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Multiplying Fractions

Welcome! In this lesson, we will learn how to multiply fractions.

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Summary

Multiplying Fractions

a/b × c/d = (a × c) / (b × d)

Example

2/3 × 3/4

1 1/2 × 2/5

Improper Fractions and Mixed Numbers

Welcome! In this lesson, we will learn about improper fractions and mixed numbers.

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Summary

Improper Fractions

An improper fraction has a numerator larger than the denominator.

Example: 7/4

Improper → Mixed Number

7 ÷ 4 = 1 remainder 3

7/4 = 1 3/4

Mixed Numbers

A mixed number has a whole number and a fraction.

Example: 2 1/3

Mixed → Improper Fraction

2 × 3 + 1 = 7

2 1/3 = 7/3

Adding and Subtracting Fractions

Welcome! In this lesson, we will learn how to add and subtract fractions.

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Summary

Adding and Subtracting Fractions

Same Denominator

If the denominators are the same, add or subtract the numerators.

Example:

1/5 + 2/5

5/7 − 2/7

Different Denominators

If the denominators are different, make them the same.

Use LCM to find a common denominator.

Example:

1/2 + 1/3

3/4 − 1/6

Simplifying Fractions

Use GCD to simplify fractions.

Example:

6/8 = 3/4

GCD and LCM

Welcome! In this lesson, we will learn about GCD and LCM.

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Summary

GCD and LCM

Idea:

GCD (Greatest Common Divisor) is the largest number that divides two or more numbers.

LCM (Least Common Multiple) is the smallest number that both numbers divide into.

GCD Example:

GCD of 18 and 24

Largest common factor = 6 → GCD(18, 24) = 6

LCM Example:

LCM of 4 and 5

Smallest common multiple = 20 → LCM(4, 5) = 20

Fractions1

Welcome! In this lesson, we will learn about fractions.

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Summary

Fractions

Idea:

Fractions represent parts of a whole.

We can convert fractions to decimals using division.

We can simplify fractions by dividing numerator and denominator by the same number.

Example 1:

1/2 = 1 ÷ 2

Example 2:

3/4 = 3 ÷ 4

Example 3:

4/8 = 1/2

Decimals from Division

Welcome to Decimals2! In this lesson, we will see how dividing numbers can create decimals.

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Summary

Decimals from Division

Idea:

Dividing numbers can create decimals.

We understand decimals as parts of 1 using multiplication and division.

Example 1:

0.2 = 2 × 0.1 = 1 ÷ 5

Example 2:

0.5 = 5 × 0.1 = 1 ÷ 2

Example 3:

1.6 = 16 × 0.1 = 8 ÷ 5

Example 4:

0.02 = 2 × 0.01 = 1 ÷ 50

Decimals

Welcome! In this lesson, we will learn about decimals.

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Summary

Decimal Place Value

Idea:

Each place after the decimal point represents a fraction of 1.

1 tenth = 0.1, 1 hundredth = 0.01, 1 thousandth = 0.001

Example:

3.257 = 3 + 0.2 + 0.05 + 0.007

Place Value

Welcome! In this lesson, we will learn about place value.

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Summary

Place Value

Idea:

When 10 of the same value are collected, the place goes up.

After 9 comes 10.

10 ones = 1 ten

Example:

10 one-dollar bills = 10 dollars

10 ten-dollar bills = 100 dollars

10 hundred-dollar bills = 1,000 dollars

Example 1:

125

125 = 100 + 20 + 5

Example 2:

1,234

1,234 = 1,000 + 200 + 30 + 4

Order of Operations

Welcome! In this lesson, we will learn bout order of operations.

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Summary

Rules:

1.Multiplication (×) and Division (÷) are done before Addition (+) and Subtraction (−).

2.If there are both × and ÷ in the same expression, calculate from left to right.

Acid-Base Reactions

Welcome! In this lesson, we will learn about acid-base reactions.

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Summary

Acid-Base Reactions:

Chemical reactions between an acid and a base

Acid: Donates H⁺ ions

Base: Donates OH⁻ ions

Products:

Salt + Water

Examples:

HCl + NaOH → NaCl + H₂O

H₂SO₄ + 2NaOH → Na₂SO₄ + 2H₂O