 45, 54, 405, 504

4. 5/8

5. 4/10 or 2/5

6. 0.77, 0.70, 0.17, 0.07

Exam Tips & Common Mistakes

• Do not compare only the last digit. Compare digits from the left.
• Do not add fraction denominators when they are equal. Keep the denominator.
• Do not forget decimal zeros. Write 0.5 as 0.50 when comparing.
• Check the order words. “Ascending” means small to large.
• Show your working clearly. Markers can follow each step.

Quick Reference

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